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
shall forbear to exasperate and attempt to reconcile such persons to this Hypothesis as devout esteem for Holy Scripture and dutifull Respect to Canonical Injunctions hath made to stand off from this Opinion and therefore for their sakes I have at the end of the Dialogues by way of supplement added an Epistle of Galileo to Her Most Serene Highness Christina Lotharinga the Grand Dutchesse Mother of Tuscany as also certain Abstracts of John Kepler Mathematician to two Emperours and Didacus à Stunica a famous Divine of Salamanca with an Epistle of Paulo Antonio Foscarini a learned Carmelite of Naples that shew the Authority of Sacred Scripture in determining of Philosophical and Natural Controversies hoping that the ingenious impartial Reader will meet with full satisfaction in the same And least what I have spoken of the prohibiting of these Pieces by the Inquisition may deterre any scrupulous person from reading of them I have purposely inserted the Imprimatur by which that Office licenced them And for a larger account of the Book or Author I refer you to the Relation of his Life which shall bring up the Reare in the Second Tome What remains of this is that Excellent Discourse of D. Benedetto Castelli Abbate di San Benedetto Aloysio concerning the Mensuration of Running Waters with other Treatises of that Learned Prelate of the Superintendent Corsini Some may alledge and I doe confess that I promised to publish the Life of Galileo in this place But the great miscarriages of Letters from some Friends in Italy and else where to whom I am a Debtor for several Remarques from whom I daily expect yet greater Helps concerning the History of that famous Personage these disappointments I say joyned with the undeniable Request of some Friends who were impatient to see Castelli in English together with a consideration of the disproportionate Bulk that would otherwise have bin betwixt the two Volumes perswaded me to this exchange This deviation from my Promise I hope is Venial and for the expiating of it I plead Supererrogation having in each Tome made so large Aditions though to my great expense that they make neer a third part more than I stood by promise bound to Publish That this is so will appear by comparing the Contents I here prefix with the Advertisment I formerly Printed For not to mention those Epitomes of Kepler and à Stunica the whole second and following Books of Castelli were not come to my hands at the time of my penning that Paper yet knowing how imperfect the Volume would be without them they being partly a supplement to the Theoremes and Problemes which the Abbot had formerly Printed and partly experiments that had procured him and his Doctrine a very great Reputation knowing this I say I apprehended a necessity of publishing them with the rest and hope that if you think not the service I have done therein worth your acknowledgement you will yet at least account the encrease of my expence a sufficient extenuation of the Trespass that those Additions have forced me to commit upon your Patience in point of Time As for the second Tome I have only this to assure the Generous Readers 1 that I am very confident I shall be much more punctual in publishing that than for the reasons above related I was able to be in setting forth this 2 that they shall not be abused in advancing of their moneys as hath bin used in the like case by selling the remaining Copyes at an under rate and 3 that I have a very great care that no disesteem may by my means arise unto this way of publishing Books for that it is of excellent use in ushering Great and Costly Volumes into the World To say nothing of the disadvantages of Translations in general this of mine doubtless is not without it's Errours and oversights but those of the Printer discounted I hope the rest may be allowed me upon the score of Human Imbecilitie The truth is I have assumed the Liberty to note the Mistakes in the Florid Version of Berneggerus in the Margent not so much to reproach him as to convince those who told me that they accounted my pains needless having his Latine Translation by them The like they said of the whole two Tomes but they thereby caused me to question their Understanding or Veracity For some of the Books were yet never extant As for instance the Mechanicks of Monsieur Des Cartes a Manuscript which I found amongst the many other Rarities that enrich the well-chosen Library of my Learned and Worthy Friend Dr. Charles Scarburgh the Experiments of Gravity and the Life of Galileo both my own Others were included in Volumes of great price or so dispersed that they were not to be purchased for any money as those of Kepler à Stunica Archimedes Tartaglia and the Mechanicks of Galileo And the remainder though easyer to procure were harder to be understood as Tartaglia his notes on Archimedes Torricellio his Doctrine of Projects Galileo his Epistle to the Dutchesse of Tuscany and above all his Dialogues de Motu never till now done into any Language which were so intermixt of Latine and Italian that the difficulty of the Stile joyned with the intricatnesse of the Subject rendered them Unpleasant if not wholly Vnintelligible to such as were not absolute Masters of both the Tongues To conclude according to the entertainment that you please to afford these Collections I shall be encouraged to proceed with the Publication of a large Body of Hydrography declaring the History Art Lawes and Apendages of that Princely Study of Navigation wherein I have omitted nothing of note that can be found either in Dudley Fournier Aurigarius Nonius Snellus Marsennus Baysius Morisetus Blondus Wagoner abroad or learnt amongst our Mariners at home touching the Office of an Admiral Commander Pilot Modellist Shipwright Gunner c. But order requiring that I should discharge my first Obligation before I contract a second I shall detein you no longer in the Portall but put you into possession of the Premises Novemb. 20. 1661. T. S. THE AUTHOR'S INTRODUCTION Judicious Reader THere was published some years since in Rome a salutiferous Edict that for the obviating of the dangerous Scandals of the present Age imposed a seasonable Silence upon the Pythagorean Opinion of the Mobility of the Earth There want not such as unadvisedly affirm that that Decree was not the production of a sober Scrutiny but of an illinformed Passion one may hear some mutter that Consultors altogether ignorant of Astronomical Observations ought not to clipp the Wings of Speculative Wits with rash Prohibitions My zeale cannot keep silence when I hear these inconsiderate complaints I thought fit as being thoroughly acquainted with that prudent Determination to appear openly upon the Theatre of the World as a Witness of the naked Truth I was at that time in Rome and had not only the audiences but applauds of the most Eminent Prelates of
by SIGNORE BARTOLOTTI in that affair of the DIVERSION of FIUME MORTO IX HIS CONSIDERATION upon the DRAINING of the PONTINE FENNS in CALABRIA X. HIS CONSIDERATION upon the DRAINING of the TERRITORIES of BOLOGNA FERRARA and ROMAGNA XI HIS LETTER to D. FERRANTE CESARINI applying his DOCTRINE to the MENSURATION of the LENGTH and DISTRIBUTION of the QUANTITY of the WATERS of RIVERS SPRINGS AQUEDUCTS c. XII D. CORSINUS SUPERINTENDENT of the GENERAL DRAINS and PRESIDENT of ROMAGNA his RELATION of the state of the VVATERS in the TERRITORIES of BOLOGNA and FERRARA A Table of the most observable Persons and Matters mentioned in the Second Part. The CONTENTS of the SECOND TOME PART THE FIRST Treatise I. GALILEUS GALILEUS his MATHEMATICAL DISCOURSES and DEMONSTRATIOMS touching two NEVV SCIENCES pertaining to the MECHANICKS and LOCAL MOTION with an APPENDIX of the CENTRE of GRAVITY of some SOLIDS in Four DIALOGUES II. HIS MECHANICKS a New PEICE III. RHENATUS DES CARTES his MECHANICKS translated from his FRENCH MANUSCRIPT a New PEICE IV. ARCHIMEDES his Tract DE INSIDENTIBUS HUMIDO with the NOTES and DEMONSTRASIONS of NICOLAUS TARTALEUS in Two BOOKS V. GALILEUS his DISCOURSE of the things that move in or upon the WATER VI. NICOLAUS TARTALEUS his INVENTIONS for DIVING UNDER WATER RAISING OF SHIPS SUNK c. in Two BOOKS PART THE SECOND I. EVANGELISTA TORRICELLIUS his DOCTRINE OF PROJECTS and TABLES of the RANGES of GREAT GUNNS of all sorts wherein he detects sundry ERRORS in GUNNERY An EPITOME II. T. S. his EXPERIMENTS of the COMPARATIVE GRAVITY OF BODIES in the AIRE and WATER III. GALILEUS GALILEUS his LIFE in Five BOOKS BOOK I. Containing Five Chapters Chap. 1. His Country 2. His Parents and Extraction 3. His time of Birth 4. His first Education 5. His Masters II. Containing Three Chapters Chap. 1. His judgment in several Learnings 2. His Opinions and Doctrine 3. His Auditors and Scholars III. Containing Four Chapters Chap. 1. His behaviour in Civil Affairs 2. His manner of Living 3. His morall Virtues 4. His misfortunes and troubles IV. Containing Four Chapters Chap. 1. His person described 2. His Will and Death 3. His Inventions 4. His Writings 5. His Dialogues of the Systeme in particular containing Nine Sections Section 1. Of Astronomy in General its Definition Praise Original 2. Of Astronomers a Chronological Catalogue of the most famous of them 3. Of the Doctrine of the Earths Mobility c. its Antiquity and Progresse from Pythagoras to the time of Copernicus 4. Of the Followers of Copernicus unto the time of Galileus 5. Of the severall Systemes amongst Astronomers 6. Of the Allegations against the Copern Systeme in 77 Arguments taken out of Ricciolo with Answers to them 7. Of the Allegations for the Copern Systeme in 50 Arguments 8. Of the Scriptures Authorities produced against and for the Earths mobility 9. The Conclusion of the whole Chapter V. Containing Four Chapters Chap. 1. His Patrons Friends and Emulators 2. Authors judgments of him 3. Authors that have writ for or against him 4. A Conclusion in certain Reflections upon his whole Life A Table of the whole Second TOME GALILAEUS Galilaeus Lyncaeus HIS SYSTEME OF THE WORLD The First Dialogue INTERLOCVTORS SALVIATUS SAGREDUS and SIMPLICIUS SALVIATUS IT was our yesterdayes resolution and agreement that we should to day discourse the most distinctly and particularly we could possible of the natural reasons and their efficacy that have been hitherto alledged on the one or other part by the maintainers of the Positions Aristotelian and Ptolomaique and by the followers of the Copernican Systeme And because Copernicus placing the Earth among the moveable Bodies of Heaven comes to constitute a Globe for the fame like to a Planet it would be good that we began our disputation with the examination of what and how great the energy of the Peripateticks arguments is when they demonstrate that this Hypothesis is impossible Since that it is necessary to introduce in Nature substances different betwixt themselves that is the Coelestial and Elementary that impassible and immortal this alterable and corruptible Which argument Aristotle handleth in his book De Coelo insinuating it first by some discourses dependent on certain general assumptions and afterwards confirming it with experiments and perticular demonstrations following the same method I will propound and freely speak my judgement submitting my self to your censure and particularly to Simplicius a Stout Champion and contender for the Aristotelian Doctrine And the first Step of the Peripatetick arguments is that where Aristotle proveth the integrity and perfection of the World telling us that it is not a simple line nor a bare superficies but a body adorned with Longitude Latitude and Profundity and because there are no more dimensions but these three The World having them hath all and having all is to be concluded perfect And again that by simple length that magnitude is constituted which is called a Line to which adding breadth there is framed the Superficies and yet further adding the altitude or profoundity there results the Body and after these three dimensions there is no passing farther so that in these three the integrity and to so speak totality is terminated which I might but with justice have required Aristotle to have proved to me by necessary consequences the rather in regard he was able to do it very plainly and speedily SIMPL. What say you to the excellent demonstrations in the 2. 3. and 4. Texts after the definition of Continual have you it not first there proved that there is no more but three dimensions for that those three are all things and that they are every where And is not this confirmed by the Doctrine and Authority of the Pythagorians who say that all things are determined by three beginning middle and end which is the number of All And where leave you that reason namely that as it were by the law of Nature this number is used in the sacrifices of the Gods And why being so dictated by nature do we atribute to those things that are three and not to lesse the title of all why of two is it said both and not all unless they be three And all this Doctrine you have in the second Text. Afterwards in the third Ad pleniorem scientiam we read that All the Whole and Perfect are formally one and the same and that therefore onely the Body amongst magnitudes is perfect because it is determined by three which is All and being divisible three manner of waies it is every way divisible but of the others some are dividible in one manner and some in two because according to the number affixed they have their division and continuity and thus one magnitude is continuate one way another two a third namely the Body every way Moreover in the fourth Text doth he not after some other Doctrines prove it by another demonstration Scilicet That no transition is made but
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
averred by Solomon saying For in the long Garment that he had on was the whole World and in the foure rows of the stones was the Glory of the Fathers graven and thy Majesty in the Diadem of his Head The same likewise is signified to us by the Grape and in like manner by all other Fruits but especially the Figg Grape and Pomegranate whence these three are almost alwayes placed together in the Sacred Scriptures So Numb 20. the People of Israel complain against Moses and Aaron Wherefore have you made us to come up out of Egypt to bring us into this evil place where there can grow no Seed neither is there either Figgs or Vines or Pomegranates Intimating that these kinds of Fruits were preferred by them for their excellency before all others And in Joel The Vine is dryed up and the Figg-tree languisheth the Pomegranate-tree the Palm-tree also and the Apple-tree even all the Trees of the field are withered because joy is withered away from the Sons of Men. Likewise in Haggai Is the seed yet in the Bud and hath as yet the Vine and the Fig-tree and the Pomegranate and the Olive-tree brought forth In like manner in Deuteronomie the Land of Promise is commended to be A Land of Wheat and Barly and Vines in which grow Figg-trees and Pomegranates and Olive-trees c. And in the Structure of the Temple undertaken by Solomon upon Divine Inspiration the Chapiters of the Pillars were adorned with several rowes of Pomegranates which particular is mentioned not in one but many places of Holy Writ Yea and sometimes accidentally and occasionally the Holy hath Ghost aenigmatically represented this most admirable and Most Wise Structure of the World the Order of the Heavens and the disposure of Creatures Spiritual and Corporeal by Emblems Parables and Figures least they should be as it were dazled and blinded by the refulgent splendor of so excellent an Object Hence we see that in these Doctrinal Dubious Points we may discourse in such manner by help of the Holy Scripture as is meet for the understanding of the Prophets which seeing they are very obscure they shall be fully understood and may be aptly applyed only then when they shall be fulfilled and not before So also when once the true Systeme of the Universe is found out then and noâ— till then the meaning of these Figures and Aenigma's shall be made known unto us Thus before the coming of the Son of God had discovered unto us the Mystery of the Holy Trinity none were able to comprehend or imagine what was concealed under those words In Principio creavit Elohim Coelum Terram for that they did not see how the Noun Plural Elohim which is as much as to say Dij Gods should be joyned with the Verb Singular Creavit But the Mystery of the Unity of Essence and Trinity of Persons in God being revealed it was presently known that the Singular Number Creavit had reference to the Unity of Essence in regard that the Works of the Trinity ad extra are indivisible and the Plural Elohiâ— to the Persons Who I pray in elder times could have found out this Mystery And thus the Name of God is thrice repeated in Psal. 67. God even our God shall blesse us God shall blesse us c. Which at first might seem a Pleonasme and superfluous repetition but afterwards it was evident that David did there set out the Benedictions of several Persons implyed to wit the Father Son and Holy Ghost Innumerable Examples of the like kind may be found in the Sacred Leaves Therefore to conclude I will say with David Psal. 92. Oh Lord how glorious are thy Works thy thoughts are very deep an unwiseman knoweth not and a fool doth not understand these things These are the particulars that I have thought fit to offer as a Divine concerning the not-improbable Opinion of the Mobility of the Earth and Stability of the Sun which I hope will be acceptable to you Reverend Sir out of the love and diligence wherewith you persue Virtue and Learning But to the end that you may also receive an account of my other Studies I hope very shortly to publish in Print my Second Tome Of the Institutions of all Learnings which shall containe all the Liberall Arts as I have already signified in that Syntax and Spicimen by me heretofore put forth and published under your Name The other five following Tomes by me promised which shall treat of Phylosophy and Theology are not altogether so forward nevertheless they will be speedily finished In the mean time there will come forth my Book Concerning Oracles now finished together with a Treatise Of Artificial Divination And for a pledge thereof I send you at this time annexed to this Epistle a Tract Concerning Natural Cosmological Divination or of Natural Prognosticks and Presages of the Changes of Weather and other things which fall within the compasse of Nature God grant you all Happinesse NAPLES from the Covent of the Carmelites Jan. 6. 1615. Most Reverend Sir Your Most Humble Servant PAOLO ANTONIO FOSCARINI FINIS Imprimatur P. ANT. GHIBERT Vic. Gen. JOANNES LONGUS Can. Cur. Archiep. Neap. THEOL Vidit MATHEMATICAL COLLECTIONS AND TRANSLATIONS THE SECOND TOME THE SECOND PART Containing I. D. BENEDICTUS CASTELLUS his DISCOURSE of the MENSURATION of RUNNING WATERS II. His Geometrical DEMONSTRATIONS of the Measure of RUNNING WATERS III. His LETTERS and CONSIDERATIONS touching the Draining of FENNS Diversions of RIVERS c. IV. D. CORSINUS His RELATION of the state of the Inundations c. in the Territories of BOLOGNA and FERRARA By THOMAS SALUSBURY Esq. LONDON Printed by WILLIAM LEYBOURNE MDCLXI OF THE MENSURATION OF RUNNING WATERS An Excellent Piece Written in ITALIAN BY DON BENEDETTO CASTELLI Abbot of St. BENEDETTO ALOYSIO and Professour of the Mathematicks to Pope URBAN VIII in ROME Englished from the Third and best Edition with the addition of a Second Book not before extant By THOMAS SALUSBURY LONDON Printed by WILLIAM LEYBOURN 1661. THE AUTHOURS EPISTLE TO Pope VRBAN VIII I Lay at the Feet of your Holinesse these my Considerations concerning the MENSURATION OF RUNNING WATERS Wherein if I shall have succeeded being a matter so difficult and unhandled by Writers both Ancient Modern the discovery of any thing of truth hath been the Effect of Your Holinesses Command and if through inability I have missed the Mark the same Command will serve me for an Excuse with Men of better Judgment and more especially with Your Holinesse to whom I humbly prostrate my self and kisse Your Sacred Feet From ROME Your Holinesses Most humble Servant BENEDETTO A Monk of Cassino AN ACCOUNT OF THE Authour and Work DON BENEDETTO CASTELLI the famous Authour of these ensuing Discourses of the Mensuration of Running Waters is descended from the Worshipful FAMILY of the CASTELLII and took his first breath near to the lake
CASTELLI hath been so great a Master that none have presumed to take Pencil in hand for the finishing of what he Pourfoild this small Tract like the Arabian Phoenix of which it is said Unica semper Avis did for several years together continue single in the World till that to verifie it to be truly Phoenician it renewed its Age by undergoing a second Impression And as if this did not make out the Immortal vertue of it it hath had Anno 1660 a third Circulation and risen in this last Edition as it were from the Vrne of its Authour and that so improved by the Addition of a second part that it promiseth to perpetuate his Merits to all Posterity To be brief the meer Fame of this Work resounded the Honourable Name of CASTELLI into all the Corners of Italy I may say of Europe insomuch that in hopes to reap great benefit by his Art the respective Grandees of the adjacent Countries courted his Judgment and Advice about their Draining of Fenns Diversion of Rivers Evacuation of Ports Preventing of Inundations c. So that every Summer he made one or more of these Journies or Visitations Particularly the Senate of Venice consulted him about their Lake to whom he delivered his Opinion in May 1641. and upon farther thoughts he presented them with another Paper of Considerations the 20 December following Prince LEOPOLDO of TUSCANY likewise requested his Advice in the beginning of the ensuing year 1642 which occasioned his Letter to Father Francesco di San Giuseppe bearing date February 1 To which Signore Bartolotti opposing he writes a second Letter directed to one of the Commissioners of Sewers vindicating his former and refuting Bartolotti both which I here give you § The Preferments which his Merits recommended him unto were first to be Abbot of Cassino from which he was removed Anno 1640 or thereabouts unto the Abbey of Santo Benedetto Aloysio and much about the same time preferred to the Dignity of Chief Mathematician to his grand Patron Pope URBAN VIII and Publique Professour of Mathematicks in the Vniversity of ROME § Here a Stop was put to the Carier of his Fortunes and being fuller of Honour than of Years was by Death the Importunate Intrerupter of Generous Designs prevented in doing that farther Good which the World had good reason to promise it self from so Profound and Industrious a Personage leaving many Friends and Disciples of all Degrees and Qualities to lament his losse and honour his Memory § His singular Virtues and Abilities had gained him the Friendship of very many as to instance in some he had contracted strict Amity with Monsignore Maffei Barberino a Florentine Praefect of the Publique Wayes and afterwards Pope with the Name of URBAN VIII as was said before with the above-named Monsignore Corsini Superintendant of the General Draines with Monsignore Piccolomini Arch-Bishop of Siena with Cardinal Serra with Cardinal Caponi who hath studied much and writ well upon this Subject and with Cardinal Gaetano who frequently consulted with him in his design of Draining the Fenns of ROMAGNA Moreover Prince LEOPOLDO and his Brother the Grand Duke had very great kindnesse for him which speaks no small attractions in him considering him as a favourite of the Family of Barberini between whom and the House of Medeci there is an inveterate Fewd Amongst persons of a lower Quality he acknowledgeth Signore Ciampoli the Popes Secretary Sig. Ferrante Cesarini Sig. Giovanni Basadonna Senator of Venice and I find mentioned Sig. Lana Sig. Albano Padre Serafino Pad Francesco de San. Giuseppe and many others § The Works in which he will survive to all succeeding Ages are first His solid and sober Confutation of the Arguments of Signore Lodovico dell Columbo and Signore Vincentio di Gratia against the Tract of Galileo Delle cose che stanno sopra Aqua wherein he vindicates bis said Master with a Gratitude that Tutors very rarely reap from the pains they take in Cultivating their Pupils This Apology was first Printed Anno 1615. and was a second time published as also those of his Antagonists amongst the Works of GALILEO set forth by the Learned Viviani 1656. He hath likewise writ several other curious Pieces as I am informed by the most Courteous Carolo Manolessi of Bologna amongst others an excellent Treatise concerning Colours which he putteth me in hopes to see printed very speedily And last of all these Discourses and Reflections upon the Mensuration of Running Waters with the addition of a Second Book three Epistles and four Considerations upon the same Argument which conduce much to Illustrate his Doctrine and Facilitate the Practice of it and which with a Relation of Monsignore Corsini make the second part of my First Tome § I might here sally forth into the Citation of sundry Authours of Good Account that have transmitted his Character to Posterity but shall confine my self to onely two the one is of his Master the other of his Scholar than whom there cannot be two more competent Judges of his Accomplishments To begin with his Master the Quick-sighted and truly Lyncean GALILEO who speaking of his Abilities in Astronomy saith Che la felicità del suo ingegno non la fà bisognosa dell ' opera suo And again submitting a certain Demonstration which he intended to divulge to the Judgment of this our Abbot he writes to him in this manner Questo lo comunico a V. S. per lettera prima che ad alcun altro con attenderne principalmente il parer suo e doppo quello de' nostri Amici discosti conpensiero d' inviaâ—ne poi altre Copie ad altri Amici d'Italia e di Francia quando io ne venga da lei consigliato e qui pregandola a farci parte d' alcuna delle sue peregrine speculationi con sincerissimo affetto c. And the most acute Mathematician Signore Evangelista Terricelli late Professour to the Grand Duke in immediate Succession after GALILEO maketh this Honourable and Grateful Mention of him and his Book Omitto magnum illum nutantis Maris motum Praetereo etiam omnem Fluminum Aquarumque Currentium tum mensurum tum usum quarum omnis doctrina reperta primum fuit ab Abbate BENEDICTO CASTELLIO Preceptore meo Scripsit ille Scientiam suam illam non solum demonstratione verum etiam opere confirmavit maxima cum Principum populorum utilitate majore cum admiratione Phylosophorum Extat illius Liber vere aureus § I have onely two particulars more to offer the English Reader The one concerns the Book and it is this That after the general Aprobation it hath had in Italy I cannot but think it deserveth the same Civil Entertainment with us in regard that it cometh with no lesse Novelty Facility Verity and Utility to us than to those whom the Authour favoured with the Original Our Rivers and Sewers through Publique Distractions and Private Incroachments are in great disorder as
he who desires more full and absolute solidity of Reasons may overpass this prefatory discourse and onely consider what is treated of in the demonstrations placed towards the end and return afterwards to the consideration of the things collected in the Corollaries and Appendices which demonstrations notwithstanding may be pretermitted by him that hath not seen at least the first six Books of the Elements of Euclid so that he diligently observeth that which followeth I say therefore that having in times past on divers occasions heard speak of the measures of the waters of Rivers and Fountains saying such a River is two or three thousand feet of water such a spring-water is twenty thirty or forty inches c. Although in such manner I have found all to treat thereof in word and writing without variety and as we are wont to say constanti sermone yea even Artists and Ingeneers as if it were a thing that admitted not of any doubt yet howsoever I remained still infolded in such an obscurity that I well knew I understood nothing at all of that which others pretended full and clearly to understand And my doubt arose from my frequent observation of many Trenches and Channels which carry water to turn Mills in which Trenches and Channels the water being measured was found pretty deep but if afterwards the same water was measured in the fall it made to turn the Wheel of the Mill it was much lesse not amounting often to the tenth part nor sometimes to the twentieth insomuch that the same running water came to be one while more another while less in measure in divers parts of its Channel and for that reason this vulgar manner of measuring running Waters as indeterminate and uncertain was by me justly suspected the measure being to be determinate and the same And here I freely confesse that I had singular help to resolve this difficulty from the excellent accurate way of discoursing as in allother matters so also in this of the Right Honourable and Truly Noble Signior Ciampoli Secretary of the Popes secret affairs Who moreover not sparing â—or the costs of the same generously gave me occasion a few years past to try by exact experiments that which past concerning this particular And to explain all more clearly with an example we suppose a Vessel filled with Water as for instance a Butt which is kept full though still water runneth out and the Water run out by two Taps equal of bignesse one put in the bottom of the Vessel and the other in the upper part it is manifest that in the time wherein from the upper part shall issue a determinate measure of water from the inferiour part there shall issue four five and many more of the same measures according to the difference of the height of the Taps and the distance of the upper Tap from the Superficies and level of the water of the Vessel and all this will alwayes follow though as hath been said the Taps be equal and the water in discharging keep the said Taps alwayes full Where first we note that although the measure of the Taps be equal neverthelesse there issueth from them in equal times unequal quantities of water And if we should more attentively consider this businesse we should find that the water by the lower Tap runneth and passeth with much greater velocity then it doth by the upper whatever is the reason If therefore we would have such a quantity of Water discharge from the upper tap as would discharge from the neather in the same time it is plain that either the upper Taps must be multiplyed in such sort that so many more Taps in number be placed above than below as the neather tap shall be more swift than the upper or the upper Tap made so much bigger than the nether by how much that beneath shall be more swift than that above and so then in equal times the same quantity of Water shall discharge from the upper as doth fromthâ—e neather part I will declare my self by another example If we should imagine that two cords or lines of equal thickness be drawn through two holes of equal bore but so that the first pass with quadruple velocity to the second It is manifest that if in a determinate time we shall by the first bore have drawn four Ells of the line in the same time by the second hole we shall have drawn but one Ell of cord onely and if by the first there passe twelve Ells then through the second there shall passe onely three Ells and in short the quantity of cord shall have the same proportion to the cord that the volocity hath to the velocity And therefore we desiring to compensate the tardity of the second cord and maintaining the same tardity to draw through the second hole as much cord as through the first it will be necessary to draw through the second bore four ends of cord so that the thickness of all the cords by the second hole have the same proportion to the thickness of the cord which passeth onely by the first as the velocity of the cord by the first hole hath reciprocally to the velocity of the codâ—s by the second hole And thus its clear that when there is drawn through two holes equal quantity of cords in equal time but with unequal velocity it will be necessary that the thickness of all the four cords shall have the same reciprocal proportion to the thickness of the swifter cord that the velocity of the swifter cord hath to the velocity of the slower The which is verified likewise in the fluid Element of Water And to the end that this principal fundamental be well understood I will also note a certain observation made my me in the Art of Wyer-drawing or spinning Gold Silver Brass and Iron and it is this That such Artificers desiring more and more to disgrosse and subtillize the said Metals having wound about a Rocket or Barrel the thread of the Metal they place the Rocket in a frame upon a stedfast Axis in such sort that the Rocket may turn about in it self then making one end of the thread to passe by force through a Plate of Steel pierced with divers holes greater and lesser as need requireth fastning the same end of the thread to another Rocket they wind up the thread which passing through a bore less than the thicknesse of the thread is of force constrained to disgrosse and subtillize Now that which is intensly to be observed in this business is this That the parts of the thread before the hole are of such a thicknesse but the parts of the same thread after it is passed the hole are of a lesser thicknesse and yet neverthelesse the masse and weight of the thread which is drawn forth is ever equal to the masse and weight of the thread which is winded up But if we should well consider the matter we should finde that the thicker the thread before the hole
distend for to this instance we answer with that which we have given notice of in the First Consideration touching the Lake of Venice treating of the abatement that is caused by the Brent let into the Lake And moreover if I shall adde thereto that which I write in the Second Consideration it will be very apparent how greatly harmfull and prejudicial these excursions of Waters from Fiume Sisto may be which are not kept under and confined within the River Therefore proceeding to the provisions and operations that are to be accounted Principall I reduce them to three Heads In the first place it is necessary to throw down those Weares and to take the Pisciaries quite away observing a Maxime in my judgment infallible that Fishing and Sowing are two things that can never consist together Fishing being on the Water and Sowing on land Secondly it will be necessary to cut under Water in the bottome of the River those Weeds and Plants that grow and increase in the River and leave them to be carried into the Sea by the Stream for by this means these Reeds shall not spring up and distend along the bottome of the River by means of the Beasts treading upon them And the same ought to be done often and with care and must not be delaied till the mischief increase and the Champain Grounds be drowned but one ought to order matters so as that they may not drown And I will affirm that otherwise this principal point would become a most considerable inconvenience Thirdly it is necessary to make good the Banks of Fiume Sisto on the left hand and to procure that those Waters may run in the Chanel and not break forth And it is to be noted that it is not enough to do one or two of those things but we are to put them all in execution for omitting any thing the whole machine will be out of tune and spoiled But proceeding with due care you shall not only Drain the Pontine Fens but by means of this last particular the Current of Fiume Sisto shall scowr its own Chanel of its self even to the carrying part of it away and haply with this abundance of water that it shall bear the Mouth della Torre may be opened and kept open into the Sea And it would last of all be of admirable benefit to cleanse Fiume Sisto from many Trees and Bushes wherewith it is overgrown And with this I conclude that the Improvement or Drain possible to be made consisteth in these three particulars First in taking away the Fishing Weares leaving the Course of the Waters free Secondly in keeping the Principal Rivers clear from Weeds and Plants Thirdly in keeping the water of Fiume Sisto in its own Chanel All which are things that may be done with very little charge and to the manifest benefit of the whole Country and to the rendering the Air wholsomer in all those Places adjoyning to the Pontine Fens A CONSIDERATION Upon the DRAINING Of the Territories of Bologna Ferrara AND Romagna BY D. BENEDETTO CASTELLI Abbot of S. BENEDETTO ALOISIO Mathematician to P. Vrban VIII and Professor in the University of ROME THe weghty businesse of the Draining of the Territories of Bologna Ferrara and Romagna having been punctually handled and declared in writing from the excellent memory of the Right Honourable and Noble Monsignore Corsini who was heretofore Deputed Commissary General and Visitor of those Waters I am not able to make such another Discourse upon the same Subject but will only say somewhat for farther confirmation of that which I have said in this Book upon the Lake of Venice upon the Pontine Fens and upon the Draining of those Plains of Pisa lying between the Rivers Arno and Serchio whereby it is manifest that in all the aforementioned Cases and in the present one that we are in hand with there have in times past very grosse Errours been committed through the not having ever well understood the true measure of Running waters and here it is to be noted that the businesse is that in Venice the diversion of the waters of the Lake by diverting the Brent was debated and in part executed without consideration had how great abatement of water might follow iâ— the Lake if the Brent were diverted as I have shewn in the first Consideration upon this particular from which act there hath insued very bad consequences not only the difficulty of Navigation but it hath infected the wholsomnesse of the Air and caused the stoppage of the Ports of Venice And on the contrary the same inadvertency of not considering what rising of the Water the Reno and other Rivers being opened into the Valleys of Bologna and Ferrara might cause in the said Valleys is the certain cause that so many rich and fertile Fields are drowned under water converting the happy habitations and dwellings of men into miserable receptacles for Fishes Things which doubtlesse would never have happened if those Rivers had been kept at their height and Reno had been turn'd into Main-Po and the other Rivers into that of Argenta and of Volano Now there having sufficient been spoken by the above-named Monsig Corsini in his Relation I will only adde one conceit of my own which after the Rivers should be regulated as hath been said I verily believe would be of extraordinary profit I much doubt indeed that I shall finde it a hard matter to perswade men to be of my mind but yet nevertheless I will not question but that those at least who shall have understood what I have said and demonstrated concerning the manners and proportions according to which the abatements and risings of Running waters proceed that are made by the Diversions and Introductions of VVaters will apprehend that my conjecture is grounded upon Reason And although I descend not to the exactnesse of particulars I will open the way to others who having observed the requisite Rules of considering the quantity of the waters that are introduced or that happen to be diverted shall be able with punctuality to examine the whole businesse and then resolve on that which shall be expedient to be done Reflecting therefore upon the first Proposition that the Risings of a Running Water made by the accession of new water into the River are to one another as the Square-Roots of the quantity of the water that runneth and consequently that the same cometh to pass in the Diversions Insomuch that a River running in height one such a certain measure to make it encrease double in height the water is to be encreased to three times as much as it ran before so that when the water shall be quadruple the height shall be double and if the water were centuple the height would be decuple onely and so from one quantity to another And on the contrary in the Diversions If of the 100. parts of water that run thorow a River there shall be diverted 19 1â—â— the height of the River diminisheth onely 1 10