mean of their flight hath nothing to do with the universal motion to which it is neither an help nor an hinderance and that which maintaineth the said motion unaltered in the birds is the Air it self thorough which they flie which naturally follovving the Vertigo of the Earth like as it carrieth the clouds along with it so it transporteth birds and every thing else which is pendent in the same in so much that as to the businesse of keeping pace vvith the Earth the birds need take no care thereof but for that work might sleep perpetually SAGR. That the Air can carry the clouds along with it as being matters easie for their lightnesse to be moved and deprived of all other contrary inclination yea more as being matters that partake also of the conditions and properties of the Earth I comprehend without any difficulty but that birds which as having life may move with a motion quite contrary to the diurnal once having surceased the said motion the Air should restore them to it seems to me a little strange and the rather for that they are solid and weighty bodies and withal we see as hath been said stones and other grave bodies to lie unmoved against the impetus of the air and when they suffer themselves to be overcome thereby they never acquire so much velocity as the wind which carrieth them SALV We ascribe not so little force Sagredus to the moved Air which is able to move and bear before it ships full fraught to tear up trees by the roots and overthrow Towers when it moveth swiftly and yet we cannot say that the motion of the Air in these violent operations is neer so violent as that of the diurnal revolution SIMP You see then that the moved Air may also cotinue the motion of projects according to the Doctrine of Aristotle and it seemed to me very strange that he should have erred in this particular SALV It may without doubt in case it could continue it self but lik as when the wind ceasing neither ships go on nor trees are blown down so the motion in the Air not continuing after the stone is gone out of the hand and the Air ceasing to move it followeth that it must be something else besides the Air that maketh the projects to move SIMP But how upon the winds being laid doth the ship cease to move Nay you may see that when the wind is down and the sails furl'd the vessel continueth to run whole miles SALV But this maketh against your self Simplicius for that the wind being laid that filling the sails drove on the ship yet neverthelesse doth it without help of the medium continue its course SIMP It might be said that the water was the medium which carried forward the ship and maintain'd it in motion SALV It might indeed be so affirmed if you would speak quite contrary to truth for the truth is that the water by reason of its great resistance to the division made by the hull of the ship doth with great noise resist the same nor doth it permit it of a great while to acquire that velocity which the wind would confer upon it were the obstacle of the water removed Perhaps Simplicius you have never considered with what fury the water besets a bark whil'st it forceth its way through a standing water by help of Oars or Sails for if you had ever minded that effect you would not now have produced such an absurdity And I am thinking that you have hitherto been one of those who to find out how such things succeed and to come to the knowledg of natural effects do not betake themselves to a Ship a Crosse-bow or a piece of Ordinance but retire into their studies and turn over Indexes and Tables to see whether Aristotle hath spoken any thing thereof and being assured of the true sense of the Text neither desire nor care for knowing any more SAGR. This is a great felicity and they are to be much envied for it For if knowledg be desired by all and if to be wise be to think ones self so they enjoy a very great happinesse for that they may perswade themselves that they know and understand all things in soorn of those who knowing that they understand not what these think they understand and consequently seeking that they know not the very least particle of what is knowable kill themselves with waking and studying and consume their days in experiments and observations But pray you let us return to our birds touching which you have said that the Air being moved with great velocity might restore unto them that part of the diurnal motion which amongst the windings of their flight they might have lost to which I reply that the agitated Air seemeth unable to confer on a solid and grave body so great a velocity as its own And because that of the Air is as great as that of the Earth I cannot think that the Air is able to make good the losse of the birds retardation in flight SALV Your discourse hath in it much of probability and to stick at trivial doubts is not for an acute wit yet neverthelesse the probability being removed I believed that it hath not a jot more force than the others already considered and resolved SAGR. It is most certain that if it be not necessarily concludent its efficacy must needs be just nothing at all for it is onely when the conclusion is necessary that the opponent hath nothing to alledg on the contrary SALV Your making a greater scruple of this than of the other instances dependeth if I mistake not upon the birds being animated and thereby enabled to use their strength at pleasure against the primary motion in-bred in terrene bodies like as for example we see them whil'st they are alive to fly upwards a thing altogether impossible for them to do as they are grave bodies whereas being dead they can onely fall downwards and therefore you hold that the reasons that are of force in all the kinds of projects above named cannot take place in birds Now this is very true and because it is so Sagredus that doth not appear to be done in those projects which we see the birds to do For if from the top of a Tower you let fall a dead bird and a live one the dead bird shall do the same that a stone doth that is it shall first follow the general motion diurnal and then the motion of descent as grave but if the bird let fall be a live what shall hinder it there ever remaining in it the diurnal motion from soaring by help of its wings to what place of the Horizon it shall please and this new motion as being peculiar to the bird and not participated by us must of necessity be visible to us and if it be moved by help of its wings towards the West what shall hinder it from returning with a like help of its wings unto the Tower
worth than the wool of a goat and whereas our argumentations should continually be conversant about serious and weighty points we consume our time in frivolous and impertinent wranglings Let us call to minde I pray you that the search of the worlds constitution is one of the greatest and noblest Problems that are in nature and so much the greater inasmuch as it is directed to the resolving of that other to wit of the cause of the Seas ebbing and flowing enquired into by all the famous men that have hitherto been in the world and possibly found out by none of them Therefore if we have nothing more remaining for the full confutation of the argument taken from the Earths vertigo which was the last alledged to prove its immobility upon its own centre let us passe to the examination of those things that are alledged for and against the Annual Motion SAGR. I would not have you Salviatus measure our wits by the scale of yours you who use to be continually busied about the sublimest contemplations esteem those notions frivolous and below you which we think matters worthy of our profoundest thoughts yet sometimes for our satisfaction do not disdain to stoop so low as to give way a little to our curiosity As to the refutation of the last argument taken from the extrusions of the diurnal vertigo far less than what hath been said would have given me satisfaction and yet the things superfluously spoken seemed to me so ingenious that they have been so far from wearying my fancy as that they have by reason of their novelty entertained me all along with so great delight that I know not how to desire greater Therefore if you have any other speculation to add produce it for I as to my own particular shall gladly hearken to it SALV I have always taken great delight in those things which I have had the fortune to discover and next to that which is my chief content I find great pleasure in imparting them to some friends that apprehendeth and seemeth to like them Now in regard you are one of these slacking a little the reins of my ambition which is much pleased when I shew my self more perspicacious than some other that hath the reputation of a sharp sight I will for a full and true measure of the past dispute produce another fallacy of the Sectators of Ptolomey and Aristotle which I take from the argument alledged SAGR. See how greedily I wait to hear it SALV We have hitherto over-passed and granted to Ptolomey as an effect indubitable that the extrusion of the stone proceeding from the velocity of the wheel turn'd round upon its centre the cause of the said extrusion encreaseth in proportion as the velocity of the vertigo or whirling is augmented from whence it was inferred that the velocity of the Earth's vertigo being very much greater than that of any machin whatsoever that we can make to turn round artificially the extrusion of stones of animals c. would consequently be far more violent Now I observe that there is a great fallacy in this discourse in that we do compare these velocities indifferently and absolutely to one another It 's true that if I compare the velocities of the same wheel or of two wheels equal to each other that which shall be more swiftly turn'd round shall extrude the stone with greater violence and the velocity encreasing the cause of the projection shall likewise encrease but when the velocity is augmented not by encreasing the velocity in the same wheel which would be by causing it to make a greater number of revolutions in equal times but by encreasing the diameter and making the wheel greater so as that the conversion taking up the same time in the lesser wheel as in the greater the velocity is greater onely in the bigger wheel for that its circumference is bigger there is no man that thinketh that the cause of the extrusion in the great wheel will encrease according to the proportion of the velocity of its circumference to the velocity of the circumference of the other lesser wheel for that this is most false as by a most expeditious experiment I shall thus grosly declare We may sling a stone with a stick of a yard long farther than we can do with a stick six yards long though the motion of the end of the long stick that is of the stone placed in the slit thereof were more than double as swift as the motion of the end of the other shorter stick as it would be if the velocities were such that the lesser stick should turn thrice round in the time whilst the greater is making one onely conversion SAGR. This which you tell me Salviatus must I see needs succeed in this very manner but I do not so readily apprehend the cause why equal velocities should not operate equally in extruding projects but that of the lesser wheel much more than the other of the greater wheel therefore I intreat you to tell me how this cometh to pass SIMP Herein Sagredus you seem to differ much from your self for that you were wont to penetrate all things in an instant and now you have overlook'd a fallacy couched in the experiment of the stick which I my self have been able to discover and this is the different manner of operating in making the projection one while with the short sling and another while with the long one for if you will have the stone fly out of the slit you need not continue its motion uniformly but at such time as it is at the swiftest you are to stay your arm and stop the velocity of the stick whereupon the stone which was in its swiftest motion flyeth out and moveth with impetuosity but now that stop cannot be made in the great stick which by reason of its length and flexibility doth not entirely obey the check of the arm but continueth to accompany the stone for some space and holdeth it in with so much less force and not as if you had with a stiff sling sent it going with a jerk for if both the sticks or slings should be check'd by one and the same obstacle I do believe they would fly aswell out of the one as out of the other howbeit their motions were equally swift SAGR. With the permission of Salviatus I will answer something to Simplicius in regard he hath addressed himself to me and I say that in his discourse there is somewhat good and somewhat bad good because it is almost all true bad because it doth not agree with our case Truth is that when that which carrieth the stones with velocity shall meet with a check that is immoveable they shall fly out with great impetuosity the same effect following in that case which we see dayly to fall out in a boat that running a swift course runs a-ground or meets with some sudden stop for all those in the boat being surprized stumble forwards
doth not oblige us to receive those Precepts which they have not so much as in their intentions enjoyned But if they did reflect and consider thereon they would long since have condemned it if they had judged it erroneous which we do not find that they have done Nay after that some Divines have began to consider it we find that they have not deem'd it erroneous as we read in the Commentaries of Didacus a Stunica upon Job in Cap. 9 v. 6. on the words Qui commovet Terram de loco suo c. Where he at large discourseth upon the Copernican Hypothesis and concludeth That the Mobility of the Earth is not contrary to Scripture Withal I may justly question the truth of that determination namely That the Church enjoyneth us to hold such like Natural Conclusions as matters of Faith onely because they bear the stamp of an unanimous Interpretation of all the Fathers And I do suppose that it may possibly be that those who hold in this manner might possibly have gone about in favour of their own Opinion to have amplified the Decretal of the Councils which I cannot finde in this case to prohibit any other save onely Perverting to Senses contrary to that of Holy Church or of the concurrent consent of Fathers those places and those onely that do pertain either to Faith or Manners or concern our edification in the Doctrine of Christianity And thus speaks the Council of Trent Sess. 4. But the Mobility or Stability of the Earth or of the Sun are not matters of Faith nor contrary to Manners nor is there any one that for the stablishing of this Opinion will pervert places of Scripture in opposition to the Holy Church or to the Fathers Nay Those who have writ of this Doctrine did never make use of Texts of Scripture that they might leave it still in the breasts of Grave and Prudent Divines to interpret the said Places according to their true meaning And how far the Decrees of Councills do comply with the Holy Fathers in these particulars may be sufficiently manifest in that they are so far from enjoyning to receive such like Natural Conclusions for matters of Faith or from censuring the contrary Opinions as erronious that rather respecting the Primitive and primary intention of the Holy Church they do adjudge it unprofitable to be busied in examining the truth thereof Let your Highness be pleased to hear once again what S. Augustine answers to to those Brethren who put the Question Whether it be true that Heaven moveth or standeth still To these I answer That Points of this nature require a curious and profound examination that it may truly appear whether they be true or false a work inconsistent with my leasure to undertake or go thorow with nor is it any way necessary for those whom we desire to inform of things that more nearly concern their own salvation and The Churches Benefit But yet although in Natural Propositions we were to take the resolution of condemning or admitting them from Texts of Scripture unanimously expounded in the same Sense by all the Fathers yet do I not see how this Rule can hold in our Case for that upon the same Places we read several Expositions in the Fathers Dionysius Areopagita saying That the Primum Mobile and not the Sun stand still Saint Augustine is of the same Opinion All the Celestial Bodies were immoveable And with them concurreth Abulensis But which is more amongst the Jewish Authors whom Josephus applauds some have held That The Sun did not really stand still but seemed so to do during the short time in which Israel gave the overthrow to their Enemies So for the Miracle in the time of Hezekiah Paulus Burgensis is of opinion that it was not wrought on the Sun but on the Diall But that in short it is necessary to Glosse and Interpret the words of the Text in Joshua when ever the Worlds Systeme is in dispute I shall shew anon Now finally granting to these Gentlemen more than they demand to wit That we are wholly to acquiesce in the judgment of Judicious Divines and that in regard that such a particular Disquisition is not found to have been made by the Ancient Fathers it may be undertaken by the Sages of our Age who having first heard the Experiments Observations Reasons and Demonstrations of Philosophers and Astronomers on the one side and on the other seeing that the Controversie is about Natural Problems and Necessary Dilemma's and which cannot possibly be otherwise than in one of the two manners in controversie they may with competent certainty determine what Divine Inspirations shall dictate to them But that without minutely examining and discussing all the Reasons on both sides and without ever comming to any certainty of the truth of the Case such a Resolution should be taken Is not to be hoped from those who do not stick to hazzard the Majesty and Dignity of the Sacred Scripture in defending the reputation of their vain Fancies Nor to be feared from those who make it their whole businesse to examine with all intensness what the Grounds of this Doctrine are and that only in an Holy Zeal for Truth the Sacred Scriptures and for the Majesty Dignity and Authority in which every Christian should indeavour to have them maintained Which Dignity who seeth not that it is with greater Zeal desired and procured by those who absolutely submitting themselves to the Holy Church desire not that this or that opinion may be prohibited but onely that such things may be proposed to consideration as may the more ascertain her in the safest choice than by those who being blinded by their particular Interest or stimulated by malitious suggestions preach that she should without more ado thunder out Curses for that she had power so to do Not considering that all that may be done is not alwayes convenient to be done The Holy Fathers of old were not of this opinion but rather knowing of how great prejudice and how much against the primary intent of the Catholick Church it would be to go about from Texts of Scripture to decide Natural Conclusions touching which either Experiments or necessary Demonstrations might in time to come evince the contrary of that which the naked sense of the Words soundeth they have not only proceeded with great circumspection but have left the following Precepts for the instruction of others In points obscure and remote from our Sight if we come to read any thing out of Sacred Writ that with a Salvo to the Faith that we have imbued may correspond with several constructions let us not so farre throw our selves upon any of them with a precipitous obstinacy as that if perhaps the Truth being more diligently search't into it should justly fall to the ground we might fall together with it and so shew that we contend not for the sense of Divine Scriptures but our own in that we
would have that which is our own to be the sense of Scriptures vvhen as vve should rather desire the Scriptures meaning to be ours He goeth on and a little after teacheth us that no Proposition can be against the Faith unlesse first it be demonstrated false saying T is not all the while contrary to Faith until it be disproved by most certain Truth which if it should so be the Holy Scripture affirm'd it not but Humane Ignorance supposed it Whereby we see that the senses which we impose on Texts of Scripture would be false when ever they should disagree with Truths demonstrated And therefore we ought by help of demonstrated Truth to seek the undoubted sense of Scripture and not according to the sound of the words that may seem true to our weaknesse to go about as it were to force Nature and to deny Experiments and Necessary Demonstrations Let Your Highnesse be pleased to observe farther with how great circumspection this Holy Man proceedeth before he affirmeth any Interpretation of Scripture to be sure and in such wise certain as that it need not fear the encounter of any difficulty that may procure it disturbance for not contenting himself that some sense of Scripture agreeth with some Demonstration he subjoynes But if right Reason shall demonstrate this to be true yet is it questionable whether in these words of Sacred Scripture the Pen-man would have this to be understood or somewhat else no lesse true And in case the Context of his Words shall prove that he intended not this yet will not that which he would have to be understood be therefore false but most true aad that which is more profitable to be knovvn But that which increaseth our wonder concerning the circumspection wherewith this Pious Author proceedeth is that not trusting to his observing that both Demonstrative Reasons and the sense that the words of Scripture and the rest of the Context both precedent and subsequent do conspire to prove the same thing he addeth the following words But if the Context do not hold forth any thing that may disprove this to be the Authors Sense it yet remains to enquire Whether the other may not be intended also And not yet resolving to accept of one Sense or reject another but thinking that he could never use sufficient caution he proceedeth But if so be we finde that the other may be also meant it vvill be doubted which of them he would have to stand or which in probability he may be thought to aim at if the true circumstances on both sides be weighed And lastly intending to render a Reason of this his Rule by shewing us to what perils those men expose the Scriptures and the Church who more respecting the support of their own errours than the Scriptures Dignity would stretch its Authority beyond the Bounds which it prescribeth to it self he subjoyns the ensuing words which of themselves alone might suffice to repress and moderate the excessive liberty which some think that they may assume to themselves For it many times falls out that a Christian may not so fully understand a Point concerning the Earth Heaven and the rest of this Worlds Elements the Motion Conversion Magnitude and Distances of the Stars the certain defects of the Sun and Moon the Revolutions of Years and Times the Nature of Animals Fruits Stones and other things of like nature as to defend the same by right Reason or make it out by Experiments But it s too great an absurdity yea most pernicious and chiefly to be avoided to let an Infidel finde a Christian so stupid that he should argue these matters as if they were according to Christian Doctrine and make him as the Proverb saith scarce able to contain his laughter seeing him so far from the Mark. Nor is the matter so much that one in an errour should be laught at but that our Authors should be thought by them that are without to be of the same Opinion and to the great prejudice of those whose salvation we wait for sensured and rejected as unlearned For when they shal confute any one of the Christians in that matter vvhich they themselvs thorovvly understand and shall thereupon express their light esteem of our Books hovv shall these Volumes be believed touching the Resurrection of the Dead the Hope of eternal Life and the Kingdom of Heaven vvhen as to these Points vvhich admit of present Demonstration or undoubted Reasons they conceive them to be falsly vvritten And how much the truly Wise and Prudent Fathers are displeased with these men who in defence of Propositions which they do not understand do apply and in a certain sense pawn Texts of Scripture and afterwards go on to encrease their first Errour by producing other places less understood than the former The same Saint declareth in the expressions following What trouble and sorrow weak undertakers bring upon their knowing Brethren is not to be expressed since vvhen they begin to be told and convinced of their false and unsound Opinion by those vvho have no respect for the Authority of our Scriptures in defence of vvhat through a fond Temerity and most manifest falsity they have urged they fall to citing the said Sacred Books for proof of it or else repeat many vvords by heart out of them vvhich they conceive to make for their purpose not knovving either what they say or vvhereof they affirm In the number of these we may as I conceive account those who being either unwilling or unable to understand the Demonstrations and Experiments wherewith the Author and followers of this Opinion do confirm it run upon all occasions to the Scriptures not considering that the more they cite them and the more they persist in affirming that they are very clear and do admit no other senses save those which they force upon them the greater injury they do to the Dignity of them if we allowed that their judgments were of any great Authority in case that the Truth coming to be manifestly known to the contrary should occasion any confusion at least to those who are separated from the Holy Church of whom yet she is very solicitous and like a tender Mother desirous to recover them again into her Lap Your Highness therefore may see how praeposterously those Persons proceed who in Natural Disputations do range Texts of Scripture in the Front for their Arguments and such Texts too many times as are but superficially understood by them But if these men do verily think absolutely believe that they have the true sence of Such a particular place of Scripture it must needs follow of consequence that they do likewise hold for certain that they have found the absolute truth of that Natural Conclusion which they intend to dispute And that withal they do know that they have a great advantage of their Adversary whose Lot it is to defend the part that is false in regard that he
Stadia or furlongs The Cause and Reason of whose Motion neither Ptolomy nor any other Astrologers could ever comprehend And yet the Reasons of these things are most plainly explained and demonstrated by Copernicus from the Motion of the Earth with which he sheweth that all the other Phaenomena of the Universe do more aptly accord Which opinion of his is not in the least contradicted by what Solomon saith in Ecclesiastes But the Earth abideth for ever For that Text signifieth no more but this That although the succession of Ages and generations of Men on Earth be various yet the Earth it self is still one and the same and continueth without any sensible alteration For the words run thus One Generation passeth away and another Generation cometh but the Earth abideth for ever So that it hath no coherence with its Context as Philosophers shew if it be expounded to speak of the Earths immobility And although in this Chapter Ecclesiastes and in many others Holy Writ ascribes Motion to the Sun which Copernicus will have to stand fixed in the Centre of the Universe yet it makes nothing against his Position For the Motion that belongs to the Earth is by way of speech assigned to the Sun even by Copernicus himself and those who are his followers so that the Revolution of the Earth is often by them phrased The Revolution of the Sun To conclude No place can be produced out of Holy Scripture which so clearly speaks the Earths Immobility as this doth its Mobility Therefore this Text of which we have spoken is easily reconciled to this Opinion And to set forth the Wonderful power and Wisdome of God who can indue and actuate the Frame of the Whole Earth it being of a monstrous weight by Nature with Motion this our Divine pen-man addeth And the pillars thereof tremble As if he would teach us from the Doctrine laid down that it is moved from its Foundations AN EPISTLE Of the Reverend Father PAOLO ANTONIO FOSCARINI A CARMELITE Concerning The PYTHAGORIAN and COPERNICAN Opinion OF The Mobility of the EARTH AND Stability of the SVN AND Of the New Systeme or Constituion OF THE WORLD IN WHICH The Authorities of SACRED SCRIPTVRE and ASSERTIONS of DIVINES commonly alledged against this Opinion are Reconciled WRITTEN To the most Reverend FATHER SEBASTIANO FANTONI General of the Order of CARMELITES Englished from the Original BY THOMAS SALVSBVRIE So quis indiget sapientia postulet à Deo Jacobi 1. versu 5. Optaevi datus est mihi sensus Sapientiae 7. versu 7. LONDON Printed by WILLIAM LEYBOVRN MDCLXI To the Most Reverend Father SEBASTIANO FANTONI General of the Order of CARMELITES IN obedience to the command of the Noble Signore Vincenzo Carraffa a Neapolitan and Knight of S. John of Jerusalem a person to speak the truth of so great Merit that in him Nobility of Birth Affability of Manners Universal knowledge of Arts and things Piety and Vertue do all contend for preheminence I resolved with my self to undertake the Defence of the Writings of the New or rather Renewed and from the Dust of Oblivion in which it hath long lain hid lately Revived Opinion Of the Mobility of the Earth and Stability of the Sun in times past found out first by Pythagoras and at last reduced into Practice by Copernicus who likewise hath deduced the Position of the Systeme and Constitution of the World and its parts from that Hypothesis on which Subject I have formerly writ to You Most Reverend Sir But in regard I am bound for Rome to preach there by your Command and since this Speculation may seem more proper for another Treatise to wit a Volume of Cosmography which I am in hand with and which I am daily busie about that it may come forth in company with my Compendium of the Liberal Arts which I have already finished rather than now to discuss it by it self I thought to forbear imparting what I have done for the present Yet I was desirous to give in the mean time a brief account of this my Determination and to shew You Most Reverend Father to whom I owe all my indeavours and my very self the Foundations on which this Opinion may be grounded least whilst otherwise it is favoured with much probability it be found in reality to be extreamly repugnant as at first sight it seems not onely to Physical Reasons and Common Principles received on all hands which cannot do so much harm but also which would be of far worse consequence to many Authorities of sacred Scripture Upon which account many at their first looking into it explode it as the most fond Paradox and Monstrous Capriccio that ever was heard of Which thing proceeds only from an antiquated and long confirmed Custome which hath so hardened men in and habituated them to Vulgar Plausible and for that cause by all men aswell learned as unlearned Approved Opinions that they cannot be removed one step from them So great is the force of Custome which not unfitly is stiled a second Nature prevailing over the whole World that touching things men are rather pleased with delighted in and desirous of those which though evil and obnoxious are by use made familiar to them than such wherewith though better they are not accustomed and acquainted So in like manner and that chiefly in Opinions which when once they are rooted in the Mind men start at and reject all others whatsoever not only those that are contrary to but even all that ever so little disagree with or vary from theirs as harsh to the Ear discoloured to the Eye unpleasant to the Smell nauseous to the Tast rough to the Touch. And no wonder For Physical Truths are ordinarily judged and considered by men not according to their Essence but according to the prescript of some one whose description or definition of them gaines him Authority amongst the vulgar Which authority nevertheless since 't is no more than humane ought not to be so esteemed as that that which doth manifestly appear to the contrary whether from better Reasons lately found out or from Sense it self should for its sake be contemned and slighted Nor is Posterity so to be confined but that it may and dares not only proceed farther but also bring to light better and truer Experiments than those which have been delivered to us by the Ancients For the Genius's of the Antients as in Inventions they did not much surpass the Wits of our times so for the perfecting of Inventions this Age of ours seems not only to equal but far to excell former Ages Knowledge whether in the Liberal or Mechanical Arts daily growing to a greater height Which Assertion might be easily proved were it not that in so clear a case there would be more danger of obscuring than hopes of illustrating it with any farther light But that I may not wholly be silent in this point have not the several Experiments of Moderns in many things stopped the mouth
MATHEMATICAL Collections and Translations In two TOMES THE SYSTEME OF THE WORLD IN FOUR DIALOGUES Wherein the Two GRAND SYSTEMES OF PTOLOMY and COPERNICUS are largely discoursed of And the REASONS both Phylosophical and Physical as well on the one side as the other impartially and indefinitely propounded By GALILEUS GALILEUS LINCEUS A Gentleman of FLORENCE Extraordinary Professor of the Mathematicks in the UNIVERSITY of PISA and Chief Mathematician to the GRAND DUKE of TVSCANY Englished from the Original Italian Copy by THOMAS SALUSBURY ALCINOUS 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 SENECA Inter nullos magis quam inter PHILOSOPHOS esse debet aequa LIBERTAS LONDON Printed by WILLIAM LEYBOURNE MDCLXI To the most Serene Grand DUKE OF TUSCANY THough the difference between Men and other living Creatures be very great yet happly he that should say that he could shew little less between Man and Man would not speak more than he might prove What proportion doth one bear to a thousand and yet it is a common Proverb One Man is worth a thousand when as a thousand are not worth one This difference hath dependence upon the different abilities of their Intellectuals which I reduce to the being or not being a Philosopher in regard that Philosophy as being the proper food of such as live by it distinguisheth a Man from the common Essence of the Vulgar in a more or less honourable degree according to the variety of that diet In this sence he that hath the highest looks is of highest quality and the turning over of the great Volume of Nature which is the proper Object of Philosophy is the way to make one look high in which Book although whatsoever we read as being the Work of Almighty God is therefore most proportionate yet notwithstanding that is more absolute and noble wherein we more plainly deserne his art and skill The Constitution of the Vnivers among all Physical points that fall within Humane Comprehension may in my opinion be preferred to the Precedency for if that in regard of universal extent it excell all others it ought as the Rule and Standard of the rest to goe before them in Nobility Now if ever any persons might challenge to be signally distinguished for Intellectuals from other men Ptolomey and Copernicus were they that have had the honour to see farthest into and discourse most profoundly of the World 's Systeme About the Works of which famous Men these Dialous being chiefly conversant I conceived it my duty to Dedicate them only to Your Highness For laying all the weight upon these two whom I hold to be the Ablest Wits that have left us their Works upon these Subjects to avoid a Solecisme in Manners I was obliged to address them to Him who with me is the Greatest of all Men from whom they can receive either Glory or Patrociny And if these two persons have so farre illuminated my Understanding as that this my Book may in a great part be confessed to belong to them well may it also be acknowledged to belong to Your Highness unto whose Bounteous Magnificence I owe the time and leasure I had to write it as also unto Your Powerful Assistance never weary of honouring me the means that at length I have had to publish it May Your Highness therefore be pleased to accept of it according to Your accustomed Goodness and if any thing shall be found therein that may be subservient towards the information or satisfaction of those that are Lovers of Truth let them acknowledge it to be due to Your Self who are so expert in doing good that Your Happy Dominion cannot shew the man that is concerned in any of those general Calamities that disturb the World so that Praying for Your Prosperity and continuance in this Your Pious and Laudable Custome I humbly kiss Your Hands Your Most Serene Highnesses Most Humble and most devoted Servant and Subject GALILEO GALILEI To the Noble and most perfectly Accomplished Sr. JOHN DENHAM Knight of the Noble Order of the BATH And Surveyor General of his Maties Works c. SIR I Humbly begge your Pardon for bringing this Book under your Protection Were it a VVork of my own or I any thing but the Translatour I should master my Thoughts to a meaner Dedication But being a Collection of some of the greatest Masters in the VVorld and never made English till now I conceived I might sooner procure their VVelcome to a person so eminent for Noble Candor as well as for all those Intellectual Excellencies wherewith Your Rich Soul is known to be furnished I resolv'd to be as kind to this Book as I could and seriously considering which way to effect it I at last concluded to prefix Your Name whom His Majesty and all his Subjects who have a higher Sense and Judgement of Excellent Parts know best able to defend my Imperfections And yet I confess there 's one thing makes against me which is your eminent Integrity and great Affection to Truth whereby my Lapses in a VVork of this Nature might justly despair of Shelter but that the Excellency of Your Native Candor strives for Predominancy over all Your great Abilities For 't is all-most impossible to think what Your Matchless VVit is not able to Conquer would Your known Modesty but give leave therefore Galileus Kepler and those other Worthies in Learning are now brought before You in English Habit having chang'd their Latine Italian and French whereby they were almost Strangers to our Nation unless to such as You who so perfectly master the Originals I know you have so much and great imployment for His Majesty and his good Subjects that I shall not robb you of another Minutes loss besides the liberty of subscribing my Self SIR Your Honours Most Humble and Most obedient Servant THOMAS SALUSBURY MATHEMATICAL COLLECTIONS AND TRANSLATIONS THE FIRST TOME IN TWO PARTS THE FIRST PART Containing I. GALILEUS GALILEUS His SYSTEM of the WORLD II. GALILEUS His EPISTLE to the GRAND DUTCHESSE MOTHER concerning the Authority of Holy SCRIPTURE in Philosophical Controversies III. JOHANNES KEPLERUS His Reconcilings of SCRIPTURE Texts c. IV. DIDACUS à STUNICA His Reconcilings of SCRIPTURE Texts c. V. P. A. FOSCARINUS His Epistle to Father FANTONUS reconciling the Authority of SCRIPTURE and Judgments of Divines alledged against this SYSTEM By THOMAS SALUSBURY Esq. LONDON Printed by WILLIAM LEYBOURN MDCLXI MATHEMATICAL COLLECTIONS AND TRANSLATIONS THE FIRST TOME THE FIRST PART Containing I. GALILEUS GALILEUS His SYSTEME of the World II. GALILEUS his EPISTLE to the GRAND DUTCHESSE Mother concerning the Authority of Sacred SCRIPTURE in Phylosophical Controversies III. JOHANNES KEPLERUS his Reconcilings of SCRIPTURE Texts c. IV. DIDACUS a STUNICA his Reconcilings of SCRIPTURE Texts c. V. P. A. FOSCARINUS his Epistle to Father FANTONUS reconciling the Authority of Sacred SCRIPTURE and Judgments of Divines alledged against c. By THOMAS SALUSBURY Esq. LONDON Printed by WILLIAM LEYBOURNE MDCLXI READER MAthematical Learning to speak nothing
that Court nor was that Decree Published without Previous Notice given me thereof Therefore it is my resolution in the present case to give Foraign Nations to see that this point is as well understood in Italy and particularly in Rome as Transalpine Diligence can imagine it to be and collecting together all the proper Speculations that concern the Copernican Systeme to let them know that the notice of all preceded the Censure of the Roman Court and that there proceed from this Climate not only Doctrines for the health of the Soul but also ingenious Discoveries for the recreating of the Mind To this end I have personated the Copernican in this Discourse proceeding upon an Hypothesis purely Mathematical striving by all artificial wayes to represent it Superiour not to that of the Immobility of the Earth absolutely but according as it is mentioned by some that retein no more but the name of Peripateticks and are content without going farther to adore Shadows not philosophizing with requisit caution but with the sole remembrance of four Principles but badly understood We shall treat of three principall heads First I will endeavour to shew that all Experiments that can be made upon the Earth are insufficient means to conclude it's Mobility but are indifferently applicable to the Earth moveable or immoveable and I hope that on this occasion we shall discover many observable passages unknown to the Ancients Secondly we will examine the Coelestiall Phoenomena that make for the Copernican Hypothesis as if it were to prove absolutely victorious adding by the way certain new Observations which yet serve only for the Astronomical Facility not for Natural Necessity In the third place I will propose an ingenuous Fancy I remember that I have said many years since that the unknown Probleme of the Tide might receive some light admitting the Earths Motion This Position of mine passing from one to another had found charitable Fathers that adopted it for the Issue of their own wit Now because no stranger may ever appear that defending himself with our armes shall charge us with want of caution in so principal an Accident I have thought good to lay down those probabilities that would render it credible admitting that the Earth did move I hope that by these Considerations the World will come to know that if other Nations have Navigated more than we we have not studied less than they that our returning to assert the Earths Stability and to take the contrary only for a Mathematical Capriccio proceeds not from inadvertency of what others have thought thereof but had we no other inducements from those Reasons that Piâ—ty Religion the Knowledge of the Divine Omnipotency and a consciousness of the incapacity of mans Vnderstanding dictate unto us With all I conceived it very proper to express these conceits by way of Dialogue which as not being bound up to the riggid observance of Mathematical Laws gives place also to Digressions that are sometimes no less curious than the principal Argument I chanced to be several years since at several times in the Stupendious Citty of Venice where I conversed with Signore Giovan Francesco Sagredo of a Noble Extraction and piercing wit There came thither from Florence at the same time Signore Filippo Salviati whose least glory was the Eminence of his Blood and Magnificence of his Estate a sublime Wit that fed not more hungerly upon any pleasure than on elevated Speculations In the company of these two I often discoursed of these matters before a certain Peripatetick Philosopher who seemed to have no geater obstacle in understanding of the Truth than the Fame he had acquired by Aristotelical Interpretations Now seeing that inexorable Death hath deprived Venice and Florence of those two great Lights in the very Meridian of their years I did resolve as far as my poor ability would permit to perpetuate their lives to their honour in these leaves bringing them in as Interlocutors in the present Controversy Nor shall the Honest Peripatetick want his place to whom for his excessive affection towards the Commentaries of Simplicius I thought fit without mentioning his own Name to leave that of the Author he so much respected Let those two great Souls ever venerable to my heart please to accept this publick Monument of my never-dying Love and let the remembrance of their Eloquence assist me in delivering to Posterity the Considerations that I have promised There casually happened as was usuall several discourses at times between these Gentlemen the which had rather inflamed than satisfied in their wits the thirst they had to be learning whereupon they took a discreet resolution to meet together for certain dayes in which all other business set aside they might betake themselves more methodically to contemplate the Wonders of God in Heaven and in the Earth the place appointed for their meeting being in the Palace of the Noble Sagredo after the due but very short complements Signore Salviati began in this manner The CONTENTS of the FIRST TOME PART THE FIRST Treatise I. GALILEUS GALILEUS his SYSTEME of the WORLD in Four DIALOGUES II. HIS EPISTLE to her SERENE HIGHNESSE CHRISTIANA LOTHERINGA GRAND DUTCHESSE of TUSCANY touching the Ancient and Modern DOCTRINE of HOLY FATHERS and JUDICIOUS DIVINES concerning the AUTHORITY of SACRED SCRIPTURE in PHYLOSOPHICAL CONTROVERSIES III. JOHANNES KEPLERUS his RECONCILINGS of TEXTS of SACRED SCRIPTURE that seem to oppose the DOCTRINE of the EARTHS MOBILITY abstracted from his INTRODUCTION unto his LEARNED COMMENTARIES upon the PLANET MARS IV. DIDACUS A STUNICA a learned SPANISH DIVINE his RECONCILINGS of the said DOCTRINE with the TEXTS of SACRED SCRIPTURE abstracted from his COMMENTARIE upon JOB V. PAULUâ— ANTONIUS FOSCARINUS a CARMELITE his EPISTLE to SEBASTIANUS FANTONUS the GENERAL of his ORDER concerning the PYTHAGOREAN and COPERNICAN OPINION of the MOBILITY OF THE EARTH and STABILITY OF THE SUN and of the NEW SYSTEME or CONSTITUTION of the WORLD in which he reconcileth the TEXTS OF SACRED SCRIPTURE and ASSERTIONS of DIVINES commonly alledged against this OPINION A Table of the most observable Persons and Matters mentioned in the First Part. PART THE SECOND I. D. BENEDICTUS CASTELLUS ABBOT OF S. BENEDICTUS ALOYSIUS his DISCOURSE of the MENSURATION OF RUNNING WATERS The First BOOK II. HIS LETTER to GALILEUS representing the state of the Lake of PERUGIA in TUSCANY III. HIS GEOMETRICAL DEMONSTRATIONS of the MEASURE of RUNNING WATERS IV. HIS DISCOURSE of the MENSURATION OF RUNNING WATERS The Second BOOK V. HIS CONSIDERATIONS concerning the LAKE OF VENICE In two DISCOURSES VI. HIS RULE for computing the quantity of MUD and SAND that LAND-FLOODS bring down to and leave in the LAKE of VENICE VII HIS LETTER to Father FRANCESCO DI S. GIVSEPPE wherein at the instance of PRINCE LEOPALDO he delivereth his judgment concerning the turning FIUME MORTO a River near PISA in TUSCANY into the SEA and into the River SEARCHIO VIII HIS second LETTER in answer to certain OBJECTIONS proposed and DIFFICULTIES observed
other SIMPL. Who can deny it the first particular of the worlds dimensions is taken from Aristotle himself and its denomination of ordinate seems onely to be assumed from the order which it most exactly keeps SALV This principle then established one may immediately conclude that if the entire parts of the World should be by their nature moveable it is impossible that their motions should be right or other than circular and the reason is sufficiently easie and manifest for that whatsoever moveth with a right motion changeth place and continuing to move doth by degrees more and more remove from the term from whence it departed and from all the places thorow which it successively passed and if such motion naturally suited with it then it was not at the beginning in its proper place and so the parts of the World were not disposed with perfect order But we suppose them to be perfectly ordinate therefore as such it is impossible that they should by nature change place and consequently move in a right motion Again the right motion being by nature infinite for that the right line is infinite and indeterminate it is impossible that any moveable can have a natural principle of moving in a right line namely toward the place whither it is impossible to arrive there being no prae-finite term and nature as Aristotle himself saith well never attempts to do that which can never be done nor essaies to move whither it is impossible to arrive And if any one should yet object that albeit the right line and consequently the motion by it is producible in infinitum that is to say is interminate yet nevertheless Nature as one may say arbitrarily hath assigned them some terms and given natural instincts to its natural bodies to move unto the same I will reply that this might perhaps be fabled to have come to pass in the first Chaos where indistinct matter 's confusedly and inordinately wandered to regulate which Nature very appositely made use of right motions by which like as the well-constituted moving disorder themselves so were they which were before depravedly disposed by this motion ranged in order but after their exquisite distribution and collocation it is impossible that there should remain natural inclinations in them of longer moving in a right motion from which now would ensue their removal from their proper and natural place that is to say their disordination we may therefore say that the right motion serves to conduct the matter to erect the work but once erected that it is to rest immoveable or if moveable to move it self onely circularly Unless we will say with Plato that these mundane bodies after they had been made and finished were for a certain time moved by their Maker in a right motion but that after their attainment to certain and determinate places they were revolved one by one in Spheres passing from the right to the circular motion wherein they have been ever since kept and maintained A sublime conceipt and worthy indeed of Plato upon which I remember to have heard our common friend the Lyncean Academick discourse in this manner if I have not forgot it Every body for any reason constituted in a state of rest but which is by nature moveable being set at liberty doth move provided withal that it have an inclination to some particular place for should it stand indifferently affected to all it would remain in its rest not having greater inducement to move one way than another From the having of this inclination necessarily proceeds that it in its moving shall continually increase its acceleration and beginning with a most slow motion it shall not acquire any degree of velocity before it shall have passed thorow all the degrees of less velocity or greater tardity for passing from the state of quiet which is the infinite degree of tardity of motion there is no reason by which it should enter into such a determinate degree of velocity before it shall have entred into a less and into yet a less before it entred into that but rather it stands with reason to pass first by those degrees nearest to that from which it departed and from those to the more remote but the degree from whence the moveable began to move is that of extreme tardity namely of rest Now this acceleration of motion is never made but when the moveable in moving acquireth it nor is its acquist other than an approaching to the place desired to wit whither its natural inclination attracts it and thither it tendeth by the shortest way namely by a right line We may upon good grounds therefore say That Nature to confer upon a moveable first constituted in rest a determinate velocity useth to make it move according to a certain time and space with a right motion This presupposed let us imagine God to have created the Orb v. g. of Jupiter on which he had determined to confer such a certain velocity which it ought afterwards to retain perpetually uniform we may with Plato say that he gave it at the beginning a right and accelerate motion and that it afterwards being arrived to that intended degree of velocity he converted its right into a circular motion the velocity of which came afterwards naturally to be uniform SAGR. I hearken to this Discourse with great delight and I believe the content I take therein will be greater when you have satisfied me in a doubt that is which I do not very well comprehend how it of necessity ensues that a moveable departing from its rest and entring into a motion to which it had a natural inclination it passeth thorow all the precedent degrees of tardity comprehended between any assigned degree of velocity and the state of rest which degrees are infinite so that Nature was not able to confer them upon the body of Jupiter his circular motion being instantly created with such and such velocity SALV I neither did nor dare say that it was impossible for God or Nature to confer that velocity which you speak of immediately but this I say that de facto she did not do it so that the doing it would be a work extra-natural and by consequence miraculous SAGR. Then you believe that a stone leaving its rest and entring into its natural motion towards the centre of the Earth passeth thorow all the degrees of tardity inferiour to any degree of velocity SALV I do believe it nay am certain of it and so certain that I am able to make you also very well satisfied with the truth thereof SAGR. Though by all this daies discourse I should gain no more but such a knowledge I should think my time very well bestowed SALV By what I collect from our discourse a great part of your scruple lieth in that it should in a time and that very short pass thorow those infinite degrees of tardity precedent
it continue to move with this self-same degree uniformly that is to say without accelerating or retarding in as much more time as it was in coming by the inclining plane it would pass double the space of the plane inclined namely for example if the ball had past the plane DA in an hour continuing to move uniformly with that degree of velocity which it is found to have in its arriving at the term A it shall pass in an hour a space double the length DA and because as we have said the degrees of velocity acquired in the points B and A by the moveables that depart from any point taken in the perpendicular CB and that descend the one by the inclined plane the other by the said perpendicular are always equal therefore the cadent by the perpendicular may depart from a term so near to B that the degree of velocity acquired in B would not suffice still maintaining the same to conduct the moveable by a space double the length of the plane inclined in a year nor in ten no nor in a hundred We may therefore conclude that if it be true that according to the ordinary course of nature a moveable all external and accidental impediments removed moves upon an inclining plane with greater and greater tardity according as the inclination shall be less so that in the end the tardity comes to be infinite which is when the inclination concludeth in and joyneth to the horizontal plane and if it be true likewise that the degree of velocity acquired in some point of the inclined plane is equal to that degree of velocity which is found to be in the moveable that descends by the perpendicular in the point cut by a parallel to the Horizon which passeth by that point of the inclining plane it must of necessity be granted that the cadent departing from rest passeth thorow all the infinite degrees of tardity and that consequently to acquire a determinate degree of velocity it is necessary that it move first by right lines descending by a short or long space according as the velocity to be acquired ought to be either less or greater and according as the plane on which it descendeth is more or less inclined so that a plane may be given with so small inclination that to acquire in it the assigned degree of velocity it must first move in a very great space and take a very long time whereupon in the horizontal plane any how little soever velocity would never be naturally acquired since that the moveable in this case will never move but the motion by the horizontal line which is neither declined or inclined is a circular motion about the centre therefore the circular motion is never acquired naturally without the right motion precede it but being once acquired it will continue perpetually with uniform velocity I could with other discourses evince and demonstrate the same truth but I will not by so great a digression interrupt our principal argument but rather will return to it upon some other occasion especially since we not assumed the same not to serve for a necessary demonstration but to adorn a Platonick Conceit to which I will add another particular observation of our Academick which hath in it something of admirable Let us suppose amongst the decrees of the divine Architect a purpose of creating in the World these Globes which we behold continually moving round and of assigning the centre of their conversions and that in it he had placed the Sun immoveable and had afterwards made all the said Globes in the same place and with the intended inclinations of moving towards the Centre till they had acquired those degrees of velocity which at first seemed good to the same Divine Minde the which being acquired we lastly suppose that they were turned round each in his Sphere retaining the said acquired velocity it is now demanded in what altitude and distance from the Sun the place was where the said Orbs were primarily created and whether it be possible that they might all be created in the same place To make this investigation we must take from the most skilfull Astronomers the magnitude of the Spheres in which the Planets revolve and likewise the time of their revolutions from which two cognitions is gathered how much for example Jupiter is swifter than Saturne and being found as indeed it is that Jupiter moves more swiftly it is requisite that departing from the same altitude Jupiter be descended more than Saturne as we really know it is its Orbe being inferiour to that of Saturne But by proceeding forwards from the proportions of the two velocities of Jupiter and Saturne and from the distance between their Orbs and from the proportion of acceleration of natural motion one may finde in what altitude and distance from the centre of their revolutions was the place from whence they first departed This found out and agreed upon it is to be sought whether Mars descending from thence to his Orb the magnitude of the Orb and the velocity of the motion agree with that which is found by calculation and let the like be done of the Earth of Venus and of Mercury the greatness of which Spheres and the velocity of their motions agree so nearly to what computation gives that it is very admirable SAGR. I have hearkened to this conceit with extreme delight and but that I believe the making of these calculations truly would be a long and painfull task and perhaps too hard for me to comprehend I would make a trial of them SALV The operation indeed is long and difficult nor could I be certain to finde it so readily therefore we shall refer it to another time and for the present we will return to our first proposal going on there where we made digression which if I well remember was about the proving the motion by a right line of no use in the ordinate parts of the World and we did proceed to say that it was not so in circular motions of which that which is made by the moveable in it self still retains it in the same place and that which carrieth the moveable by the circumference of a circle about its fixed centre neither puts it self nor those about it in disorder for that such a motion primarily is finite and terminate though not yet finished and determined but there is no point in the circumference that is not the first and last term in the circulation and continuing it in the circumference assigned it it leaveth all the rest within and without that free for the use of others without ever impeding or disordering them This being a motion that makes the moveable continually leave and continually arrive at the end it alone therefore can primarily be uniform for that acceleration of motion is made in the moveable when it goeth towards the term to which it hath inclination and the retardation happens by the repugnance that it hath to
that hath been found to assigne a reason of that same appearance and withal to maintain the incorruptability and ingenerability of the Heavens and if this doth not suffice there wants not more elevated wits which will give you other more convincing SALV If this of which we dispute were some point of Law or other part of the Studies called Humanity wherein there is neither truth nor falshood if we will give sufficient credit to the acutenesse of the wit readinesse of answers and the general practice of Writers then he who most aboundeth in these makes his reason more probable and plausible but in Natural Sciences the conclusions of which are true and necessary and wherewith the judgment of men hath nothing to do one is to be more cautious how he goeth abouâ— to maintain any thing that is false for a man but of an ordinary wit if it be his good fortune to be of the right side may lay a thousand Demosthenes and a thousand Aristotles at his feet Therefore reject those hopes and conceits wherewith you flatter your self that there can be any men so much more learned read and versed in Authors than we that in despite of nature they should be able to make that become true which is false And seeing that of all the opinions that have been hitherto alledged touching the essence of these Solar spots this instanced in by you is in your judgment the truest it followeth if this be so that all the rest are false and to deliver you from this also which doubtlesse is a most false Chimaera over-passing infinite other improbabilities that are therein I shall propose against it onely two experiments one is that many of those spots are seen to arise in the midst of the Solar ring and many likewise to dissolve and vanish at a great distance from the circumference of the Sun a necessary Argument that they generate and dissolve for if without generating or corrrupting they should appear there by onely local motion they would all be seen to enter and pass out by extreme circumference The other observation to such as are not situate in the lowest degree of ignorance in Perspective by the mutation of the appearing figures and by the apparent mutations of the velocity of motion is necessarily concluding that the spots are contiguous to the body of the Sun and that touching its superficies they move either with it or upon it and that they in no wise move in circles remote from the same The motion proves it which towards the circumference of the Solar Circle appeareth very slow and towards the midst more swift the figures of the spots confirmeth it which towards the circumference appear exceeding narrow in comparison of that which they seem to be in the parts nearer the middle and this because in the midst they are seen in their full luster and as they truly be and towards the circumference by reason of the convexity of the globous superficies they seem more compress'd And both these diminutions of figure and motion to such as know how to observe and calculate them exactly precisely answer to that which should appear the spots being contiguous to the Sun and differ irreconcileably from a motion in circles remote though but for smal intervalls from the body of the Sun as hath been diffusely demonstrated by our Friend in his Letters about the Solar spots to Marcus Velserus It may be gathered from the same mutation of figure that none of them are stars or other bodies of spherical figure for that amongst all figures the sphere never appeareth compressed nor can ever be represented but onely perfectly round and thus in case any particular spot were a round body as all the stars are held to be the said roundness would as well appear in the midst of the Solar ring as when the spot is near the extreme whereas it s so great compression and shewing its self so small towards the extreme and contrariwise spatious and large towards the middle assureth us that these spots are flat plates of small thickness or depth in comparison of their length and breadth Lastly whereas you say that the spots after their determinate periods are observed to return to their former aspect believe it not Simplicius for he that told you so will deceive you and that I speak the truth you may observe them to be hid in the face of the Sun far from the circumference nor hath your Observator told you a word of that compression which necessarily argueth them to be contiguous to the Sun That which he tells you of the return of the said spots is nothing else but what is read in the forementioned Letters namely that some of them may sometimes so happen that are of so long a duration that they cannot be dissipated by one sole conversion about the Sun which is accomplished in less than a moneth SIMPL. I for my part have not made either so long or so exact observations as to enable me to boast my self Master of the Quod est of this matter but I will more accurately consider the same and make tryal my self for my own satisfaction whether I can reconcile that which experience shews us with that which Aristotle teacheth us for it 's a certain Maxim that two Truths cannot be contrary to one another SALV If you would reconcile that which sense shewed you with the solider Doctrines of Aristotle you will find no great difficulty in the undertaking and that so it is doth not Aristotle say that one cannot treat confidently of the things of Heaven by reason of their great remoteness SIMPL. He expresly saith so SALV And doth he not likewise affirm that we ought to prefer that which sense demonstrates before all Arguments though in appearance never so well grounded and saith he not this without the least doubt or haesitation SIMPL. He doth so SALV Why then the second of these propositions which are both the doctrine of Aristotle that saith that sense is to take place of Logick is a doctrine much more solid and undoubted than that other which holdeth the Heavens to be unalterable and therefore you shall argue more Aristotelically saying the Heavens are alterable for that so my sense telleth me than if you should say the Heavens are ualterable for that Logick so perswaded Aristotle Furthermore we may discourse of Coelestial matters much better than Aristotle because he confessing the knowledg thereof to be difficult to him by reason of their remoteness from the senses he thereby acknowledgeth that one to whom the senses can better represent the same may philosophate upon them with more certainty Now we by help of the Telescope are brought thirty or forty times nearer to the Heavens than ever Aristotle came so that we may discover in them an hundred things which he could not see and amongst the rest these spots in the Sun which were to him absolutely
us consider what would succeed were the glasse of a spherical figure for without doubt we should find that of the reflection made by the whole surface illuminated that to be but a very small part which arriveth to the eye of a particular beholder by reason that that is but an incosiderable particle of the whole spherical superficies the inclination of which casts the ray to the particular place of the eye whence the part of the spherical superficies which shews it self shining to the eye must needs be very small all the rest being represented obscure So that were the Moon smooth as a Looking-glasse a very small part would be seen by any particular eye to be illustrated by the Sun although its whole Hemisphere were exposed to the Suns rayes and the rest would appear to the eye of the beholder as not illuminated and therefore invisible and finally the whole Moon would be likewise invisible for so much as that particle whence the reflection should come by reason of its smalnesse and remotenesse would be lost And as it would be invisible to the eye so would it not afford any light for it is altogether impossible that a bright body should take away our darknesse by its splendor and we not to see it SALV Stay good Sagredus for I see some emotions in the face and eyes of Simplicius which are to me as indices that he is not either very apprehensive of or satisfied with this which you with admirable proof and absolute truth have spoken And yet I now call to mind that I can by another experiment remove all scruple I have seen above in a Chamber a great spherical Looking-glasse let us send for it hither and whilest it is in bringing let Simplicius return to consider how great the clarity is which cometh to the Wall here under the penthouse from the reflection of the flat glasse SIMPL. I see it is little lesse shining than if the Sun had directly beat upon it SALV So indeed it is Now tell me if taking away that small flat glasse we should put that great spherical one in the same place what effect think you would its reflection have upon the same Wall SIMPL. I believe that it would eject upon it a far greater and more diffused light SALV But if the illumination should be nothing or so small that you would scarse discern it what would you say then SIMPL. When I have seen the effect I will bethink my self of an answer SALV See here is the glasse which I would have to be placed close to the other But first let us go yonder towards the reflection of that flat one and attentively observe its clarity see how bright it is here where it shines and how distinctly one may discern these small unevennesses in the Wall SIMPL. I have seen and very well observed the same now place the other glasse by the side of the first SALV See where it is It was placed there assoon as you began to look upon the Walls small unevennesses and you perceived it not so great was the encrease of the light all over the rest of the Wall Now take away the flat glasse Behold now all reflection removed though the great convex glasse still remaineth Remove this also and place it there again if you please and you shall see no alteration of light in all the Wall See here then demonstrated to sense that the reflection of the Sun made upon a spherical convex glasse doth not sensibly illuminate the places neer unto it Now what say you to this experiment SIMPL. I am afraid that there may be some Leigerdemain used in this affair yet in beholding that glasse I see it dart forth a great splendor which dazleth my eyes and that which imports most of all I see it from what place soever I look upon it and I see it go changing situation upon the superficies of the glasse which way soever I place my self to look upon it a necessary argument that the light is livelily reflected towards every side and consequently as strongly upon all that Wall as upon my eye SALV Now you see how cautiously and reservedly you ought to proceed in lending your assent to that which discourse alone representeth to you There is no doubt but that this which you say carrieth with it probability enough yet you may see how sensible experience proves the contrary SIMPL. How then doth this come to pass SALV I will deliver you my thoughts thereof but I cannot tell how you may be pleas'd therewith And first that lively splendor which you see upon the glass and which you think occupieth a good part thereof is nothing near so great nay is very exceeding small but its liveliness occasioneth in your eye by means of the reflection made on the humidity of the extream parts of the eye-brows which distendeth upon the pupil an adventitious irradiation like to that blaze which we think we see about the flame of a candle placed at some distance or if you will you may resemble it to the adventitious splendor of a star for if you should compare the small body v. g. of the Canicula seen in the day time with the Telescope when it is seen without such irradiation with the same seen by night by the eye it self you will doubtless comprehend that being irradiated it appeareth above a thousand times bigger than the naked and real body and a like or greater augmentation doth the image of the Sun make which you see in that glass I say greater for that it is more lively than the star as is manifest from our being able to behold the star with much less offence than this reflection of the glass The reverberation therefore which is to dispere it self all over this wall cometh from a small part of that glass and that which even now came from the whole flat glass dispersed and restrain'd it self to a very small part of the said wall What wonder is it then that the first reflection very lively illuminates and that this other is almost imperceptible SIMPL. I find my self more perplexed than ever and there presents it self unto me the other difficulty how it can be that that wall being of a matter so obscure and of a superficies so unpolish'd should be able to dart from it greater light than a glass very smooth and polite SALV Greater light it is not but more universal for as to the degree of brightness you see that the reflection of that small flat glass where it beamed forth yonder under the shadow of the penthouse illuminateth very much and the rest of the wall which receiveth the reflection of the wall on which the glass is placed is not in any great measure illuminated as was the small part on which the reflection of the glass fell And if you would understand the whole of this business you must consider that the superficies of that wall 's being rough is the same as
true than the contrary for that I affirmed no such thing nor would I have any of the Propositions in controversie be made to speak to any definitive sense but I onely intended to produce on either part those reasons and answers arguments and solutions which have been hitherto thought upon by others together with certain others which I have stumbled upon in my long searching thereinto alwayes remitting the decision thereof to the judgment of others SAGR. I was unawares transported by my own sense of the thing and believing that others ought to judg as I did I made that conclusion universal which should have been particular and therefore confesse I have erred and the rather in that I know not what Simplicius his judgment is in this particular SIMPL. I must confesse that I have been ruminating all this night of what past yesterday and to say the truth I meet therein with many acute new aud plausible notions yet nevertheless I find my self over-perswaded by the authority of so many great Writers and in particular c. I see you shake your head Sagredus and smile to your self as if I had uttered some great absurdity SAGR. I not onely smile but to tell you true am ready to burst with holding in my self from laughing outright for you have put me in mind of a very pretty passage that I was a witnesse of not many years since together with some others of my worthy friends which I could yet name unto you SALV It would be well that you told us what it was that so Simplicius may not still think that he gave you the occasion of laughter SAGR. I am content I found one day at home in his house at Venice a famous Phisician to whom some flockt for their studies and others out of curiosity sometimes came thither to see certain Anatomies diffected by the hand of a no lesse learned than careful and experienced Anatomist It chanced upon that day when I was there that he was in search of the original and rise of the Nerves about which there is a famous controversie between the Galenists and Peripateticks and the Anatomist shewing how that the great number of Nerves departing from the Brain as their root and passing by the nape of the Neck distend themselves afterwards along by the Back-bone and branch themselves thorow all the Body and that a very small filament as fine as a thred went to the Heart he turned to a Gentleman whom he knew to be a Peripatetick Philosopher and for whose sake he had with extraordinary exactnesse discovered and proved every thing and demanded of him if he was at length satisfied and perswaded that the original of the Nerves proceeded from the Brain and not from the Heart To which the Philosopher after he had stood musing a while answered you have made me to see this businesse so plainly and sensibly that did not the Text of Aristotle assert the contrary which positively affirmeth the Nerves to proceed from the Heart I should be constrained to confesse your opinion to be true SIMPL. I would have you know my Masters that this controversie about the original of the Nerves is not yet so proved and decided as some may perhaps perswade themselves SAGR. Nor questionlesse ever shall it be if it find such like contradictors but that which you say doth not at all lessen the extravagance of the answer of that Peripatetick who against such sensible experience produced not other experiments or reasons of Aristotle but his bare authority and pure ipse dixit SIMPL. Aristotle had not gained so great authority but for the force of his Demonstrations and the profoundnesse of his arguments but it is requisite that we understand him and not onely understand him but have so great familiarity with his Books that we form a perfect Idea thereof in our minds so as that every saying of his may be alwayes as it were present in our memory for he did not write to the vulgar nor is he obliged to spin out his Sillogismes with the trivial method of disputes nay rather using a freedome he hath sometimes placed the proof of one Proposition amongst Texts which seem to treat of quite another point and therefore it is requisite to be master of all that vast Idea and to learn how to connect this passage with that and to combine this Text with another far remote from it for it is not to be questioned but that he who hath thus studied him knows how to gather from his Books the demonstrations of every knowable deduction for that they contein all things SAGR. But good Simplicius like as the things scattered here and there in Aristotle give you no trouble in collecting them but that you perswade your self to be able by comparing and connecting several small sentences to extract thence the juice of some desired conclusion so this which you and other egregious Philosophers do with the Text of Aristotle I could do by the verses of Virgil or of Ovid composing thereof Centones and therewith explaining all the affairs of men and secrets of Nature But what talk I of Virgil or any other Poet I have a little Book much shorter than Aristotle and Ovid in which are conteined all the Sciences and with very little study one may gather out of it a most perfect Idea and this is the Alphabet and there is no doubt but that he who knows how to couple and dispose aright this and that vowel with those or those other consonants may gather thence the infallible answers to all doubts and deduce from them the principles of all Sciences and Arts just in the same manner as the Painter from divers simple colours laid severally upon his Pallate proceedeth by mixing a little of this and a little of that with a little of a third to represent to the life men plants buildings birds fishes and in a word counterfeiting what ever object is visible though there be not on the Pallate all the while either eyes or feathers or fins or leaves or stones Nay farther it is necessary that none of the things to be imitated or any part of them be actually among colours if you would be able therewith to represent all things for should there be amongst them v. gr feathers these would serve to represent nothing save birds and plumed creatures SALV And there are certain Gentlemen yet living and in health who were present when a Doctor that was Professor in a famous Academy hearing the description of the Telescope by him not seen as then said that the invention was taken from Aristotle and causing his works to be fetch 't he turned to a place where the Philosopher gives the reason whence it commeth that from the bottom of a very deep Well one may see the stars in Heaven at noon day and addressing himself to the company see here saith he the Well which representeth the Tube see here the gross vapours
from each other of which the gravity attends only to the drawing of the moveable towards the centre and the vertue impress't to the conducting it about the centre there remaineth no occasion of impediment SIMPL. Your argumentation to give you your due is very probable but in reality it is invelloped with certain intricacies that are not easie to be extricated You have all along built upon a supposition which the Peripatetick Schools will not easily grant you as being directly contrary to Aristotle and it is to take for known and manifest That the project separated from the projicient continueth the motion by vertue impressed on it by the said projicient which vertue impressed is a thing as much detested in Peripatetick Philosophy as the passage of any accident from one subject into another Which doctrine doth hold as I believe it is well known unto you that the project is carried by the medium which in our case happeneth to be the Air. And therefore if that stone let fall from the round top ought to follow the motion of the ship that effect should be ascribed to the Air and not to the vertue impressed But you presuppose that the Air doth not follow the motion of the ship but is tranquil Moreover he that letteth it fall is not to throw it or to give it impetus with his arm but ought barely to open his hand and let it go and by this means the stone neither through the vertue impressed by the projicient nor through the help of the Air shall be able to follow the ships motion and therefore shall be left behind SALV I think then that you would say that if the stone be not thrown by the arm of that person it is no longer a projection SIMPL. It cannot be properly called a motion of projection SALV So then that which Aristotle speaks of the motion the moveable and the mover of the projects hath nothing to do with the businesse in hand and if it concern not our purpose why do you alledg the same SIMP I produce it on the oceasion of that impressed vertue named and introduced by you which having no being in the World can be of no force for non-entium nullae sunt operationes and therefore not onely of projected but of all other preternatural motions the moving cause ought to be ascribed to the medium of which there hath been no due consideration had and therefore all that hath been said hitherto is to no purpose SALV Go to now in good time But tell me seeing that your instance is wholly grounded upon the nullity of the vertue impressed if I shall demonstrate to you that the medium hath nothing to do in the continuation of projects after they are separated from the projicient will you admit of the impressed vertue or will you make another attempt to overthrow it SIMP The operation of the medium being removed I see not how one can have recourse to any thing else save the faculty impressed by the mover SALV It would be well for the removing as much as is possible the occasions of multiplying contentions that you would explain with as much distinctnesse as may be what is that operation of the medium in continuing the motion of the project SIMP The projicient hath the stone in his hand and with force and violence throws his arm with which jactation the stone doth not move so much as the circumambient Air so that when the stone at its being forsaken by the hand findeth it self in the Air which at the same time moveth with impetousity it is thereby born away for if the air did not operate the stone would fall at the foot of the projicient or thrower SALV And was you so credulous as to suffer your self to be perswaded to believe these fopperies so long as you had your senses about you to confute them and to understand the truth thereof Therefore tell me that great stone and that Canon bullet which but onely laid upon a table did continue immoveable against the most impetuous winds according as you a little before did affirm if it had been a ball of cork or other light stuffe think you that the wind would have removed it from its place SIMP Yes and I am assured that it would have blown it quite away and with so much more velocity by how much the matter was lighter for upon this reason we see the clouds to be transported with a velocity equal to that of the wind that drives them SALV And what is the Wind SIMP The Wind is defined to be nothing else but air moved SALV Then the moved air doth carry light things more swiftly and to a greater distance then it doth heavy SIMP Yes certainly SALV But if you were to throw with your arm a stone and a lock of cotton wool which would move swiftest and farthest SIMP The stone by much nay the wool would fall at my feet SALV But if that which moveth the projected substance after it is delivered from the hand be no other than the air moved by the arm and the moved air do more easily bear away light than grave matters how cometh it that the project of wool flieth not farther and swifter than that of stone Certainly it argueth that the stone hath some other impulse besides the motion of the air Furthermore if two strings of equal length did hang at yonder beam and at the end of one there was fastened a bullet of lead and a ball of cotton wool at the other and both were carried to an equal distance from the perpendicular and then let go it is not to be doubted but that both the one and the other would move towards the perpendicular and that being carried by their own impetus they would go a certain space beyond it and afterwards return thither again But which of these two pendent Globes do you think would continue longest in motion before that it would come to rest in its perpendicularity SIMP The ball of lead would swing to and again many times and that of wool but two or three at the most SALV So that the impetus and that mobility whatsoever is the cause thereof would conserve its self longer in grave substances than light I proceed now to another particular and demand of you why the air doth not carry away that Lemon which is upon that same Table SIMP Because that the air it self is not moved SALV It is requisite then that the projicient do confer motion on the Air with which it afterward moveth the project But if such a motion cannot be impressed i. e. imparted it being impossible to make an accident passe out of one subject into another how can it passe from the arm into the Air Will you say that the Air is not a subject different from the arm SIMP To this it is answered that the Air in regard it is neither heavy nor light in its own Region is disposed with facility
else was the first hinter of its mobility said that it did move Now that such a foolish conceit I mean of thinking that those who admit the motion of the Earth have first thought it to stand still from its creation untill the time of Pythagoras and have onely made it moveable after that Pythagoras esteemed it so findeth a place in the mindes of the vulgar and men of shallow capacities I do not much wonder but that such persons as Aristotle and Ptolomy should also run into this childish mistake is to my thinking a more admirable and unpardonable folly SAGR. You believe then Salviatus that Ptolomy thought that in his Disputation he was to maintain the stability of the Earth against such persons as granting it to have been immoveable untill the time of Pythagoras did affirm it to have been but then made moveable when the said Pythagoras ascribed unto it motion SALV We can think no other if we do but consider the way he taketh to confute their assertion the confutation of which consists in the demolition of buildings and the tossing of stones living creatures and men themselves up into the Air. And because such overthrows and extrusions cannot be made upon buildings and men which were not before on the Earth nor can men be placed nor buildings erected upon the Earth unlesse when it standeth still hence therefore it is cleer that Ptolomy argueth against those who having granted the stability of the Earth for some time that is so long as living creatures stones and Masons were able to abide there and to build Palaces and Cities make it afterwards precipitately moveable to the overthrow and destructiof Edifices and living creatures c. For if he had undertook to dispute against such as had ascribed that revolution to the Earth from its first creation he would have confuted them by saying that if the Earth had alwayes moved there could never have been placed upon it either men or stones much less could buildings have been erected or Cities founded c. SIMP I do not well conceive these Aristotelick and Ptolomaick inconveniences SALV Ptolomey either argueth against those who have esteemed the Earth always moveable or against such as have held that it stood for some time still and hath since been set on moving If against the first he ought to say that the Earth did not always move for that then there would never have been men animals or edifices on the Earth its vertigo not permitting them to stay thereon But in that he arguing saith that the Earth doth not move because that beasts men and houses before plac'd on the Earth would precipitate he supposeth the Earth to have been once in such a state as that it did admit men and beasts to stay and build thereon the which draweth on the consequence that it did for some time stand still to wit was apt for the abode of animals and erection of buildings Do you now conceive what I would say SIMP I do and I do not but this little importeth to the merit of the cause nor can a small mistake of Ptolomey committed through inadvertencie be sufficient to move the Earth when it is immoveable But omitting cavils let us come to the substance of the argument which to me seems unanswerable SALV And I Simplicius will drive it home and re-inforce it by shewing yet more sensibly that it is true that grave bodies turn'd with velocity about a settled centre do acquire an impetus of moving and receding to a distance from that centre even then when they are in a state of having a propension of moving naturally to the same Tie a bottle that hath water in it to the end of a cord and holding the other end fast in your hand and making the cord and your arm the semi-diameter and the knitting of the shoulder the centre swing the bottle very fast about so as that it may describe the circumference of a circle which whether it be parallel to the Horizon or perpendicular to it or any way inclined it shall in all cases follow that the water will not fall out of the bottle nay he that shall swing it shall find the cord always draw and strive to go farther from the shoulder And if you bore a hole in the bottom of the bottle you shall see the water spout forth no less upwards into the skie than laterally and downwards to the Earth and if instead of water you shall put little pebble stones into the bottle and swing it in the same manner you shall find that they will strive in the like manner against the cord And lastly we see boys throw stones a great way by swinging round a piece of a stick at the end of which the stone is let into a slit which stick is called by them a sling all which are arguments of the truth of the conclusion to wit that the vertigo or swing conferreth upon the moveable a motion towards the circumference in case the motion be swift and therefore if the Earth revolve about its own centre the motion of the superficies and especially towards the great circle as being incomparably more swift than those before named ought to extrude all things up into the air SIMP The Argument seemeth to me very well proved and inforced and I believe it would be an hard matter to answer and overthrow it SALV It s solution dependeth upon certain notions no less known and believed by you than by my self but because they come not into your mind therefore it is that you perceive not the answer wherefore without telling you it for that you know the same already I shall with onely assisting your memory make you to refute this argument SIMP I have often thought of your way of arguing which hath made me almost think that you lean to that opinion of Plato Quòd nostrum scire sit quoddam reminisci therefore I intreat you to free me from this doubt by letting me know your judgment SALV What I think of the opinion of Plato you may gather from my words and actions I have already in the precedent conferences expresly declared my self more than once I will pursue the same style in the present case which may hereafter serve you for an example thereby the more easily to gather what my opinion is touching the attainment of knowledg when a time shall offer upon some other day but I would not have Sagredâ—s offended at this digression SAGR. I am rather very much pleased with it for that I remember that when I studied Logick I could never comprehend that so much cry'd up and most potent demonstration of Aristotle SALV Let us go on therefore and let Simplicius tell me what that motion is which the stone maketh that is held fast in the slit of the sling when the boy swings it about to throw it a great way SIMP The motion of the stone so long as it is in the slit is circular that is
downwards is no less natural and intrinsecal than that principle of light bodies vvhich moveth them upwards so that I propose to your consideration a ball of lead vvhich descending through the Air from a great altitude and so moving by an intern principle and comming to a depth of vvater continueth its descent and without any other externe mover submergeth a great vvay and yet the motion of descent in the vvater is preternatural unto it but yet nevertheless dependeth on a principle that is internal and not external to the ball You see it demonstrated then that a moveable may be moved by one and the same internal principle with contrary motions SIMP I believe there are solutions to all these objections though for the present I do not remember them but however it be the Author continueth to demand on what principle this circular motion of grave and light bodies dependeth that is whether on a principle internal or external and proceeding forvvards sheweth that it can be neither on the one nor on the other saying Si ab externo Deusne illum excitat per continuum miraculum an verò Angelus an aër Et hunc quidem multi assignant Sed contra In English thus If from an externe principle Whether God doth not excite it by a continued Miracle or an Angel or the Air And indeed many do assign this But on the contrary SALV Trouble not your self to read his argument for I am none of those who ascribe that principle to the ambient air As to the Miracle or an Angel I should rather incline to this side for that which taketh beginning from a Divine Miracle or from an Angelical operation as for instance the transportation of a Cannon ball or bullet into the concave of the Moon doth in all probability depend on the vertue of the same principle for performing the rest But as to the Air it serveth my turn that it doth not hinder the circular motion of the moveables which we did suppose to move thorow it And to prove that it sufficeth nor is more required that it moveth with the same motion and finisheth its circulations with the same velocity that the Terrestrial Globe doth SIMP And he likewise makes his opposition to this also demanding who carrieth the air about Nature or Violence And proveth that it cannot be Nature alledging that that is contrary to truth experience and to Copernicus himself SALV It is not contrary to Copernicus in the least who writeth no such thing and this Author ascribes these things to him with two excessive courtesie It 's true he saith and for my part I think he saith well that the part of the air neer to the Earth being rather a terrestrial evaporation may have the same nature and naturally follow its motion or as being contiguous to it may follow it in the same manner as the Peripateticks say that the superiour part of it and the Element of fire follow the motion of the Lunar Concave so that it lyeth upon them to declare whether that motion be natural or violent SIMP The Author will reply that if Copernicus maketh only the inferiour part of the Air to move and supposeth the upper part thereof to want the said motion he cannot give a reason how that quiet air can be able to carry those grave bodies along with it and make them keep pace with the motion of the Earth SALV Copernicus will say that this natural propension of the elementary bodies to follow the motion of the Earth hath a limited Sphere out of which such a natural inclination would cease besides that as I have said the Air is not that which carrieth the moveables along with it which being separated from the Earth do follow its motion so that all the objections come to nothing which this Author produceth to prove that the Air cannot cause such effects SIMP To shew therefore that that cannot be it will be necessary to say that such like effects depend on an interne principle against which position oboriuntur difficillimae immò inextricabiles quaestiones secundae of which sort are these that follow Principium illud internum vel est accidens vel substantia Si primum quale nam illud nam qualitas locomotiva circum hactenus nulla videtur agniâ—a In English thus Contrary to which position there do arise most difficult yea inextricable second questions such as these That intern principle is either an accident or a substance If the first what manner of accident is it For a locomotive quality about the centre seemeth to be hitherto acknowledged by none SALV How is there no such thing acknowledged Is it not known to us that all these elementary matters move round together with the Earth You see how this Author supposeth for true that which is in question SIMP He saith that we do not see the same and me thinks he hath therein reason on his side SALV We see it not because we turn round together with them SIMP Hear his other Argument Quae etiam si esset quomodò tamen inveniretur in rebus tam contrariis in igne ut in aquâ in aëre ut in terra in viventibus ut in animà carentibus in English thus Which although it were yet how could it be found in things so contrary in the fire as in the water in the air as in the earth in living creatures as in things wanting life SALV Supposing for this time that water and fire are contraries as also the air and earth of which yet much may be said the most that could follow from thence would be that those motions cannot be common to them that are contrary to one another so that v. g. the motion upwards which naturally agreeth to fire cannot agree to water but that like as it is by nature contrary to fire so to it that motion suiteth which is contrary to the motion of fire which shall be the motion deorsum but the circular motion which is not contrary either to the motion sursum or to the motion deorsum but may mix with both as Aristotle himself affirmeth why may it not equally suit with grave bodies and with light The motions in the next place which cannot be common to things alive and dead are those which depend on the soul but those which belong to the body in as much as it is elementary and consequently participateth of the qualities of the elements why may not they be common as well to the dead corps as to the living body And therefore if the circular motion be proper to the elements it ought to be common to the mixt bodies also SAGR. It must needs be that this Author holdeth that a dead cat falling from a window it is not possible that a live cat also could fall it not being a thing convenient that a carcase should partake of the qualities which suit with things alive SALV Therefore the discourse of this Author concludeth nothing against one
I ask you whether the Astronomers in observing with their Instruments and seeking v. gr how great the elevation of a Star is above the Horizon may deviate from the truth aswell in making it too great as too little that is may erroneously compute that it is sometime higher than the truth and sometimes lower or else whether the errour must needs be alwayes of one kinde to wit that erring they alwayes make it too much and never too little or alwayes too little and never too much SIMP I doubt not but that it is as easie to commit an errour the one way as the other SALV I believe the Author would answer the same Now of these two kinds of errours which are contraries and into which the observators of the new star may equally have fallen applied to calculations one sort will make the star higher and the other lower than really it is And because we have already agreed that all the observations are false upon what ground would this Author have us to accept those for most congruous with the truth that shew the star to have been near at hand than the others that shew it excessively remote SIMP By what I have as yet collected of the Authors mind I see not that he doth refuse those observations and indagations that might make the star more remote than the Moon and also than the Sun but only those that make it remote as you your self have said more than an infinite distance the which distance because you also do refuse it as impossible he also passeth over as being convicted of infinite falshood as also those observations are of impossibility Methinks therefore that if you would convince the Author you ought to produce supputations more exact or more in number or of more diligent observers which constitute the star in such and such a distance above the Moon or above the Sun and to be brief in a place possible for it to be in like as he produceth these twelve which all place the star beneath the Moon in places that have a being in the world and where it is possible for it to be SALV But Simplicius yours and the Authors Equivocation lyeth in this yours in one respect and the Authors in another I discover by your speech that you have formed a conceit to your self that the exorbitancies that are commited in the establishing the distance of the Star do encrease successively according to the proportion of the errors that are made by the Instrument in taking the observations and that by conversion from the greatness of the exorbitancies may be argued the greatnesse of the error and that thereforefore hearing it to be infered from such an observation that the distance of the star is infinite it is necessary that the errour in observing was infinite and therefore not to be amended and as such to be refused but the businesse doth not succeed in that manner my Simplicius and I excuse you for not having comprehended the matter as it is in regard of your small experience in such affairs but yet cannot I under that cloak palliate the error of the Author who dissembling the knowledge of this which he did perswade himself that we in good earnest did not understand hath hoped to make use of our ignorance to gain the better credit to his Doctrine among the multitude of illiterate men Therefore for an advertisement to those who are more credulous then intelligent and to recover you from error know that its possible and that for the most part it will come to passe that an observation that giveth you the star v. gr at the distance of Saturn by the adition or substraction of but one sole minute from the elevation taken with the instrument shall make it to become infinitely distant and therefore of possible impossible and by conversion those calculations which being grounded upon those observations make the star infinitely remote may possibly oftentimes with the addition or subduction of one sole minute reduce it to a possible scituation and this which I say of a minute may also happen in the correction of half a minute a sixth part and less Now fix it well in your mind that in the highest distances that is v. g. the height of Saturn or that of the fixed Stars very small errors made by the Observator with the instrument render the scituation determinate and possible infinite impossible This doth not so evene in the sublunary distances and near the earth where it may happen that the observation by which the Star is collected to be remote v. g. 4. Semidiameters terrestrial may encrease or diminish not onely one minute but ten and an hundred and many more without being rendred by the calculation either infinitely remote or so much as superior to the Moon You may hence comprehend that the greatnesse of the error to so speak instrumental are not to be valued by the event of the calculation but by the quantity it self of degrees and minutes numbred upon the instrument and these observations are to be called more just or less erroneous which with the addition or substraction of fewer minutes restore the star to a possible situation and amongst the possible places the true one may be believed to have been that about which a greater number of distances concurre upon calculating the more exact observations SIMP I do not very well apprehend this which you say nor can I of my self conceive how it can be that in greater distances greater exorbitancies can arise from the errour of one minute only than in the smaller from ten or an hundred and therefore would gladly understand the same SALV You shall see it if not Theorically yet at least Practically by this short assumption that I have made of all the combinations and of part of the workings pretermitted by the Author which I have calculated upon this same paper SAGR. You must then from yesterday till now which yet is not above eighteen hours have done nothing but compute without taking either food or sleep SALV I have refreshed my self both those wayes but truth is make these supputations with great brevity and if I may speak the truth I have much admired that this Author goeth so farre about and introduceth so many computations no wise necessary to the question in dispute And for a full knowledge of this and also to the end it may soon be seen how that from the observations of the Astronomers whereof this Author makes use it is more probably gathered that the new star might have been above the Moon and also above all the Planets yea amongst the fixed stars and yet higher still than they I have transcribed upon this paper all the observations set down by the said Authour which were made by thirteen Astronomers wherein are noted the Polar altitude and the altitudes of the star in the meridian aswell the lesser under the Pole as the greater and higher and they are these Tycho  gr m.
to belong to the said Sun than to the Earth in as much as in a moveable Sphere it is more reasonable that the centre stand still than any other place remote from the said centre to the Earth therefore which is constituted in the midst of moveable parts of the Universe I mean between Venus and Mars one of which maketh its revolution in nine moneths and the other in two years may the motion of a year very commodiously be assigned leaving rest to the Sun And if that be so it followeth of necessary consequence that likewise the diurnal motion belongeth to the Earth for if the Sun standing still the Earth should not revolve about its self but have onely the annual motion about the Sun our year would be no other than one day and one night that is six moneths of day and six moneths of night as hath already been said You may consider withal how commodiously the precipitate motion of 24 hours is taken away from the Universe and the fixed stars that are so many Suns are made in conformity to our Sun to enjoy a perpetual rest You see moreover what facility one meets with in this rough draught to render the reason of so great appearances in the Celestial bodies SAGR. I very well perceive that facility but as you from this simplicity collect great probabilities for the truth of that System others haply could make thence contrary deductions doubting not without reason why that same being the ancient Systeme of Pythagoreans and so well accommodated to the Phaenomena hath in the succession of so many thousand years had so few followers and hath been even by Aristotle himself refuted and since that Copernicus himself hath had no better fortune SALV If you had at any time been assaulted as I have been many and many a time with the relation of such kind of frivolous reasons as serve to make the vulgar contumacious and difficult to be perswaded to hearken I will not say to consent to this novelty I believe that you wonder at the paucity of those who are followers of that opinion would be much diminished But small regard in my judgement ought to be had of such thick sculs as think it a most convincing proof to confirm and steadfastly settle them in the belief of the earths immobility to see that if this day they cannot Dine at Constantinople nor Sup in Jappan that then the Earth as being a most grave body cannot clamber above the Sun and then slide headlong down again Of such as these I say whose number is infinite we need not make any reckoning nor need we to record their foolieries or to strive to gain to our side as our partakers in subul and sublime opinions men in whose definition the kind onely is concerned and the difference is wanting Moreover what ground do you think you could be able to gain with all the demonstrations of the World upon brains so stupid as are not able of themselves to know their down right follies But my admiration Sagredus is very different from yours you wonder that so few are followers of the Pythagorean Opinion and I am amazed how there could be any yet left till now that do embrace and follow it Nor can I sufficiently admire the eminencie of those mens wits that have received and held it to be true and with the sprightlinesse of their judgements offered such violence to their own sences as that they have been able to prefer that which their reason dictated to them to that which sensible experiments represented most manifestly on the contrary That the reasons against the Diurnal virtiginous revolution of the Earth by you already examined do carry great probability with them we have already seen as also that the Ptolomaicks and Aristotelicks with all their Sectators did receive them for true is indeed a very great argument of their efficacie but those experiments which apertly contradict the annual motion are of yet so much more manifestly repugnant that I say it again I cannot find any bounds for my admiration how that reason was able in Aristarchus and Copernicus to commit such a rape upon their Sences as in despight thereof to make her self mistress of their credulity SAGR. Are we then to have still more of these strong oppositions against this annual motion SALV We are and they be so evident and sensible that if a sence more sublime and excellent than those common and vulgar did not take part with reason I much fear that I also should have been much more averse to the Copernican Systeem than I have been since the time that a clearer lamp than ordinary hath enlightned me SAGR. Now therefore Salviatus let us come to joyn battail for every word that is spent on any thing else I take to be cast away SALV I am ready to serve you You have already seen me draw the form of the Copernican Systeme against the truth of which Mars himself in the first place makes an hot charge who in case it were true that its distances from the earth should so much vary as that from the least distance to the greatest there were twice as much differences as from the earth to the Sun it would be necessary that when it is nearest unto us its discus would shew more than 60. times bigger than it seems when it is farthest from us nevertheless that diversity of apparent magnitude is not to be seen nay in its opposition with the Sun when its nearest to the Earth it doth not shew so much as quadruple and quintuple in bigness to what it is when towards the conjunction it cometh to be occulted under the Suns rayes Another and greater difficulty doth Venus exhibit For if revolving about the Sun as Copernicus affirmeth it were one while above another while below the same receding and approaching to us so much as the Diameter of the circle described would be at such time as it should be below the Sun and nearest to us its discus would shew little less than 40 times bigger than when it is above the Sun near to its other conjunction yet neverthelesse the difference is almost imperceptible Let us add another difficulty that in case the body of Venus be of it self dark and onely shineth as the Moon by the illumination of the Sun which seemeth most reasonable it would shew forked or horned at such time as it is under the Sun as the Moon doth when she is in like manner near the Sun an accident that is not to be discovered in her Whereupon Copernicus affirmeth that either she is light of her self or else that her substance is of such a nature that it can imbue the Solar light and transmit the same through all its whole depth so as to be able to appear to us alwayes shining and in this manner Copernicus excuseth the not changing figure in Venus but of her small variation of Magnitude
he maketh no mention at all and much less of Mars than was needful I believe as being unable so well as he desired to salve a Phaenomenon so contrary to his Hypothesis and yet being convinced by so many other occurrences and reasons he maintained and held the same Hypothesis to be true Besides these things to make the Planets together with the Earth to move above the Sun as the Centre of their conversions and the Moon onely to break that order and to have a motion by it self about the earth and to make both her the Earth and the whole Elementary Sphere to move all together about the Sun in a year this seemeth to pervert the order of this Systeme which rendreth it unlikely and false These are those difficulties that make me wonder how Aristarchus and Copernicus who must needs have observed them not having been able for all that to salve them have yet notwithstanding by other admirable occurrences been induced to conside so much in that which reason dictated to them as that they have considently affirmed that the structure of the Universe could have no other figure than that which they designed to themselves There are also several other very serious and curious doubts not so easie to be resolved by the middle sort of wits but yet penetrated and declared by Coperninus which we shall defer till by and by after we have answered to other objections that seem to make against this opinion Now coming to the declarations and answers to those three before named grand Objections I say that the two first not onely contradict not the Copernican Systeme but greatly and absolutely favour it For both Mars and Venus seems unequal to themselves according to the proportions assigned and Venus under the Sun seemeth horned and goeth changing figures in it self exactly like the Moon SAGR. But how came this to be concealed from Copernicus and revealed to you SALV These things cannot be comprehended save onely by the sense of seeing the which by nature was not granted to man so perfect as that it was able to attain to the discovery of such differences nay even the very instrument of sight is an impediment to it self But since that it hath pleased God in our age to vouchsafe to humane ingenuity so admirable an invention of perfecting our sight by multiplying it four six ten twenty thirty and fourty times infinite objects that either by reason of their distance or for their extream smallnesse were invisible unto us have by help of the Telescope been rendered visible SAGR. But Venus and Mars are none of the objects invisible for their distance or smallnesse yea we do discern them with our bare natural sight why then do we not distinguish the differences of their magnitudes and figures SALV In this the impediment of our very eye it self hath a great share as but even now I hinted by which the resplendent and remote objects are not represented to us simple and pure but gives them us fringed with strange and adventitious rayes so long and dense that their naked body sheweth to us agrandized ten twenty an hundred yea a thousand times more than it would appear if the capillitious rayes were taken away SAGR. Now I remember that I have read something on this subject I know not whether in the Solar Letters or in the Saggiatore of our common Friend but it would be very good aswell for recalling it into my memory as for the information of Simplicius who it may be never saw those writings that you would declare unto us more distinctly how this businesse stands the knowledge whereof I think to be very necessary for the assisting of us to understand that of which we now speak SIMP I must confesse that all that which Salviatus hath spoken is new unto me for truth is I never have had the curiosity to read those Books nor have I hitherto given any great credit to the Telescope newly introduced rather treading in the steps of other Peripatetick Philosophers my companions I have thought those things to be fallacies and delusions of the Chrystals which others have so much admired for stupendious operations and therefore if I have hitherto been in an errour I shall be glad to be freed from it and allured by these novelties already heard from you I shall the more attentively hearken to the rest SALV The confidence that these men have in their own apprehensivenesse is no less unreasonable than the small esteem they have of the judgment of others yet it s much that should esteem themselves able to judge better of such an instrument without ever having made trial of it than those who have made and daily do make a thousand experiments of the same But I pray you let us leave this kind of pertinacious men whom we cannot so much as tax without doing them too great honour And returning to our purpose I say that resplendent objects whether it is that their light doth refract on the humidity that is upon the pupils or that it doth reflect on the edges of the eye-browes diffusing its reflex rayes upon the said pupils or whether it is for some other reason they do appear to our eye as if they were environ'd with new rayes and therefore much bigger than their bodies would represent themselves to us were they divested of those irradiations And this aggrandizement is made with a greater and greater proportion by how much those lucid objects are lesser and lesser in the same manner for all the world as if we should suppose that the augmentation of shining locks were v. g. four inches which addition being made about a circle that hath four inches diameter would increase its appearance to nine times its former bignesse but SIMP I believe you would have said three times for adding four inches to this side and four inches to that side of the diameter of a circle which is likewise four inches its quantity is thereby tripled and not made nine times bigger SALV A little more Geometry would do well Simplicius True it is that the diameter is tripled but the superficies which is that of which we speak increaseth nine times for you must know Simplicius that the superficies of circles are to one another as the squares of their diameters and a circle that hath four inches diameter is to another that hath twelve as the square of four to the square of twelve that is as 16. is to 144. and therefore it shall be increased nine times and not three this by way of advertisement to Simplicius And proceeding forwards if we should add the said irradiation of four inches to a circle that hath but two inches of diameter onely the diameter of the irradiation or Garland would be ten inches and the superficial content of the circle would be the area of the naked body as 100. to 4. for those are the squares of 10. and of 2. the agrandizement would
that the same must necessarily ensue for I do not think that you will deny me but that if we walk only 60. miles towards the North the Pole will rise unto us a degree higher and that if we move 60. miles farther Northwards the Pole will be elevated to us a degree more c. Now if the approaching or receding 60. miles onely make so notable a change in the Polar altitudes what alteration would follow if the Earth and we with it should be transported I will not say 60. miles but 60. thousand miles that way SALV It would follow if it should proceed in the same proportion that the Pole shall be elevated a thousand degrees See Simplicius what a long rooted opinion can do Yea by reason you have fixed it in your mind for so many years that it is Heaven that revolveth in twenty four hours and not the Earth and that consequently the Poles of that Revolution are in Heaven and not in the Terrestrial Globe cannot now in an hours time shake off this habituated conceipt and take up the contrary fancying to your self that the Earth is that which moveth only for so long time as may suffice to conceive of what would follow thereupon should that lye be a truth If the Earth Simplicius be that which moveth in its self in twenty four hours in it are the Poles in it is the Axis in it is the Equinoctial that is the grand Circle described by the point equidistant from the Poles in it are the infinite Parallels bigger and lesser described by the points of the superficies more and lesse distant from the Poles in it are all these things and not in the starry Sphere which as being immoveable wants them all and can only by the imagination be conceived to be therein prolonging the Axis of the Earth so far till that determining it shall mark out two points placed right over our Poles and the plane of the Equinoctial being extended it shall describe in Heaven a circle like it self Now if the true Axis the true Poles the true Equinoctial do not change in the Earth so long as you continue in the same place of the Earth and though the Earth be transported as you do please yet you shall not change your habitude either to the Poles or to the circles or to any other Earthly thing and this because that that transposition being common to you and to all Terrestrial things and that motion where it is common is as if it never were and as you change not habitude to the Terrestrial Poles habitude I say whether that they rise or descend so neither shall you change position to the Poles imagined in Heaven alwayes provided that by Celestial Poles we understand as hath been already defined those two points that come to be marked out by the prolongation of the Terrestrial Axis unto that length T is true those points in Heaven do change when the Earths transportment is made after such a manner that its Axis cometh to passe by other and other points of the immoveable Celestial Sphere but our habitude thereunto changeth not so as that the second should be more elevated to us than the first If any one will have one of the points of the Firmament which do answer to the Poles of the Earth to ascend and the other to descend he must walk along the Earth towards the one receding from the other for the transportment of the Earth and with it us our selves as I told you before operates nothing at all SAGR. Permit me I beseech you Salviatus to make this a little more clear by an example which although grosse is acommodated to this purpose Suppose your self Simplicius to be aboard a Ship and that standing in the Poope or Hin-deck you have directed a Quadrant or some other Astronomical Instrument towards the top of the Top-gallant-Mast as if you would take its height which suppose it were v. gr 40. degrees there is no doubt but that if you walk along the Hatches towards the Mast 25. or 30. paces and then again direct the said Instrument to the same Top-Gallant-Top You shall find its elevation to be greater and to be encreased v. gr 10. degrees but if instead of walking those 25. or 30. paces towards the Mast you stand still at the Sterne and make the whole Ship to move thitherwards do you believe that by reason of the 25. or 30. paces that it had past the elevation of the Top-Gallant-Top would shew 10. degrees encreased SIMP I believe and know that it would not gain an hairs breadth in the passing of 30. paces nor of a thousand no nor of an hundred thousand miles but yet I believe withal that looking through the sights at the Top and Top-Gallant if I should find a fixed Star that was in the same elevation I believe I say that holding still the Quadrant after I had sailed towards the star 60. miles the eye would meet with the top of the said Mast as before but not with the star which would be elevated to me one degree SAGR. Then you do not think that the sight would fall upon that point of the Starry Sphere that answereth to the direction of the Top-Gallant Top SIMP No For the point would be changed and would be beneath the star first observed SAGR. You are in the right Now like as that which in this example answereth to the elevation of the Top-Gallant-Top is not the star but the point of the Firmament that lyeth in a right line with the eye and the said top of the Mast so in the case exemplified that which in the Firmament answers to the Pole of the Earth is not a star or other fixed thing in the Firmament but is that point in which the Axis of the Earth continued streight out till it cometh thither doth determine which point is not fixed but obeyeth the mutations that the Pole of the Earth doth make And therefore Tycho or who ever else that did alledg this objection ought to have said that upon that same motion of the Earth were it true one might observe some difference in the elevation and depression not of the Pole but of some fixed star toward that part which answereth to our Pole SIMP I already very well understand the mistake by them committed but yet therefore which to me seems very great of the argument brought on the contrary is not lessened supposing relation to be had to the variation of the stars and not of the Pole for if the moving of the Ship but 60. miles make a fixed star rise to me one degree shall I not find alike yea and very much greater mutation if the Ship should sail towards the said star for so much space as is the Diameter of the Grand Orb which you affirm to be double the distance that is between the Earth and Sun SAGR. Herein Simplicius there is another fallacy which truth is you understand but do
so between them both compose this our Globe writeth that the seeing the small * particles of water shape themselves into rotundity as in the drops and in the dew daily apparent upon the leaves of several herbs is a strong argument and because according to the trite Axiome there is the same reason for the whole as for the parts the parts affecting that same figure it is necessary that the same is proper to the whole Element and truth is methinks it is a great oversight that these men should not perceive so apparent a vanity and consider that if their argument had run right it would have followed that not only the small drops but that any whatsoever greater quantity of water separated from the whole Element should be reduced into a Globe Which is not seen to happen though indeed the Senses may see and the Understanding perceive that the Element of Water loving to form it self into a Spherical Figure about the common centre of gravity to which all grave bodies tend that is the centre of the Terrestrial Globe it therein is followed by all its parts according to the Axiome so that all the surfaces of Seas Lakes Pools and in a word of all the parts of Waters conteined in vessels distend themselves into a Spherical Figure but that Figure is an arch of that Sphere that hath for its centre the centre of the Terrestrial Globe and do not make particular Spheres of themselves SALV The errour indeed is childish and if it had been onely the single mistake of Sacrobosco I would easily have allowed him in it but to pardon it also to his Commentators and to other famous men and even to Ptolomy himselfe this I cannot do without blushing for their reputation But it is high time to take leave it now being very late and we being to meet again to morrow at the usual hour to bring all the foregoing Discourses to a final conclusion Place this Plate at the end of the third Dialogue GALILAEUS Gailaeus Lyncaeus HIS SYSTEME OF THE WORLD The Fourth Dialogue INTERLOCVTORS SALVIATUS SAGREDUS SIMPLICIUS SAGR. I know not whether your return to our accustomed conferences hath really been later than usual or whether the desire of hearing the thoughts of Salviatus touching a matter so curious hath made me think it so But I have tarried a long hour at this window expecting every moment when the Gondola would appear that I sent to fetch you SALV I verily believe that your imagination more than our tarriance hath prolonged the time and to make no longer demurre it would be well if without interposing more words we came to the matter it self and did shew that nature hath permitted whether the business in rei veritate be so or else to play and sport with our Fancies hath I say hath permitted that the motions for every other respect except to resolve the ebbing and flowing of the Sea assigned long since to the earth should be found now at last to answer exactly to the cause thereof and as it were with mutual a emulation the said ebbing and flowing to appear in confirmation of the Terrestrial motion the judices whereof have hitherto been taken from the coelestial Phaenomena in regard that of those things that happen on Earth not any one was of force to prove one opinion more than another as we already have at large proved by shewing that all the terrene occurrences upon which the stability of the Earth and mobility of the Sun and Firmament is commonly inferred are to seem to us performed in the same manner though we supposed the mobility of the Earth and the immobility of them The Element of Water onely as being most vast and which is not annexed and concatenated to the Terrestrial Globe as all its other solid parts are yea rather which by reason of its fluidity remaineth apart sui juris and free is to be ranked amongst those sublunary things from which we may collect some hinte and intimation of what the Earth doth in relation to motion and rest After I had many and many a time examined with my self the effects and accidents partly seen and partly understood from others that are to be observed in the motions of waters and moreover read and heard the great vanities produced by many as the causes of those accidents I have been induced upon no slight reasons to omit these two conclusions having made withal the necessary presupposals that in case the terrestrial Globe be immoveable the flux and reflux of the Sea cannot be natural and that in case those motions be conferred upon the said Globe which have been long since assigned to it it is necessary that the Sea be subject to ebbing and flowing according to all that which we observe to happen in the same SAGR. The Proposition is very considerable as well for it self as for what followeth upon the same by way of consequence so that I shall the more intensly hearken to the explanation and confirmation of it SALV Because in natural questions of which number this which we have in hand is one the knowledge of the effects is a means to guide us to the investigation and discovery of the causes and without which we should walk in the dark nay with more uncertainty for that we know not whither we would go whereas the blind at least know where they desire to arrive therefore first of all it is necessary to know the effects whereof we enquire the causes of which effects you Sagredus ought more abundantly and more certainly to be informed than I am as one that besides your being born and having for a long time dwelt in Venice where the Tides are very notable for their greatnesse have also sailed into Syria and as an ingenuous and apprehensive wit must needs have made many Observations upon this subject whereas I that could onely for a time and that very short observe what happened in these extream parts of the Adriatick Gulph and in our Seas below about the Tyrrhene shores must needs take many things upon the relation of others who for the most part not very well agreeing and consequently being very uncertain contribute more of confusion than confirmation to our speculations Neverthelesse from those that we are sure of and which are the principal I think I am able to attain to the true and primary causes not that I pretend to be able to produce all the proper and adequate reasons of those effects that are new unto me and which consequently I could never have thought upon And that which I have to say I propose only as a key that openeth the door to a path never yet trodden by any in certain hope that some wits more speculative than mine will make a further progresse herin and penetrate much farther than I shall have done in this my first Discovery And although that in other Seas remote from us there may â—appen several accidents which
indeavoured to believe by the example of the unfortunate Orlando that that might not possibly be true which yet the testimony of so many credible men set before my eyes wonder not therefore if this once contrary to your custome you do not foresee what I intend and if you will needs admire I believe that the event as far as I can judge unexpected will make you cease your wonderment SAGR. I thank God that he did not permit that desperation of yours to end in the Exit that is fabled of the miserable Orlando nor in that which haply is no lesse fabulously related of Aristotle that so neither my self nor others should be deprived of the discovery of a thing as abstruse as it was desirable I beseech you therefore to satisfie my eager appetite as soon as you can SALV I am ready to serve you We were upon an inquiry in what manner the additions and substractions of the Terrestriall conversion from the Annual motion could be made one while in a greater and another while in a lesser proportion which diversity and no other thing could be assigned for the cause of the alterations Monethly and Annual that are seen in the greatnesse of the Ebbings and Flowings I will now consider how this proportion of the additions and substractions of the Diurnal Revolution and Annual motion may grow greater and lesser three several wayes One is by increasing and diminishing the velocity of the Annual motion retaining the additions and substractions made by the Diurnal conversion in the same greatnesse because the Annual motion being about three times greater that is more velocious than the Diurnal motion considered likewise in the Grand Circle if we increase it anew the additions and substractions of the Diurnal motion will occasion lesse alteration therein but on the other side making it more slow it will be altered in greater proportion by that same diurnal motion just as the adding or substracting four degrees of velocity from one that moveth with twenty degrees altereth his course lesse than those very four degrees would do added or substracted from one that should move onely with ten degrees The second way would be by making the additions and substractions greater and lesser retaining the annual motion in the same velocity which is as easie to be understood as it is manifest that a velocity v. gr of 20 degr is more altered by the addition or substraction of 10. deg than by the addition or substraction of 4. The third way would be in case these two were joyned together diminishing the annual motion increasing the diurnal additions and substractions Hitherto as you see it was no hard matter to attain but yet it proved to me very hard to find by what means this might be effected in Nature Yet in the end I finde that she doth admirably make use thereof and in wayes almost incredible I mean admirable and incredible to us but not to her who worketh even those very things which to our capacity are of infinite wonder with extraordinary facility and simplicity and that which it is hard for us to understand is easie for her to effect Now to proceed having shewn that the proportion between the additions and substractions of the Diurnal conversion and Annual motion may be made greater and lesser two wayes and I say two because the third is comprized in the two first I adde that Nature maketh use of them both and farthermore I subjoyn that if she did make use but of one alone it would be necessary to take away one of the two Periodical alterations That of the Monethly Period would cease if the annual motion should not alter And in case the additions and substractions of the diurnal revolution should continually be equal the alterations of the annual Period would fail SAGR. It seems then that the Monethly alteration of ebbings and flowings dependeth on the alteration of the annual motion of the Earth And the annual alteration of those ebbings and flowings do it seems depend on the additions and substractions of the diurnal conversion And here now I finde my self worse puzzled than before and more out of hope of being able to comprehend how this intricacy may be which is more inextricable in my judgment than the Gordian knot And I envy Simplicius from whose silence I argue that he doth apprehend the whole businesse and is acquit of that confusion which greatly puzzleth my brains SIMP I believe verily Sagredus that you are put to a a stand and I believe that I know also the cause of your confusion which if I mistake not riseth from your understanding part of those particulars but even now alledged by Salviatus and but a part It is true likewise that I find my self free from the like confusion but not for that cause as you think to wit because I apprehend the whole nay it happens upon the quite contrary account namely from my not comprehending any thing and confusion is in the plurality of things and not in nothing SAGR. You see Salviatus how a few checks given to Simplicius in the dayes preceding have rendered him gentle and brought him from the capriol to the amble But I beseech you without farther delay put us both out of suspence SALV I will endeavour it to the utmost of my harsh way of expressing my self the obtusenesse of which the acutenesse of your wit shall supply The accidents of which we are to enquire the causes are two The first respecteth the varieties that happen in the ebbings and flowings in the Monethly Period and the othr relateth to the Annual We will first speak of the Monethly and then treat of the Annual and it is convenient that we resolve them all according to the Fundamentals and Hypothesis already laid down without introducing any novelty either in Astronomy or in the Universe in favour of the ebbings and flowings therefore let us demonstrate that of all the several accidents in them observed the causes reside in the things already known and received for true and undoubted I say therefore that it is a truly natural yea necessary thing that one and the same moveable made to move round by the same moving virtue in a longer time do make its course by a greater circle rather than by a lesser and this is a truth received by all and confirmed by all experiments of which we will produce a few In the wheel-clocks and particularly in the great ones to moderate the time the Artificers that make them accomodate a certain voluble staffe horozontally and at each end of it they fasten two Weights of Lead and when the time goeth too slow by the onely removing those Leads a little nearer to the centre of the staffe they render its vibrations more frequent and on the contrary to retard it it is but drawing those Weights more towards the ends for so the vibrations are made more seldome and consequently the intervals of the hours
are prolonged Here the movent vertue is the same namely the counterpoise the moveables are those same Weights of lead and their vibrations are more frequent when they are neerer to the centre that is when they move by lesser circles Hanging equal Weights at unequal cords and being removed from their perpendicularity letting them go we shall see those that are pendent at the shorter cords to make their vibrations under shorter times as those that move by lesser circles Again let such a kind of Weight be fastened to a cord which cord let play upon a staple fastened in the Seeling and do you hold the other end of the cord in your hand and having given the motion to the pendent Weight whilst it is making its vibrations pull the end of the cord that you hold in your hand so that the Weight may rise higher and higher In its rising you shall see the frequency of its vibrations encrease in regard that they are made successively by lesser and lesser circies And here I desire you to take notice of two particulars worthy to be observed One is that the vibrations of one of those plummets are made with such a necessity under such determinate times that it is altogether impossible to cause them to be made under other times unlesse it be by prolonging or abreviating the cord of which you may also at this very instant ascertain your selves by experience tying a stone to a pack-threed and holding the other end in your hand trying whether you can ever by any artifice be able to swing it this way and that way in other than one determinate time unlesse by lengthening of shortening the string which you will find to be absolutely impossible The other particular truly admirable is that the self same pendulum makes its vibrations with one and the same frequency or very little and as it were insensibly different whether they be made by very great or very small arches of the self-same circumference I mean that whether we remove the pendulum from perpendicularity one two or three degrees onely or whether we remove it 70. 80. nay to an entire quadrant it being let go will in the one case and in the other make its vibrations with the same frequency as well the former where it is to move by an arch of but four or six degrees as the second where it is to passe arches of 160. or more degrees Which may the better be seen by hanging two weights at two strings of equal length and then removing them from perpendicularity one a little way and the other very far the which being set at liberty will go return under the same times the one by arches very small the other by very great ones from whence followeth the conclusion of an admirable Problem which is That a Quadrant of a Circle being given take a little diagram of the same in Fig. 3. as for instance AB erect to the Horizon so as that it rest upon the plain touching in the point B. and an Arch being made with a Hoop well plained and smoothed in the concave part bending it according to the curvity of the Circumference ADB So that a Bullet very round and smooth may freely run to and again within it the rim of a Sieve is very proper for the experiment I say that the Bullet being put in any what ever place neer or far from the lowest term B. As for instance putting it in the point C or here in D or in E and then let go it will in equal times or insensibly different arrive at the term B departing from C or from D or from E or from whatever other place an accident truly wonderfull We may add another accident no less strange than this which is That moreover by all the cords drawn from the point B to the points C D E and to any other whatsoever taken not onely in the Quadrant BA but in all the whole circumference of the Circle the said moveable shall descend in times absolutely equal insomuch that it shall be no longer in descending by the whole Diameter erect perpendicularly upon the point B then it shall in descending by B. C. although it do sublend but one sole degree or a lesser Arch. Let us add the other wonder which is That the motions of the falling bodies made by the Arches of the Quadrant AB are made in shorter times than those that are made by the cords of those same Arches so that the swiftest motion and made by a moveable in the shortest time to arrive from the point A to the term B shall be that which is made not by the right line A B although it be the shortest of all those that can de drawn between the points A. B. but by the circumference ADB And any point being taken in the said Arch as for example The point D. and two cords drawn AD and D. B. the moveable departing from the qoint A shall in a less time come to B moving by the two cords AD and DB. than by the sole cord A B. But the shortest of all the times shall be that of the fall by the Arch ADB And the self same accidents are to be understood of all the other lesser Arches taken from the lowermost term B. upwards SAGR. No more no more for you so confund and fill me with Wonders and distract my thoughts so many several wayes that I fear I shall have but a small part of it left free and disingaged to apply to the principal matter that is treated of and which of it self is but even too obscure and intricate So that I intreat you to vouchsafe me having once dispatcht the business of the ebbings and flowings to do this honour to my house and yours some other dayes and to discourse upon the so many other Problems that we have left in suspence and which perhaps are no less curious and admirable than this that hath been discussed these dayes past and that now ought to draw to a conclusion SALV I shall be ready to serve you but we must make more than one or two Sessions if besides the other questions reserved to be handled apart we would discusse those many that pertain to the local motion as well of natural moveables as of the rejected an Argument largely treated of by our Lyncean Accademick But turning to our first purpose where we were about to declare That the bodies moving circularly by a movent virtue which continually remaineth the same the times of the circulation were prefixt and determined and impossible to be made longer or shorter having given examples and produced experiments thereof sensible and feasible we may confirm the same truth by the experiences of the Celestial motions of the Planets in which we see the same rule observed for those that move by greater Circles confirm longer times in passing them A most pertinent observation of this we have from the Medicaean Planets which
think a greater part should rather be imployed than a lesser 105 PRINCIPLES By denying Principles in Sciences any Paradox may be maintained 28 Contrary Principles cannot naturally reside in the same Subject 211 PROJECT c. The Project according to Aristotle is not moved by virtue impressed but by the Medium 130 Operation of the Medium in continuing the Motion of the Project 131 Many Experiments and Reasons against the Motions of Projects assigned by Aristotle 132 The Medium doth impede and not conferre the Motion of Projects 134 An admirable accident in the Motion of Projects 135 Sundry curious Problems touching the Motion of Projects 137 Projects continue their Motion by a Right Line that follows the direction of the Motion made together with the Projicient whilst they were conjoyned therewith 154 The Motion impressed by the Projicient is onely in a Right Line 170 The Project moveth by the Tangent of the Circle of the Motion preceeding in the instant of Seperation 172 A Grave Project assoon as it is seperated from the Projicient beginneth to decline 173 The Cause of the Projection encreaseth not according to the Proportion of Velocity encreased by making the Wheel bigger 189 The Virtue which carrieth Grave Projects upwards is no lesse Natural to them than the Gravity which moveth them downwards 211 PTOLOMY c. Inconveniences that are in the System of Ptolomy 309 Ptolomies System full of defects 476 The Learned both of elder and later times dissatisfied with the Ptolomaick System 477 PYTHAGORAS c. Pythagorick Mistery of Numbers fabulous 3 Pythagoras offered an Hecatombe for a Geometrical Demonstration which he found 38 Pythagoras and many other Ancients enumerated that held the Earths Mobility 437 468 R RAYS Shining Objects seem fringed and environed with adventitious Rays 304 REST. Rest. Vide Motion Rest the Infinite degree of Tardity 11 RETROGRADATIONS Retrogradations more frequent in Saturn lesse frequent in Jupiter and yet lesse in Mars and why 311 The Retrogradations of Venus and Mercury demonstrated by Apollonius and Copernicus 311 S SATURN Saturn for its slownesse and Mercury for its late appearing were amongst those that were last observed 416 SCARCITY Scarcity and Plenty enhanse and debase the price of all things 43 SCHEINER Christopher Scheiner the Jesuit his Book of Conclusions confuted 78 195 seq 323 A Canon Bullet would spend more than six dayes in falling from the Concave of the Moon to the Center of the Earth according to Scheiner 195 Christopher Scheiner his Book entituled Apelles post Tabulam censured and disproved 313 The Objections of Scheiner by way of Interrogation 336 Answers to the Interrogations of Scheiner 336 Questions put to Scheiner by which the weaknesse of his is made appear 336 SCIENCES In Natural Sciences the Art of Oratory is of no use 40 In Natural Sciences it is not necessary to seek Mathematical evidence 206 SCRIPTURE c. The Caution we are to use in determining the Sense of Scripture in difficult points of Phylosophy 427 Scripture studiously condescendeth to the apprehension of the Vulgar 432 In dicussing of Natural Questions we ought not to begin at Scripture but at Sensible Experiments and Necessary Demonstrations 433 The intent of Scripture is by its Authority to recommend those Truths to our beliefe which being un-intelligible could no other wayes be rendered credible 434 Scripture Authority to be preferred even in Natural Controversies to such Sciences as are not confined to a Demonstrative Method 434 The Pen-men of Scripture though read in Astronomy intentionally forbear to teach us any thing of the Nature of the Stars 435 The Spirit had no intent at the Writing of the Scripture to teach us whether the Earth moveth or standeth still as nothing concerning our Salvation 436 Inconveniencies that arise from licentious usurping of Scripture to stuffe out Books that treat of Nat. Arguments 438 The Literal Sense of Scripture joyned with the universal consent of the Fathers is to be received without farther dispute 444 A Text of Scripture ought no lesse diligently to be reconciled with a Demonstrated Proposition in Philosophy than with another Text of Scripture sounding to a contrary Sense 446 Demonstrated Truth ought to assist the Commentator in finding the true Sense of Scripture 446 It was necessary by way of condescension to Vulgar Capacities that the Scripture should speak of the Rest and Motion of the Sun and Earth in the same manner that it doth 447 Not onely the Incapacity of the Vulgar but the Current Opinion of those times made the Sacred Writers of the Scripture to accommodate themselves to Popular Esteem more than Truth 447 The Scripture had much more reason to affirm the Sun Moveable and the Earth Immoveable than otherwise 448 Circumspection of the Fathers about imposing positive Senses on Doubtful Texts of Scripture 451 T is Cowardice makes the Anti-Copernican fly to Scripture Authorities thinking thereby to affright their Adversaries 455 Scripture speaks in Vulgar and Common Points after the manner of Men. 462 The intent of Scripture is to be observed in Places that seem to affirme the Earths Stability 464 Scripture Authorities that seem to affirm the Motion of the Sun and Stability of the Earth divided into six Classes 478 Six Maximes to be observed in Expounding Dark Texts of Scripture 481 Scripture Texts speaking of things inconvenient to be understood in their Literal Sense are to be interpreted one of the four wayes named 81 Why the Sacred Scripture accommodates it self to the Sense of the Vulgar 487 SEA The Seas Surface would shew at a distance more obscure than the Land 49 The Seas Reflection of Light much weaker than that of the Earth 81 The Isles are tokens of the unevennesse of the Bottoms of Seas 383 SELEUCUS Opinion of Seleucus the Mathematician censured 422 SENSE He who denieth Sense deserves to be deprived of it 21 Sense sheweth that things Grave move ad Medium and the Light to the Concave 21 It is not probable that God who gave us our Senses would have us lay them aside and look for other Proofs for such Natural Points as Sense sets before our Eyes 434 Sense and Reason lesse certain than Faith 475 SILVER Silver burnished appears much more obscure than the unburnished and why 64 SIMPLICIUS Simplicius his Declamation 43 SOCRATES The Answer of the Oracle true in judging Socrates the Wisest of his time 85 SORITES The Forked Sylogisme called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 29 SPEAKING We cannot abstract our manner of Speaking from our Sense of Seeing 461 SPHERE The Motion of 24 hours ascribed to the Highest Sphere disorders the Period of the Inferiour 102 The Sphere although Material toucheth the Material Plane but in one point onely 182 The Definition of the Sphere 182 A Demonstration that the Sphere toucheth the Plane but in one point 183 Why the Sphere in abstract toucheth the Plane onely in one point and not the Material in Concrete 184 Contact in a Single Point is not
the said Divine Wisdome surpasseth all humane Judgment and Conjecture But that that self same God who hath indued us with Senses Discourse and Understanding hath intended laying aside the use of these to give the knowledg of those things by other means which we may attain by these so as that even in those Natural Conclusions which either by Sensible Experiments or Necessary Demonstrations are set before our eyes or our Understanding we ought to deny Sense and Reason I do not conceive that I am bound to believe it and especially in those Sciences of which but a small part and that divided into Conclusions is to be found in the Scripture Such as for instance is that of Astronomy of which there is so small a part in Holy Writ that it doth not so much as name any of the Planets except the Sun and the Moon and once or twice onely Venus under the name of Lucifer For if the Holy Writers had had any intention to perswade People to believe the Dispositions and Motions of the Coelestial Bodies and that consequently we are still to derive that knowledge from the Sacred Books they would not in my opinion have spoken so little thereof that it is as much as nothing in comparison of the infinite admirable Conclusions which in that Science are comprized and demonstrated Nay that the Authours of the Holy Volumes did not only not pretend to teach us the Constitutions and Motions of the Heavens and Stars their Figures Magnitudes and Distances but that intentionally albeit that all these things were very well known unto them they forbore to speak of them is the opinion of the Most Holy Most Learned Fathers and in S. Augustine we read the following words It is likewise commonly asked of what Form and Figure we may believe Heaven to be according to the Scriptures For many contend much about those matters which the greater prudence of our Authors hath forborn to speak of as nothing furthering their Learners in relation to a blessed life and which is the chiefest thing taking up much of that time which should be spent in holy exercises For what is it to me whether Heaven as a Sphere doth on all sides environ the Earth a Mass ballanced in the middle of the World or whether like a Dish it doth onely cover or overcast the same But because belief of Scripture is urged for that cause which we have oft mentioned that is That none through ignorance of Divine Phrases when they shall find any thing of this nature in or hear any thing cited out of our Bibles which may seem to oppose manifest Conclusions should be induced to suspect their truth when they admonish relate deliver more profitable matters Briefly be it spoken touching the Figure of Heaven that our Authors knew the truth But the H. Spirit would not that men should learn what is profitable to none for salvation And the same intentional silence of these sacred Penmen in determining what is to be believed of these accidents of the Celestial Bodies is again hinted to us by the same Father in the ensuing 10. Chapter upon the Question Whether we are to believe that Heaven moveth or standeth still in these words There are some of the Brethren that start a question concerning the motion of Heaven Whether it be fixed or moved For if it be moved say they how is it a Firmament If it stand still how do these Stars which are held to be fixed go round from East to West the more Northern performing shorter Circuits near the Pole so that Heaven if there be another Pole to us unknown may seem to revolve upon some other Axis but if there be not another Pole it may be thought to move as a Discus To whom I reply that these points require many subtil and profound Reasons for the making out whether they be really so or no the undertakeing and discussing of which is neither consistent with my leasure nor their duty vvhom I desire to instruct in the necessary matters more directly conducing to their salvation and to the benefit of The Holy Church From which that we may come nearer to our particular case it necessarily followeth that the Holy Ghost not having intended to teach us whether Heaven moveth or standeth still nor whether its Figure be in Form of a Sphere or of a Discus or distended in Planum Nor whether the Earth be contained in the Centre of it or on one side he hath much less had an intention to assure us of other Conclusions of the same kinde and in such a manner connected to these already named that without the dedermination of them one can neither affirm one or the other part which are The determining of the Motion and Rest of the said Earth and of the Sun And if the same Holy Spirit hath purposely pretermitted to teach us those Propositions as nothing concerning his intention that is our salvation how can it be affirmed that the holding of one part rather than the other should be so necessary as that it is de Fide and the other erronious Can an Opinion be Heretical and yet nothing concerning the salvation of souls Or can it be said that the Holy Ghost purposed not to teach us a thing that concerned our salvation I might here insert the Opinion of an Ecclesiastical Person raised to the degree of Eminentissimo to wit That the intention of the Holy Ghost is to teach us how we shall go to Heaven and not how Heaven goeth But let us return to consider how much necessary Demonstrations and sensible Experiments ought to be esteemed in Natural Conclusions and of what Authority Holy and Learned Divines have accounted them from whom amongst an hundred other attestations we have these that follow We must also carefully heed and altogether avoid in handling the Doctrine of Moses to avouch or speak any thing affirmatively and confidently which contradicteth the manifest Experiments and Reasons of Philosophy or other Sciences For since all Truth is agreeable to Truth the Truth of Holy Writ cannot be contrary to the solid Reasons and Experiments of Humane Learning And in St. Augustine we read If any one shall object the Authority of Sacred Writ against clear and manifest Reason he that doth so knows not what he undertakes For he objects against the Truth not the sense of the Scripture which is beyond his comprehension but rather his own not what is in it but what finding it in himself he fancyed to be in it This granted and it being true as hath been said that two Truths cannot be contrary to each other it is the office of a Judicious Expositor to study to finde the true Senses of Sacred Texts which undoubtedly shall accord with those Natural Conclusions of which manifest Sense and Necessary Demonstrations had before made us sure and certain Yea in regard that the Scriptures as hath been said
for the Reasons alledged admit in many places Expositions far from the Sense of the words and moreover we not being able to affirm that all Interpreters speak by Divine Inspiration For if it were so then there would be no difference between them about the Senses of the same places I should think that it would be an act of great prudence to make it unlawful for any one to usurp Texts of Scripture and as it were to force them to maintain this or that Naturall Conclusion for truth of which Sence Demonstrative and necessary Reasons may one time or other assure us the contrary For who will prescribe bounds to the Wits of men Who will assert that all that is sensible and knowable in the World is already discovered and known Will not they that in other points disagree with us confess this and it is a great truth that Eaquae scimus sint minima pars corum quae ignoramus That those Truths which we know are very few in comparison of those which we know not Nay more if we have it from the Mouth of the Holy Ghost that Deus tradidit Mundum disputationi eorum ut non inveniat homo opus quod operatus est Deus ab initio ad finem One ought not as I conceive to stop the way to free Philosophating touching the things of the World and of Nature as if that they were already certainly found and all manifest nor ought it to be counted rashness if one do not sit down satisfied with the opinions now become as it were commune nor ought any persons to be displeased if others do not hold in natural Disputes to that opinion which best pleaseth them and especially touching Problems that have for thousands of years been controverted amongst the greatest Philosophers as is the Stability of the Sun and Mobility of the Earth an opinion held by Pythagoras and by his whole Sect by Heraclides Ponticus who was of the same opininion by Phylolaus the Master of Plato and by Plato himself as Aristotle relateth and of which Plutarch writeth in the life of Numa that the said Plato when he was grown old said It is a most absurd thing to think otherwise The same was believed by Aristarchus Samius as we have it in Archimedes and probably by Archimedes himself by Nicetas the Philosopher upon the testimony of Scicero and by many others And this opinion hath finally been amplified and with many Observations and Demonstrations confirmed by Nicholaus Copernicus And Seneca a most eminent Philosopher in his Book De Cometis advertizeth us that we ought with great diligence seek for an assured knowledge whether it be Heaven or the Earth in which the Diurnal Conversion resides And for this cause it would probably be prudent and profitable counsel if besides the Articles which concern our Salvation and the establishment of our Faith against the stability of which there is no fear that any valid and solid Doctrine can ever rise up men would not aggregate and heap up more without necessity And if it be so it would certainly be a preposterous thing to introduce such Articles at the request of persons who besides that we know not that they speak by inspiration of Divine Grace we plainly see that there might be wished in them the understanding which would be necessary first to enable them to comprehend and then to discuss the Demonstrations wherewith the subtiler Sciences proceed in confirming such like Conclusions Nay more I should say were it lawful to speak my judgment freely on this Argument that it would haply more suit with the Decorum and Majesty of those Sacred Volumes if care were taken that every shallow and vulgar Writer might not authorize his Books which are not seldome grounded upon foolish fancies by inserting into them Places of Holy Scripture interpreted or rather distorted to Senses as remote from the right meaning of the said Scripture as they are neer to derirision who not without ostentation flourish out their Writings therewith Examples of such like abuses there might many be produced but for this time I will confine my self to two not much besides these matters of Astronomy One of which is that of those Pamphlets which were published against the Medicean Planets of which I had the fortune to make the discovery against the existence of which there were brought many places of Sacred Scripture Now that all the World seeth them to be Planets I would gladly hear with what new interpretations those very Antagonists do expound the Scripture and excuse their own simplicity The other example is of him who but very lately hath Printed against Astronomers and Philosophers that the Moon doth not receive its light from the Sun but is of its own nature resplendent which imagination he in the close confirmeth or to say better perswadeth himself that he confirmeth by sundry Texts of Scripture which he thinks cannot be reconciled unlesse his opinion should be true and necessary Neverthelesse the Moon of it self is Tenebrose and yet it is no lesse lucid than the Splendor of the Sun Hence it is manifest that these kinde of Authors in regard they did not dive into the true Sence of the Scriptures would in case their authority were of any great moment have imposed a necessity upon others to believe such Conclusions for true as were repugnant to manifest Reason and to Sense Which abuse Deus avertat that it do not gain Countenance and Authority for if it should it would in a short time be necessary to proscribe and inhibit all the Contemplative Sciences For being that by nature the number of such as are very unapt to understand perfectly both the Sacred Scriptures and the other Sciences is much greater than that of the skilfull and intelligent those of the first sort superficially running over the Scriptures would arrogate to themselves an Authority of decreeing upon all the Questions in Nature by vertue of some Word by them misunderstood and produced by the Sacred Pen-men to another purpose Nor would the small number of the Intelligent be able to repress the furious Torrent of those men who would finde so many the more followers in that the gaining the reputation of Wise men without pains or Study is far more grateful to humane Nature than the consuming our selves with restless contemplations about the most painfull Arts. Therefore we ought to return infinite thanks to Almighty God who of his Goodness freeth us from this fear in that he depriveth such kinde of persons of all Authority and reposeth the Consulting Resolving and Decreeing upon so important Determinations in the extraordinary Wisdom and Candor of most Sacred Fathers and in the Supream Authority of those who being guided by his Holy Spirit cannot but determin Holily So ordering things that of the levity of those other men there is no account made This kinde of men are those as I believe against whom not without Reason Grave and Holy Writers do so much
while to another and that there is a great difference between commanding a Methametitian or a Philosopher and the disposing of a Lawyer or a Merchant and that the demonstrated Conclusions touching the things of Nature and of the Heavens cannot be changed with the same facility as the Opinions are touching what is lawful or not in a Contract Bargain or Bill of Exchange This difference was well understood by the Learned and Holy Fathers as their having been at great pains to confute many Arguments or to say better many Philosophical Fallacies doth prove unto us and as may expresly be read in some of them and particularly we have in S. Augustine the following words This is to be held for an undoubted Truth That we may be confident that whatever the Sages of this World have demonstrated touching Natural Points is no waies contrary to our Bibles And in case they teach any thing in their Books that is contrary to the Holy Scriptures we may without any scruple conclude it to be most false And according to our ability let us make the same appear And let us so keep the Faith of our Lord in whom are hidden all the Treasures of Wisdom that we be neither seduced with the Loquacity of false Philosophy nor scared by the superstition of a counterfeit Religion From which words I conceive that I may collect this Doctrine namely That in the Books of the Wise of this World there are contained some Natural truths that are solidly demonstrated and others again that are barely taught and that as to the first sort it is the Office of wise Divines to shew that they are not contrary to the Sacred Scriptures As to the rest taught but not necessarily demonstrated if they shall contain any thing contrary to the Sacred Leaves it ought to be held undoubtedly false and such it ought by all possible waies to be demonstrated If therefore Natural Conclusions veritably demonstrated are not to be postposed to the Places of Scripture but that it ought to be shewn how those Places do not interfer with the said Conclusions then it s necessary before a Physical Proposition be condemned to shew that it is not necessarily demonstrated and this is to be done not by them who hold it to be true but by those who judge it to be false And this seemeth very reasonable and agreeable to Nature that is to say that they may much more easily find the fallacies in a Discourse who believe it to be false than those who account it true and concludent Nay in this particular it will come to passe that the followers of this opinion the more that they shall turn over Books examine the Arguments repeat the Observations and compare the Experiments the more shall they be confirmed in this belief And your Highness knoweth what happened to the late Mathematick Professor in the University of Pisa Who betook himself in his old age to look into the Doctrine of Copernicus with hope that he might be able solidly to confute it for that he held it so far to be false as that he had never studied it but it was his fortune that as soon as he had understood the grounds proceedings and demonstrations of Copernicus he found himself to be perswaded and of an opposer became his most confident Defender I might also nominate other Mathematicians who being moved by my last Discoveries have confessed it necessary to change the formerly received Constitution of the World it not being able by any means to subsist any longer If for the banishing this Opinion and Hypothesis out of the World it were enough to stop the mouth of one alone as it may be they perswade themselves who measuring others judgements by their own think it impossible that this Doctrine should be able to subsist and finde any followers this would be very easie to be done but the business standeth otherwise For to execute such a determination it would be necessary to prohibite not onely the Book of Copernicus and the Writings of the other Authors that follow the same opinion but to interdict the whole Science of Astronomy and which is more to forbid men looking towards Heaven that so they might not see Mars and Venus at one time neer to the Earth and at another farther off with such a difference that the latter is found to be fourty times and the former sixty times bigger in surface at one time than at another and to the end that the same Venus might not be discovered to be one while round and another while forked with most subtil hornes and many other sensible Observations which can never by any means be reconciled to the Ptolomaick Systeme but are unanswerable Arguments for the Copernican But the prohibiting of Copernicus his Book now that by many new Observations and by the application of many of the Learned to the reading of him his Hypothesis and Doctrine doth every day appear to be more true having admitted and tolerated it for so many years whilst he was lesse followed studied and confirmed would seem in my judgment an affront to Truth and a seeking the more to obscure and suppresse her the more she sheweth her self clear and perspicuous The abolishing and censuring not of the whole Book but onely so much of it as concerns this particular opinion of the Earths Mobility would if I mistake not be a greater detriment to souls it being an occasion of great scandal to see a Position proved and to see it afterwards made an Heresie to believe it The prohibiting of the whole Science what other would it be but an open contempt of an hundred Texts of the Holy Scriptures which teach us That the Glory and the Greatnesse of Almighty God is admirably discerned in all his Works and divinely read in the Open Book of Heaven Nor let any one think that the Lecture of the lofty conceits that are written in those Leaves finish in only beholding the Splendour of the Sun and of the Stars and their rising and setting which is the term to which the eyes of bruits and of the vulgar reach but there are couched in them mysteries so profound and conceipts so sublime that the vigils labours and studies of an hundred and an hundred acute Wits have not yet been able thorowly to dive into them after the continual disquisition of some thousands of years But let the Unlearned believe that like as that which their eyes discern in beholding the aspect of a humane body is very little in comparison of the stupendious Artifices which an exquisite and curious Anatomist or Philosopher finds in the same when he is searching for the use of so many Muscles Tendons Nerves and Bones and examining the Offices of the Heart and of the other principal Members seeking the seat of the vital Faculties noting and observing the admirable structures of the Instruments of the Senses and without ever making an end of satisfying his curiosity and wonder contemplating
ascribes to the Earth Ends and Foundations which yet it hath not to the Sea a Depth not to be fathomed to Death which is a Privation and consequently a Non-entity it appropriates Actions Motion Passions and other such like Accidents of all which it is deprived as also Epithites and Adjuncts which really cannot suit with it Is not the bitternesse of Death past 1 Sam. 15. 32. Let death come upon them Psal 6. He hath prepared the Instruments of Death Psal. 7. 14. Thou raisest me from the gates of Death Psal. 84. In the midst of the shadow of Death Psal. 23. Love is strong as Death Cant. 8. 9. The First-Born of Death Job 18. 13. Destruction and Death say c. Job 28. 22. And who knows not that the whole History of the rich Glutton doth consist of the like phrases of Vulgar Speech So Ecclesiasticus Chap. 27. vers 11. The godly man abideth in wisdome as the Sun but a fool changeth as the Moon and yet the Moon according to the real truth of the matter no wayes changeth but abides the same for ever as Astronomers demonstrate one half thereof remaining alwayes lucid and the other alwayes opacous Not at any time doth this state vary in it unlesse in respect of us and according to the opinion of the Vulgar Hence it is cleer that the holy Scripture speaks according to the common form of speech used amongst the unlearned and according to the appearance of things and not according to their true Existence In like manner Genes 1. in the description of the Creation of all things the Light is said to be made first of all and yet it followeth in the Text And the Evening and the Morning made the first day and a little after the several Acts of the Creation are distinguished and assigned to several days and concerning each of them it is said in the Text And the Evening and the Morning made the second day and then the third day the fourth day c. Hence many doubts arise all which I shall propound according to the common Systeme that it may appear even from the Hypothesis of that Systeme that the sacred Scripture sometimes for the avoyding of emergent difficulties is to be understood in a vulgar sense and meaning and in respect of us and not according to the nature of things Which distinction even Aristotle himself seemeth to have hinted when he saith * Some things are more intelligible to us others by nature or secundum se. First therefore If the light were made before heaven then it rolled about without heaven to the making of the distinction of Day and Night Now this is contrary to the very doctrine of these men who affirm that no Coelestial Body can be moved unlesse per accidens and by the motion of Heaven and as a knot in a board at the motion of the board Again if it be said that the Light was created at the same time with Heaven and began to be moved with Heaven another doubt ariseth that likewise opposeth the foresaid common Hypothesis For it being said that Day and Night Morning and Evening were made that same is either in respect of the Universe or onely in respect of the Earth and us If so be that the Sun turning round according to the Hypothesis of the Common Systeme doth not cause the Night and Day but only to opacous Bodies which are destitute of all other light but that of the Sun whilst in their half part which is their Hemisphaere and no more for that the Suns light passeth over but one half of an opacous Body unless a very small matter more in those of lesser bulk they are illuminated by the Suns aspect the other half remaining dark and tenebrose by reason of a shadow proceeding from its own Body Therefore the distinction of dayes by the light of heaven according to the description of them in the sacred Scriptures must not be understood absolutely and secundum se and Nature her self but in respect of the Earth and of us its inhabitants and consequently secundum nos 'T is not therefore new nor unusual in sacred Scripture to speak of things secundum nos and only in respect of us and secundum apparentiam but not secundum se and rei naturam or Absolutely and Simply And if any one would understand these Days of sacred Scripture not only secundum nos but also secundum naturam as circulations of Coelestial Light returning to the self same point from whence it did at first proceed so as that there needs no respect to be had to Night or to Darknesse for which sole reason we are fain to imbrace the Interpretation of sacred Scripture secundum nos In opposition to this we may thus argue If the sacred Scripture be understood to speak absolutely of iterated and successive circulations of light and not respectu nostri as if these words Evening and Morning had never been inserted which in their natural acceptation denote the Suns habitude to us and to the Earth For that the Morning is that time when the Sun begins to wax light and to rise above the Horizon in the East and become visible in our Hemisphaere and Evening is the time in which the Sun declines in the West and approacheth with its light neerer to the other opposite Horizon and Hemisphaere which is contiguous to this of ours But the word Day is a Co-relative to the word Night From hence therefore it evidently appeareth that these three words Evening Morning and Day cannot be understood of a Circulation of Light secundum se and absolutè but only secundum nos and respectu nostri and in that sense indeed the Morning and Evening do make the Night and Day In like manner Gen. 1. 16. it is said God made two great Lights the greater Light to rule the Day and the lesser Light to rule the Night and the Stars Where both in the Proposition and in the specification of it things are spoken which are very disagreeing with Coelestial Bodies Therefore those words are in that place to be interpreted according to the foresaid Rules namely according to the third and fourth so that they may be said to be understood according to the sense of the vulgar and the common way of speaking which is all one as if we should say secundum apparentiam and secundum nos vel respectu nostri For first it is said in the Proposition And God made two great Lights meaning by them the Sun and Moon whereas according to the truth of the matter these are not the Greater Lights For although the Sun may be reckoned amongst the Greater the Moon may not be so unless in respect of us Because amongst those that are absolutely the Greater and a little lesser than the Sun nay in a manner equal to it and far bigger than the Moon we may with great reason enumerate Saturn or some of the Fixed Stars of the first
Magnitude such as Canopus otherwise called Arcanar in the end of a River or the Little Dog in the mouth of the Great Dog or the Foot of Orion called Rigel or his Right shoulder or any other of that Magnitude Therefore the two great Lights are to be understood in respect of us and according to vulgar estimation and not according to the true and reall existence of such Bodies Secondly in the specification of the Proposition it is said The greater Light to rule the Day hereby denoting the Sun in which the verbal sense of Scripture agreeth with the Truth of the Thing For that the Sun is the Greatest of all Luminaries and Globes But that which followeth immediately after And the lesser Light to rule the Night meaning the Moon cannot be taken in the true and real sense of the words For the Moon is not the lesser Light but Mercury which is not only much lesser than the Moon but also than any other Star And if again it be said That the Holy Text doth not speak of the Stars but onely of the Luminaries for that presently after they are mentioned apart And the Stars and that what we say is true touching the comparison of the Stars amongst themselves but not in respect of the Luminaries namely the Sun and Moon This reply doth discover a man to be utterly ignorant in these Studies and such who having not the least smattering in them doth conceive an absurd and erroneous Opinion of the Coelestial Bodies For the Moon and Sun considered in themselves and as they appear to us if they should be a far greater distance from us than indeed they are would be no other nor would appear to us otherwise than Stars as the rest do in the Firmament But Great Luminaries they neither are nor seem to be save only in respect of us And so on the other side the Stars as to themselves are no other than so many Suns and so many Moons yet are so far remote from us that by reason of their distance they appear thus small and dim of light as we behold them For the greater and lesser distance of heavenly Bodies caeteris paribus doth augment and diminish their appearance both as to Magnitude and Light And therefore the words which follow in that place of Genesis And the Stars as distinguishing the Stars from the Sun and Moon are to be taken in no other acceptation than that which we have spoken of namely according to the sense of the Vulgar and the common manner of speech For indeed according to the truth of the matter all Coelestial Bodies being shining Globes are of a vast bigness to which if we should be so neer as we are to the Moon they would seem to us of as great yea a greater magnitude than the Moon As likewise on the contrary if we were as far distant from the Sun and Moon as we are from them both Moon and Sun would shew but as stars to us And yet the splendor of the Sun would doubtless be greater intensivè than that of any other star For although it should be granted that some stars as those of the Fixed that twinkle do shine of themselves aud by their own nature as the Sun that derives not its light from others which yet remains undecided and doubtful and borrow not their light from the Sun Nevertheless since the brightness of none of the stars may be compared with the Suns splendour which was created by God first and before all other Luminaries in the highest kind of Light it would therefore notwithstanding follow that none of those stars although placed in the same proximity to us with the Sun and therefore appearing to us of the same Magnitude as the Sun can bestow upon us so much Light as we receive from the Sun As on the contrary the Sun at the same remotenesse from us as they are would indeed as to its Magnitude appear to us as one of those stars but of a splendour much more intense than that of theirs So that now the Earth is nothing else but another Moon or star and so would it appear to us if we should behold it from a convenient distance on high And in it might be observed in that variety of Light and Darkness which the Sun produceth in it by making Day and Night the same difference of Aspects that are seen in the Moon and such as are observed in tricorporate Venus in like manner also 't is very probable that the same might be discerned in other Planets which shine by no light of their own but by one borrowed from the Sun What ever therefore may touching these matters be delivered in the sacred Leaves or the common speech of men dissenting from the real truth it ought as we have said before absolutely to be received and understood secundum vulgi sententiam communem loquendi concipiendi stylum And so to return to our purpose if all this considered the Pythagorian opinion be true it will be easie according to the same Rule to reconcile the authority of sacred Scriptures with it however they seem to oppose it and in particular those of the first and second Classis scilicet by my first Maxime For that in those places the holy Records speak according to our manner of understanding and according to that which appeareth in respect of us For thus it is with those Bodies in comparison of us and as they are described by the vulgar and commune way of humane Discourse So that the Earth appears as if it were standing still and immoveable and the Sun as if it were circumambient about her And so the Holy Scripture is used in the Commune and Vulgar way of speaking because in respect of our sight the Earth seems rather to stand fixed in the Centre and the Sun to circumvolve about it than otherwise as it happens to those that are putting off from the Banks of a River to whom the shore seems to move backwards and go from them but they do not perceive which yet is the truth that they themselves go forwards Which fallacy of our sight is noted and the Reason thereof assigned by the Opticks upon wich as being strange to and besides my purpose I will not stay and on this account is Aeneas brought in by Virgil saying Provehimur portu terraeque urbesque recedunt But it will not be amiss to consider why the sacred Scripture doth so studiously comply with the opinions of the Vulgar and why it doth not rather accurately instruct men in the truth of the matters and the secrets of Nature The Reason is first the benignity of Divine Wisdome whereby it sweetly accomodates it self to all things in proportion to their Capacity and Nature Whence in Natural Sciences it useth natural and necessary causes but in Liberal Arts it worketh liberally upon Generous Persons after a sublime and lofty manner upon the Common People familiarly and humbly upon the Skilful
Therefore neither the whole Earth nor the whole Water nor the whole Air can secundum totum be driuen or forced out of their proper place site or Systeme in the Universe in respect of the order and disposition of other mundane Bodies And thus there is no Star though Erratick Orb or Sphere that can desert its natural place although it may otherwise have some kind of motion Therefore all things how moveable soever are notwithstanding said to be stable and immoveable in their proper place according to the foresaid sense i.e. secundum totum For nothing hinders but that secundum partes they may some waymove which motion shall not be natural but violent Therefore the Earth although it should be moveable yet it might be said to be immoveable according to the precedent Maxime for that its neither moved in a right Motion nor out of the Course assigned it in its Creation for the standing Rule of its motion but keep within its own site being placed in that which is called the Grand Orb above Venus and beneath Mars and being in the middle betwixt these which according to the common opinion is the Suns place it equally and continually moveth about the Sun and the two other intermediate Planets namely Venus and Mercury and hath the Moon which is another Earth but Aetherial as Macrobius after some of the ancient Philosophers will have it about it self From whence inasmuch as she persisteth uniformly in her Course and never at any time departeth from it she may be said to be stable and immoveable and in the same sense Heaven likewise with all the Elements may be said to be immoveable The fifth Maxime followeth being little different from the former Amongst the things created by God some are of such a nature that their parts may be ab invicem or by turns separated from themselves and dis-joyned from their Whole others may not at least taken collectively now those are perishable but these perpetual The Earth therefore since it is reckoned amongst those things that are permanent as hath been said already hath its parts not dissipable nor ab invicem separable from its Centre whereby its true and proper place is assigned it and from its whole taken collectively because according to its whole it is always preserved compact united and cohaerent in it self nor can its parts be seperated from the Centre or from one another unless it may so fall out per accidens and violently in some of its parts which afterwards the obstacle being removed return to their Natural Station spontaneously and without any impulse In this Sense therefore the Earth is said to be Immoveable and Immutable yea even the Sea Aire Heaven and any other thing although otherwise moveable so long as its parts are not dissipable and seperable may be said to be Immoveable at last taken collectively This Principle or Maxim differeth from the precedent only in that this referrs to the parts in order to Place and this in order to the Whole From this Speculation another Secret is discovered For hence it is manifest wherein the proper and genuine formality of the Gravity aad Levity of Bodyes consisteth a point which is not so clearly held forth nor so undeniably explained by the Peripatetick Phylosophy Gravity therefore is nothing else according to the Principles of this new Opinion than a certain power and appetite of the Parts to rejoyn with their Whole and there to rest as in their proper place Which Faculty or Disposition is by Divine Providence bestowed not only on the Earth and Terrene Bodies but as is believed on Coelestial Bodies also namely the Sun Moon and Stars all whose parts are by this Impulsion connected and conserved together cleaving closely to each other and on all sides pressing towards their Centre until they come to rest there From which Concourse and Compression a Sphaerical and Orbicular Figure of the Caelestial Orbes is produced wherein by this occult Quality naturally incident to each of them they of themselves subsist and are alwayes preserved But Levity is the Extrusion and Exclusion of a more tenuose and thin Body from the Commerce of one more Solid and dense that is Heterogeneal to it by vertue of Heat Whereupon as the Motion of Grave Bodies is Compressive so the Motion of Light Bodies is Extensive For it s the propperty of Heat to dilate and rarify those things to which it doth apply conjoine and communicate it self And for this reason we find Levity and Gravity not only in respect of this our Terestrial Globe and the Bodies adjacent to it but also in respect of those Bodies which are said to be in the Heavens in which those parts which by reason of their proclivity make towards their Centre are Grave and those that incline to the Circumference Light And so in the Sun Moon and Starrs there are parts as well Grave as Light And consequently Heaven it self that so Noble Body and of a fifth Essence shall not be constituted of a Matter different from that of the Elements being free from all Mutation in it's Substance Quantity and Quality Nor so admirable and excellent as Aristotle would make us to believe nor yet a solid Body and impermeable and much lesse as the generality of men verily believe of an impenetrable and most obdurate Density but in it as this Opinion will have it Comets may be generated and the Sun it self as t is probable exhaling or attracting sundry vapours to the surface of its Body may perhaps produce those Spots which were observed to be so various and irregular in its Discus of which Galilaeus in a perticular Treatise hath most excellently and most accurately spoken insomuch that though it were not besides my present purpose yet it is convenient that I forbear to speak any thing touching those matters least I should seem to do that which he hath done before me But now if there be found in the Sacred Scriptures any Authority contrary to these things it may be salved by the foresaid Arguments Analogically applyed And furthermore it may be said that that Solidity is to be so understood as that it admits of no vacuum cleft or penetration from whence the least vacuity might proceed For the truth is as that cannot be admitted in bodily Creatures so it is likewise repugnant to Heaven it self being indeed a Body of its own Nature the most Rare of all others and tenuose beyond all Humane Conception and happly hath the same proportion to the Aire as the Aire to the Water It is clear also from these Principles how false these words of Aristotle are that Of one simple Body there is one simple Motion and this is of two kindes Right and Circular the Right is twofold from the medium and to the medium the first of Light Bodyes as the Aire and Fire the second of Grave Bodyes as the Water and Earth the Circular which is about the
those Channels for iustance which formerly were Navigable unto the very Walls of York and Salisbury c Our Ports are choaked and obstructed by Shelfes and Setlements Our Fenns do in a great part lie waste and unimproved Now all these may be and as I find by the Confession of some whose Practises upon the Copy of the First Book onely of our Authour hath got them both Money and Reputation in part have been remedied by the Ways and Means he here sets down The truth is the Argument hath been past over with an Vniversal Silence so that to this day I have not seen any thing that hath been written Demonstratively and with Mathematical Certainty concerning the same save onely what this Learned Prelate hath delivered of his Own Invention in these Treatises who yet hath so fully and plainly handled the Whole Doctrine that I may affirm his Work to be every way absolute It must be confest the Demonstration of the Second Proposition of the Second Book did not well please the Authour and had he lived he would have supplyed that defect but being prevented by Death the Reader must content himself with the Mechanical Proof that he giveth you of the truth of so Excellent a Conclusion § The other particular that I am to offer is that out of my desire to contribute what lyeth in me to the compleating of this Piece for English Practice I have exeeded my promise not onely in giving you the Second and following Books which were not extant at the time of tendring my Overtures but also in that I have added â— Map or Plat of all the Rivers Lakes Fenns c. mentioned thorow out the Work And if I have not kept touch in point of Time let it be considered that I am the Translator and not the Printer To conclude according to your acceptance of these my endeavours you may expect some other Tracts of no lesse Profit and Delight Farewell T. S. ERRATA of the second PART of the first TOME In PREFACE read Ferdinando II. ibid. l'Aqua PAGE 2. LINE 26 for must read much P. 3. l. 22 r. and let l. 25. r. water from l. 41. r. Tappe as every where else Page 4. l. 18. r cords Page 6. l. 9. r. acquire or Page 9. l. 1. r. irreperable P. 10. l. 13. r. dissimboguement For Page 17. r. P. 15. P. 15. l. 27 r. in l. 36 r. is as l. 38 r. Panaro P. 17. l. 12 Giulto l. 17. r. Measurers l. 25 r. measured it r. necessarily P. 23. l. 19. r. for help for Page 31. r. P. 32. P. 24. l. 14 r. to l. 17 r. namly of the. l. 23 r. easie P. 25. l. 38. r. Cock p. 29. l. 7. r. lasted p. 31. l. 32. r. Soâ— p. 41. l. 20. r. to the line p. 48. l. 19. r. us the * id Figure false p. 52. l. 30 and 31. for Theorem r. Proposition p. 53. l. 29. r. again p. 57. l. 19 r. same if l. 44. r. bodily p. 58. l. 9. r. gathering l. 40. omit p. 60. l. 2. omit if p. 65. l. 1. r. tide dele p. 66. l. 35. r. Stoppage of p. 68. l. 12 for Lords the r. Lords l. ult for they r. it p. 69. l. 14. r. to one id carried dele to p. 71. l. 20 r. and that l. 25 r. Braces it l. 29. r. Braces l. 44 r the Breâ—t p. 72. l. 23. r. Serene Highnesse p. 73. l. 24 r. deliberation l. 26 for summe r. Moddel l. 40. r. Months p. 79. l. 18. r. that into p. 82. l. 22. dele p. 85. l. 9 10. dele a free drame p. 88. l. 5. r. Palmes p. 89. l. 8. r. Princes p. 92. l. 3. r. Discourses p. 93. l. 31. r. Tautologie p. 94. l. 9. r. miracle p. 97. l. 13. r. weighty p. 101. l. 21. r. Marrara p. 107. l. 28 r. Patrimony l. 40 r. above p. 111. l. 16. r. said For p. 432. r. p. 114. p. 114. l. 35. r. of 200. l. 41. r. closed p. 115. l. 29. r. constant OF THE MENSURATION OF Running Waters LIB I. WHat and of how great moment the consideration of Motion is in natural things is so manifest that the Prince of Peripateticks pronounced that in his Schools now much used Sentence Ignorato motu ignoratur natura Thence it is that true Philosophers have so travailed in the contemplation of the Celestial motions and in the speculation of the motions of Animals that they have arrived to a wonderful height and sublimity of understanding Under the same Science of Motion is comprehended all that which is written by Mechanitians concerning Engines moving of themselves Machins moving by the force of Air and those which serve to move weights and immense magnitudes with small force There appertaineth to the Science of Motion all that which hath been written of the alteration not onely of Bodies but of our Minds also and in sum this ample matter of Motion is so extended and dilated that there are few things which fall under mans notice which are not conjoyned with Motion or at least depending thereupon or to the knowledge thereof directed and of almost every of them there hath been written and composed by sublime wits learned Treatises and Instructions And because that in the years past I had occasion by Order of our Lord Pope Vrban 8. to apply my thoughts to the motion of the Waters of Rivers a matter difficult most important and little handled by others having concerning the same observed some particulars not well observed or considered till now but of great moment both in publick and private affairs I have thought good to publish them to the end that ingenious spirits might have occasion to discusse more exactly then hitherto hath been done so necessary and profitable a matter and to supply also my defects in this short and difficult Tractate Difficult I say for the truth is these knowledges though of things next our senses are sometimes more abstruce and hidden then the knowledge of things more remote and much better and with greater exquisitness are known the motions of the Planets and Periods of the Stars than those of Rivers and Seas As that singular light of Philosophie of our times and my Master Signore Galileo Galilei wisely observeth in his Book concerning the Solar spots And to proceed with a due order in Sciences I will take some suppositions and cognitions sufficiently clear from which I will afterwards proceed to the deducing of the principal conclusions But to the end that what I have written at the end of this discourse in a demonstrative and Geometrical method may also be understood of those which never have applyed their thoughts to the study of Geometry I have endeavoured to explain my conceit by an example and with the consideration of the natural things themselves must after the same order in which I began to doubt in this matter and have placed this particular Treatise here in the beginning adverting nevertheless that
Ferara yet neverthelesse from this particular Doctrine well understood good judgement may be made of other the like cases in general I say then for greater perspecuity and better understanding of the whole That about thirteen miles above Ferara near to Stellata the main of Po branching it self into two parts with one of its Arms it cometh close to Ferara retaining the name of the Po of Ferara and here again it divideth it self into two other branches and that which continueth on the right hand is called the Po of Argenta and of Primaro and that on the left the Po of Volana But for that the bed of the Po of Ferara being heretofore augmented and raised it followeth that it resteth wholly deprived of the Water of the great Po except in the time of its greater swelling for in that case this Po of Ferara being restrained with a Bank near to Bondeno would come also in the overflowings of the main Po to be free from its Waters But the Lords of Ferara are wont at such time as the Po threateneth to break out to cut the bank by which cutting there disgorgeth such a Torrent of Water that it is observed that the main Po in the space of some few hours abateth near a foot and all persons that I have spoken with hitherto moved by this experiment think that it is of great profit and benefit to keep ready this Vent and to make use of it in the time of its fullnesse And indeed the thing considered simply and at the first appearance it seemeth that none can think otherwise the rather for that many examining the matter narrowly measure that body of Water which runneth by the Channel or Bed of the Po of Ferara and make account that the body of the Water of the great Po is diminished the quantity of the body of the Water which runneth by the Po of Ferara But if we well remember what hath been said in the beginning of the Treatise and how much the variety of the velocities of the said Water importeth and the knowledge of them is necessary to conclude the true quantity of the running Water we shall finde it manifest that the benefit of this Vent is far lesse than it is generally thought And mereover we shall finde if I deceive not my self that there follow from thence so many mischiefs that I could greatly incline to believe that it were more to the purpose wholly to stop it up than to maintain it open yet I am not so wedded to my opinion but that I am ready to change my judgement upon strength of better reasons especially of one that shall have first well understood the beginning of this my discourse which I frequently inculcate because it s absolutely impossible without this advertisement to treat of these matters and not commit very great errours I propose therefore to consideration that although it be true that whilst the water of the main Po is at its greatest height the Bank and Dam then cut of the Po of Ferara and the superior waters having a very great fall into the Channel of Ferara they precipitate into the same with great violence and velocity and with the same in the beginning or little lesse they run towards the Po of Volana and of Argenta on the sea coasts yet after the space of some few hours the Po of Ferara being full and the superior Waters not finding so great a diclivity there as they had at the beginning of the cutting they fall not into the same with the former velocity but with far lesse and thereby a great deal lesse Water begins to issue from the great Po and if we diligently compare the velocity at the first cutting with the velocity of the Water after the cutting made and when the Po of Ferara shall be full of Water we shall finde perhaps that to be fifteen or twenty times greater than this and consequently the Water which issues from the great Po that first impetuosity being past shall be onely the fifteenth or twentieth part of that which issued at the beginning and therefore the Waters of the main Po will return in a small time almost to the first height And here I will pray those who rest not wholly satisfied with what hath been said that for the love of truth and the common good they would please to make diligent observation whether in the time of great Floods the said Bank or Dam at Bondeno is cut and that in few hours the main Po diminisheth as hath been said about a foot in its height that they would observe I say whether a day or two being past the Waters of the main Po return almost to their first height for if this should follow it would be very clear that the benefit which resulteth from this diversion or Vent is not so great as is universally presumed I say it is not so great as is presumed because though it be granted for true that the Waters of the main Po abate at the beginning of the Vent yet this benefit happens to be but temporary and for a few hours If the rising of Po and the dangers of breaking forth were of short duration as it ordinarily befalleth in the overflowings of Torrents in such a case the profit of the Vent would be of some esteem But because the swellings of Po continue for thirty or sometimes for forty dayes therefore the gain which results from the Vent proveth to be inconsiderable It remaineth now to consider the notable harms which follow the said Sluice or Vent that so reflection being made and the profit and the detriment compared one may rightly judge and choose that which shall be most convenient The first prejudice therefore which ariseth from this Vent or Sluice is That the Channels of Ferara Primaro and Volana filling with Water all those parts from Bondeno to the Sea side are allarmed and endangered thereby Secondly The Waters of the Po of Primaro having free ingresse into the upper Valleys they fill them to the great damage of the Fields adjacent and obstruct the course of the ordinary Trenches in the same Valleys insomuch that all the care cost and labour about the draining and freeing the upper Valleys from Water would also become vain and ineffectual Thirdly I consider that these Waters of the Po of Ferara being passed downwards towards the Sea at the time that the main Po was in its greater excrescences and heights it is manifest by experience that when the great Po diminisheth then these Waters passed by the Po of Ferara begin to retard in their course and finally come to turn the current upwards towards Stellata resting first iu the intermediate time almost fixed and standing and therefore deposing the muddinesse they fill up the Channel of the River or Current of Ferara Fourthly and lastly There followeth from this same diversion another notable damage and it is like to that which followeth the breaches made by Rivers near to which breaches
no rise at all in the Water of Po For the truth is That letting Reno into Po there would alwaies be a rising but sometimes greater sometimes lesse as the Po shall have a swifter or slower Current so that if the Po shall be constituted in a great velocity the rise will be very small and if the said Po shall be slow in its course then the rise will be notable APPENDIX V. ANd here it will not be besides the purpose to advertise That the measures partments and distributions of the Waters of Fountains cannot be made exactly unless there be considered besides the measure the velocity also of the Water which particular not being thorowly observed is the cause of continual miscariages in such like affairs APPENDIX VI. LIke consideration ought to be had with the greater diligence for that an errour therein is more prejudicial I say ought to be had by those which part and divide VVaters for the watering of fields as is done in the Territories of Brescia Bergama Crema Pavia Lodigiano Cremona and other places For if they have not regard to the most important point of the variation of the velocity of the VVater but onely to the bare Vulgar measure there will alwaies very great disorders and prejudices ensue to the persons concerned APPENDIX VII IT seemeth that one may observe that whilst the Water runneth along a Channel Current or Conduit its velocity is retarded withheld and impeded by its touching the Bank or side of the said Channel or Current which as immoveable not following the motion of the VVater interrupteth its velocity From which particular being true as I believe it to be most true and from our considerations we have an occasion of discovering a very nice mistake into which those commonly fall who divide the VVaters of Fountains VVhich division is wont to be by what I have seen here in Rome performed two wayes The first of which is with the measures of like figures as Circles or Squares having cut through a Plate of metal several Circles or Squares one of half an inch another of one inch another of two of three of four c. with which they afterwards adjust the Cocks to dispence the VVaters The other manner of dividing the VVaters of Fountains is with rectangle paralellograms of the same height but of different Bases in such sort likewise that one paralellogram be of half an inch another of one two three c. In which manner of measuring and dividing the Water it should seem that the Cocks being placed in one and the same plain equidistant from the level or superior superficies of the water of the Well and the said measures being most exactly made the VVater ought consequently also to be equally divided and parted according to the proportion of the measures But if we well consider every particular we shall finde that the Cocks as they successively are greater discharge alwaies more VVater than the just quantity in comparison of the lesser that is to speak more properly The VVater which passeth through the greater Cock hath alwaies a greater proportion to that which passeth through the lesser than the greater Cock hath to the lesser All which I will declare by an example The like errour occurreth also in the other manner of measuring the VVater of a Fountain as may easily be collected from what hath been said and observed above APPENDIX VIII THe same contemplation discovereth the errour of those Architects who being to erect a Bridge of sundry Arches over a River consider the ordinary breadth of the River which being v. g. fourty fathom and the Bridge being to consist of four Arches it sufficeth them that the breadth of all the four Arches taken together be fourty fathom not considering that in the ordinary Channel of the River the Water hath onely two impediments which retard its velocity namely the touching and gliding along the two sides or shores of the River but the same water in passing under the Bridge in our case meeteth with eight of the same impediments bearing and thrusting upon two sides of each Arch to omit the impediment of the bottom for that it is the same in the River and under the Bridge from which inadvertency sometimes follow very great disorders as quotidian practice shews us APPENDIX IX IT is also worthy to consider the great and admirable benefit that those fields receive which are wont to drink up the Rain-water with difficulty through the height of the water in the principal Ditches in which case the careful Husbandman cutteth away the reeds and rushes in the Ditches through which the waters pass whereupon may be presently seen so soon as the reeds and rushes are cut a notable Ebb in the level of the water in the Ditches insomuch that sometimes it is observed that the water is abated after the said cutting a third and more of what it was before the cutting The which effect seemingly might depend on this That before those weeds took up room in the Ditch and for that cause the water kept a higher level and the said Plants being afterwards cut and removed the water came to abate possessing the place that before was occupied by the weeds Which opinion though probable and at first sight satisfactory is nevertheless insufficient to give the total reason of that notable abatement which hath been spoken of But it is necessary to have recourse to our consideration of the velocity in the course of the water the chiefest and true cause of the variation of the measure of the same Running-Waterâ— for that multitudes of reeds weeds and plants dispersed through the current of the Ditch do chance notably to retard the course of the water and therefore the measure of the water increaseth and those impediments removed the same water gaineth velocity and therefore decreaseth in measure and consequently in height And perhaps this point well understood may be of great profit to the fields adjacent to the Pontine Fens and I doubt not but if the River Ninfa and the other principal Brooks of those Territories were kept well cleansed from weeds their waters would be at a lower level and consequently the drains of the fields would run into them more readily it being alwayes to be held for undoubted that the measure of the water before the cleansing hath the same proportion to the measure after cleansing that the velocity after the cleansing hath to the velocity before the cleansing And be cause those weeds being cleansed away the course ef the water notably increaseth it is therefore necessary that the said water abate in measure and become lower APPENDIX X. WE having above observed some errors that are committed in distributing the waters of Fountains and those that serve to water fields it seemeth now fit by way of a close to this discourse to advertise by what means these divisions may be made justly and without error I therefore think that one might two several wayes exquisitly divide
things being pre-supposed we will lay down some familiar Problems from which we shall pass to the Notions and questions more subtil and curious which will also prove profitable and not to be sleighted in this business of Waters PROPOSITION I. PROBLEME I. A Chanel of Running-Water being given the breadth of which passing through a Regulator is three Palms and the height one Palm little more or less to measure what water passeth through the Regulator in a time given FIrst we are to dam up the Chanel so that there pass not any water below the Dam then we must place in the side of the Chanel in the parts above the Regulator three or four or five Bent-pipes or Syphons according to the quantity of the water that runneth along the Chanel in such sort as that they may drink up or draw out of the Chanel all the water that the Chanel beareth and then shall we know that the Syphons drink up all the water when we see that the water at the Dam doth neither rise higher nor abate but alwaies keepeth in the same Level These things being prepared taking the Instrument to measure the time we will examine the quantity of the water that issueth by one of those Syphons in the space of twenty vibrations and the like will we do one by one with the other Syphons and then collecting the whole summe we will say that so much is the water that passeth and runneth thorow the Regulator or Chanel the Dam being taken away in the space of twenty second minutes of an hour and calculating we may easily reduce it to hours dayes months and years And it hath fallen to my turn to measure this way the waters of Mills and Fountains and I have been well assured of its exactness by often repeating the same work CONSIDERATION ANd this method must be made use of in measuring the waters that we are to bring into Conducts and carry into Cities and Castles for Fountains and that we may be able afterwards to divide and share them to particular persons justly which will prevent infinite suits and controversies that every day happen in these matters PROPOSITION II. THEOREM I. If a River moving with such a certain velocitie through its Regulator shall have a given quick height and afterwards by new water shall increase to be double it shall also increase double in velocitie LEt the quick height of a River in the Regulator ABCD be the perpendicular FB and afterwards by new water that is added to the River let the water be supposed to be raised to G so that GB may be double to EB I say that all the water GC shall be double in velocity to that of EC For the water GF having for its bed the bottom EF equally inclined as the bed BC and its quick height GE being equal to the quick height EC and having the same breadth BC it shall have of it self a velocity equal to the velocity of the first water FC but because besides its own motion which is imparted to it by the motion of the water EC it hath also over and above its own motion the motion of EC And because the two waters GC and EC are alike in velocity by the third Supposition therefore the whole water GC shall be double in velocity to the water EC which was that which we were to demonstrate This demonstration is not here inserted as perfect the Authour having by several letters to his friends confessed himself unsatisfied therewith and that he intended not to publish the Theorem without a more solid demonstration which he was in hope to light upon But being overtaken by Death he could not give the finishing touch either to this or to the rest of the second Book In consideration of which it seemed good to the Publisher of the same rather to omit it than to do any thing contrary to the mind of the Authour And this he hints by way of advertisement to those that have Manuscript Copies of this Book with the said demonstration For this time let the Reader content himself with the knowledge of so ingenious and profitable a Conclusion of the truth of which he may with small expence and much pleasure be assured by means of the experiment to be made in the same manner with that which is laid down in the second Corollary of the fourth Theorem of this with its Table and the use thereof annexed COROLLARIE HEnce it followeth that when a River increaseth in quick height by the addition of new water it also increaseth in velocity so that the velocity hath the same proportion to the velocity that the quick height hath to the quick height as may be demonstrated in the same manner PROPOS III. PROBLEME II. A Chanel of Water being given whose breadth exceeds not twenty Palms or thereabouts and whose quick height is less than five Palms to measure the quantity of the Water that runneth thorow the Chanel in a time given PLace in the Chanel a Regulator and observe the quick height in the said Regulator then let the water be turned away from the Chanel by a Chanellet of three or four Palms in breadth or thereabouts And that being done measure the quantity of the water which passeth thorow the said Chanellet as hath been taught in the second Proposition and at the same time observe exactly how much the quick height shall be abated in the greater Chanel by means of the diversion of the Chanellet and all these particulars being performed multiply the quick height of the greater Chanel into it self and likewise multiply into it self the lesser height of the said bigger Chanel and the lesser square being taken from the greater the remainder shall have the same proportion to the whole greater square as the water of the Chanellet diverted hath to the water of the bigger Chanel And because the water of the Chanellet is known by the Method said down in the first Theorem and the terms of the Theorem being also known the quantity of the water which runneth thorow the bigger Chanel shall be also known by the Golden Rule which was that that was desired to be known We will explain the whole business by an example Let a Chanel be for example 15 Palms broad its quick height before its diversion by the Chanellet shall be supposed to be 24 inches but after the diversion let the quick height of the Chanel be onely 22 inches Therefore the greater height to the lesser is as the number 11. to 12. But the square of 11. is 121 and the square of 12. is 144 the difference between the said lesser square and the greater is 23. Therefore the diverted water is to the whole water as 23. to 144 which is well near as 1 to 6â— and that is the proportion that the quantity of the water which runneth through the Chanellet shall have to all the water that runneth thorow the great Chanel Now if we should finde by
in equal times but that one of them should be four times more swift than the other the more slow should of necessity be four times more large And because the same River in any part thereof alwaies dischargeth the same quantity of Water in equal times as is demonstrated in the first Proposition of the first Book of the measure of Running Waters but yet doth not run thorowout with the same velocity Hence it is that the vulgar measures of the said River in divers parts of its Chanel are alwaies divers insomuch that if a River passing through its chanel had such velocity that it ran 100 Braces in the 1 1 60 of an hour-and afterwards the said River should be reduced to so much tardity of motion as that in the same time it should not run more than one Brace it would be necessary that that same River should become 100. times bigger in that place where it was retarded I mean 100. times bigger than it was in the place where it was swifter And let it be kept well in mind that this point rightly understood will clear the understanding to discover very many accidents worthy to be known But for this time let it suffice that we have onely declared that which makes for our purpose referring apprehensive and studious Wits to the perusal of my aforenamed Treatise for therein he shall finde profit and delight both together Now applying all to our principal intent I say That by what hath been declared it is manifest that if the Brent were 40. Braces broad and 2 1 2 high in some one part of its Chanel that afterwards the same Water of the Brent falling into the Lake and passing thorow the same to the Sea it should lose so much of its velocity that it should run but one Brace in the time wherein whilst it was in its Chanel at the place aforesaid it ran 100. Braces It would be absolutely necessary that increasing in measure it should become an hundred times thicker and therefore if we should suppose that the Lake were 20000. Braces the Brent that already hath been supposed in its Chanel 100. Braces being brought into the Lake should be 100. times 100. Brates that is shall be 10000. Braces in thickness and consequently shall be in height half a Brace that is 100 200 of a Brace and not 1â—â— 200 of a Brace as was concluded in the Argument Now one may see into what a gross errour of 99. in 100. one may fall through the not well understanding the true quantity of Running Water which being well understood doth open a direct way to our judging aright in this most considerable affair And therefore admitting that wich hath been demonstrated I say that I would if it did concern me greatly encline to consult upon the returning of the Brent again into the Lake For it being most evident that the Brent in the Chanel of its mouth is much swifter than the Brent being brought into the Lake it will certainly follow thereupon that the thickness of the Water of Brent in the Lake shall be so much greater than that of Brent in Brent by how much the Bront in Brent is swifter than thh Brent in the Lake 1. From which operation doth follow in the first place that the Lake being filled and increased by these Waters shall be more Navigable and passible than at present we see it to be 2. By the current of these Waters the Chanels will be scoured and will be kept clean from time to time 3. There will not appear at the times of low-waters so many Shelves and such heaps of Mud as do now appear 4. The Ayr will become more wholesom for that it shall not be so infected by putrid vapours exhaled by the Sun so long as the Miery Ouze shall be covered by the Waters 5. Lastly in the current of these advantagious Waters which must issue out of the Lake into the Sea besides those of the Tyde the Ports will be kept scoured and clear And this is as much as I shall offer for the present touching this weighty buisiness alwaies submitting my self to sounder judgements Of the above-said Writing I presented a Copy at Venice at a full Colledge in which I read it all and it was hearkned to with very great attention and at last I presented it to the Duke and left some Copies thereof with sundry Senators and went my way promising with all intenseness to apply my pains with reiterated studies in the publick service and if any other things should come into my minde I promised to declare them sincerely and so took leave of His serenity and that Noble Council When I was returned to Rome this business night and day continually running in my mind I hapned to think of another admirable and most important conceit which with effectual reasons confirmed by exact operations I with the Divine assistance made clear and manifest and though the thing at first sight seemed to me a most extravagant Paradox yet notwithstanding having satisfied my self of the whole business I sent it in writing to the most Illustrious and most Noble Signore Gio. Basadonna who after he had well considered my Paper carried it to the Council and after that those Lords had for many months maturely considered thereon they in the end resolved to suspend the execution of the diversion which they had before consulted to make of the River Sile and of four other Rivers which also fall into the Lake a thing by me blamed in this second Paper as most prejudicial and harmful The writing spake as followeth CONSIDERATIONS Concerning the LAKE OF VENICE CONSIDERATION II. IF the discoursing well about the truth of things Most Serene Prince were as the carrying of Burdens in which we see that an hundred Horses carry a greater weight than one Horse onely it would seem that one might make more account of the opinion of many men than of one alone But because that discoursing more resembleth running than carrying Burdens in which we see that one Barb alone runneth faster than an hundred heavy-heel'd Jades therefore I have ever more esteemed one Conclusion well managed and well considered by one understanding man although alone than the common and Vulgar opinions especially when they concern abstruce and arduous points Nay in such cases the opinions moulded and framed by the most ignorant and stupid Vulgar have been ever suspected by me as false for that it would be a great wonder if in difficult matters a common capacity should hit upon that which is handsom good and true Hence I have and do hold in very great veneration the summe of the Government of the most Serene and eternal Republick of Venice which although as being in nature a Common-wealth it ought to be governed by the greater part yet nevertheless in arduous affairs it is alwaies directed by the Grave Judgement of few and not judged blindly by the Plebeian Rout. T is true that he that propoundeth
by the addition of new Water to that which it dischargeth after the encrease is made Proposition IV. Theor. II. 54 Proportion of a River when highâ—â— to it self when low Coroll I. 55 Q Quantity of Running Waters is never certain if with the Vulgar way of Measuring them their Velocities be not considered 32 Quantities of Waters which are discharged by a River answer in equality to the Velocities and times in which they are discharged Axiome I II III. 38 Quick-Height of a River what it is Definition V. 48 R Reason of the Proverb Take heed of the still Waters Coroll VI. 7 Reasons of Monsignore Corsini against the diversion of Reno into the Po of Volano 105 Reasons of Cardinal Capponi and Monsig Corsini for the turning of Reno into Main Po. 106 Two objections on the contrary and answers to them 104 105 What ought to be the proportion of the Heights of Reno in Reno and of Reno in Po. 110 Regulator what it is Definition IV. 48 Relation of the Waters of Bologna and Ferrara by Monsignore Corsini 100 Reno in the Valleys and its bad effects 100 101 Two wayes to divert it 103 The facility and utility of those wayes Ibid. The difficulties objected 104 Reply to Bartolotti touching the dangers of turning Eiume Morto into Serchio 83 Retardment of the course of a River caused by its Banks Appendix VII 19 Risings made by Flood-Gates but small Appendix XIII 26 Rivers that are shallow swell much upon small showers such as are deep rise but little upon great Floods Corollary III. 6 Rivers the higher they are the swifter Ibid. Rivers the higher they are the lesse they encrease upon Floods 49 Rivers when they are to have equal and when like Velocity Ibid. Rivers in falling into the Sea form a Shelf of Sand called Cavallo 65 Five Rivers to be diverted from the Lake of Venice and the inconveniences that would ensue thereupon 74 75 A River of Quick-height and Velocity in its Regulator being given if the Height be redoubled by new Water it redoubleth also in Velocity Proposition II. Theorem I. 51 Keepeth the proportion of the heights to the Velocities Corollary 52 S Sand and Mud that entereth into the Lake of Venice and the way to examine it 76 Seas agitated and driven by the Winds stop up the Ports 64 65 Sections of a River what they are Definition I. 37 Sections equally swift what they are Definition II. Ibid. Sections of a River being given to conceive others equal to them of different breadth height and Velocity Petition 38 Sections of the same River and their Proportions to their Velocities Coroll I. 42 Sections of a River discharge in any whatsoever place of the said River equal quantities of Water in equal times Proposition I. 39 Sile River what mischiefes it threatneth diverted from the Lake 74 Spirtings of Waters grow bigger the higher they go Coroll XVI 16 Streams of Rivers how they encrease and vary Coroll I. 6 Streams retarded and the effects thereof Coroll IX 8 T Table of the Heights Additions and Quantities of Waters and its use 56 Thrasimenus Vide Lake Time how it s measured in these Operations of the Waters 49 Torrents encrease at the encreasing of a River though they carry no more Water than before Coroll IV. 6 Torrents when they depose and carry away the Sand. Coroll V. 7 Torrents and their effects in a River 6 7 Torrents that fall into the Valleys or into Po of Valano and their mischiefs prevented by the diverting of Reno into Main Po. 100 Tyber and the causes of its inundations Coroll VIII 8 V Valleys of Bologna and Ferrara their inundations and disorders whence they proceed 97 Velocity of the Water shewn by several Examples 3 Its proportion to the Measure 5 Velocities equal what they are 47 Velocities like what they are 47 48 Velocities of Water known how they help us in finding the Lengths 113 A Fable to explain the truth thereof Ibid. Venice Vide Lake Vse of the Regulator in measuring great Rivers Consideration I. 60 W Waters falling why they disgross Coroll XVI 16 Waters how the Length of them is Measured 70 Waters that are imployed to flow Grounds how they are to be distributed 19 53 54 Waters to be carryed in Pipes to serve Aquaducts and Conduits how they are to be Measured 15 116 Way to know the rising of Lakes by Raines 28 Way of the Vulgar to Measure the VVaters of Rivers 68 Wind Gun and Portable Fountain of Vincenzo Vincenti of Urbin 11 Windes contrary retard and make Rivers encrease Coroll VII 8 The END of the TABLE of the Second Part of the First TOME Copernicus reputeth the Earth a Globe like to a Planet Coelestial substances that are in alterable and Elementary that be alterable art necessary in the opinion of Aristotle Aristotle maketh the World perfect because it hath the threefold demension Aristotles demonstrations to prove the dimensions to be three and no more The number three celebrated amongst the Pythagorians Omne Totum Perfectum Or Solid Plato held that humane understanding partook of divinity because it understood numbers The Mystery of Pythagorick numbers fabulous De Papyrio pâ—aetextato Gellius 1. 2. 3. A Geometrical demonstration of the triple dimension In physical proofs â—eâ—metrical exactness is not necessary Parts of the world are two according to Aristotle Coelestial and Elementary contrary to one another Local motion of three kinds right circular mixt Circular and streight motions are simple as proceeding by simple lines Ad medium à 〈◊〉 circa medium The definition of Nature either imperfect or unseasonable produced by Aristotle The Helix about the Cylinder may be said to be a simple line Aristotle accommodates the rules of Architecture to the frame of the World and not the frame to the rules Right motion sometimes simple and sometimes mixt according to Arist. The circular line perfect according to Aristotle and but the right imperfect and why The world is supposed by the Author to be perfectly ordinate Streight motion impossible in the world exactly ordinate Right motion nature infinite Motion by a right line naturally impossible Nature attempts not things impossible to be effected Right motion might perhaps be in thâ— first Chaos Right motion is commodious to range in order things out of order Mundane bodies moved in the beginning in a right line and afterwards circularly according to Plato * Thus doth he coverâ—ly and modestly stile himselfe throughout this work A moveable being in a state of rest shall not move unless it have an inclination to some particular place The moveable accelerates its motion going towards the place whither it hath an inclination The moveable passing from rest goeth thorow all the degrees of tardity Rest the infinite degree of tardity The moveable doth not accelerate save only as it approacheth nearer to us term Nature to introduce in the moveable a certain degree of velocity made it move in a right line Vniform