according to some defect and so there is a transition or passing from the line to the superficies because the line is defective in breadth and that it is impossible for the perfect to want any thing it being every way so therefore there is no transition from the Solid or Body to any other magnitude Now think you not that by all these places he hath sufficiently proved how that there 's no going beyond the three dimensions Length Breadth and Thickness and that therefore the body or solid which hath them all is perfect SALV To tell you true I think not my self bound by all these reasons to grant any more but onely this That that which hath beginning middle and end may and ought to be called perfect But that then because beginning middle and end are Three the number Three is a perfect number and hath a faculty of conferring Perfection on those things that have the same I find no inducement to grant neither do I understand nor believe that for example of feet the number three is more perfect then four or two nor do I conceive the number four to be any imperfection to the Elements and that they would be more perfect if they were three Better therefore it had been to have left these subtleties to the Rhetoricians and to have proved his intent by necessary demonstration for so it behoves to do in demonstrative sciences SIMPL. You seem to scorn these reasons and yet it is all the Doctrine of the Pythagorians who attribute so much to numbers and you that be a Mathematician and believe many opinions in the Pythagorick Philosophy seem now to contemn their Mysteries SALV That the Pythagorians had the science of numbers in high esteem and that Plato himself admired humane understanding and thought that it pertook of Divinity for that it understood the nature of numbers I know very well nor should I be far from being of the same opinion But that the Mysteries for which Pythagoras and his sect had the Science of numbers in such veneration are the follies that abound in the mouths and writings of the vulgar I no waies credit but rather because I know that they to the end admirable things might not be exposed to the contempt and scorne of the vulgar censured as sacrilegious the publishing of the abstruce properties of Numbers and incommensurable and irrational quantities by them investigated and divulged that he who discovered them was tormented in the other World I believe that some one of them to deter the common sort and free himself from their inquisitiveness told them that the mysteries of numbers were those trifles which afterwards did so spread amongst the vulgar and this with a discretion and subtlety resembling that of the prudent young man that to be freed from the importunity of his inquisitive Mother or Wife I know not whether who pressed him to impart the secrets of the Senate contrived that story which afterwards brought her and many other women to be derided and laught at by the same Senate SIMPL. I will not be of the number of those who are over curious about the Pythagorick mysteries but adhering to the point in hand I reply that the reasons produced by Aristotle to prove the dimensions to be no more than three seem to me concludent and I believe That had there been any more evident demonstrations thereof Aristotle would not have omitted them SAGR. Put in at least if he had known or remembred any more But you Salviatus would do me a great pleasure to alledge unto me some arguments that may be evident and clear enough for me to comprehend SALV I will and they shall be such as are not onely to be apprehended by you but even by Simplicius himself nor onely to be comprehended but are also already known although haply unobserved and for the more easie understanding thereof we will take this Pen and Ink which I see already prepared for such occasions and describe a few figures And first we will note Fig. 1. at the end of this Dialog these two points AB and draw from the one to the other the curved lines ACB and ADB and the right line AB I demand of you which of them in your mind is that which determines the distance between the terms AB why SAGR. I should say the right line and not the crooked as well because the right is shorter as because it is one sole and determinate whereas the others are infinit unequal and longer and my determination is grounded upon that That it is one and certain SALV We have then the right line to determine the length between the two terms let us add another right line and parallel to AB which let be CD Fig. 2. so that there is put between them a superficies of which I desire you to assign me the breadth therefore departing from the point A tell me how and which way you will go to end in the line CD and so to point me out the breadth comprehended between those lines let me know whether you will terminate it according to the quantity of the curved line AE or the right line AF or any other SIMPL. According to the right AF and not according to the crooked that being already excluded from such an use SAGR. But I would take neither of them seeing the right line AF runs obliquely But would draw a line perpendicular to C D for this should seem to me the shortest and the properest of infinite that are greater and unequal to one another which may be produced from the term A to any other part of the opposite line CD SALV Your choice and the reason you bring for it in my judgment is most excellent so that by this time we have proved that the first dimension is determined by a right line the second namely the breadth with another line right also and not onely right but withall at right-angles to the other that determineth the length and thus we have the two dimensions of length and breadth definite and certain But were you to bound or terminate a height as for example how high this Roof is from the pavement that we tread on being that from any point in the Roof we may draw infinite lines both curved and right and all of diverse lengths to infinite points of the pavement which of all these lines would you make use of SAGR. I would fasten a line to the Seeling and with a plummet that should hang at it would let it freely distend it self till it should reach well near to the pavement and the length of such a thread being the streightest and shortest of all the lines that could possibly be drawn from the same point to the pavement I would say was the true height of this Room SALV Very well And when from the point noted in the pavement by this pendent thread taking the pavement to be levell and not declining you should
my self in my old perswasion for though I should be made to see that it was erroneous its being upheld by so many probable reasons would render it excuseable And if these are fallacies what true demonstrations were ever so fair SAGR. Yet its good that we hear the responsions of Salviatus which if they be true must of necessity be more fair and that by infinite degrees and those must be deformed yea most deformed if the Metaphysical Axiome hold That true and fair are one and the same thing as also false and deformed Therefore Salviatus let 's no longer lose time SALV The first Argument alledged by Simplicius if I well remember it was this The Earth cannot move circularly because such motion would be violent to the same and therefore not perpetual that it is violent the reason was Because that had it been natural its parts would likewise naturally move round which is impossible for that it is natural for the parts thereof to move with a right motion downwards To this my reply is that I could gladly wish that Aristotle had more cleerly exprest himself where he said That its parts would likewise move circularly for this moving circularly is to be understood two wayes one is that every particle or atome separated from its Whole would move circularly about its particular centre describing its small Circulets the other is that the whole Globe moving about its centre in twenty four hours the parts also would turn about the same centre in four and twenty hours The first would be no lesse an impertinency than if one should say that every part of the circumference of a Circle ought to be a Circle or because that the Earth is Spherical that therefore every part thereof be a Globe for so doth the Axiome require Eadem est ratio totius partium But if he took it in the other sense to wit that the parts in imitation of the Whole should move naturally round the Centre of the whole Globe in twenty four hours I say that they do so and it concerns you instead of Aristotle to prove that they do not SIMPL. This is proved by Aristotle in the same place when he saith that the natural motion of the parts is the right motion downwards to the centre of the Universe so that the circular motion cannot naturally agree therewith SALV But do not you see that those very words carry in them a confutation of this solution SIMPL. How and where SALV Doth not he say that the circular motion of the Earth would be violent and therefore not eternal and that this is absurd for that the order of the World is eternal SIMPL. He saith so SALV But if that which is violent cannot be eternal then by conversion that which cannot be eternal cannot be natural but the motion of the Earth downwards cannot be otherwise eternal therefore much lesse can it be natural nor can any other motion be natural to it save onely that which is eternal But if we make the Earth move with a circular motion this may be eternal to it and to its parts and therefore natural SIMPL. The right motion is most natural to the parts of the Earth and is to them eternal nor shall it ever happen that they move not with a right motion alwayes provided that the impediments be removed SALV You equivocate Simplicius and I will try to free you from the equivoke Tell me therefore do you think that a Ship which should sail from the Strait of Gibralter towards Palestina can eternally move towards that Coast keeping alwayes an equal course SIMPL. No doubtlesse SALV And why not SIMPL. Because that Voyage is bounded and terminated between the Herculean Pillars and the shore of the Holy-land and the distance being limited it is past in a finite time unlesse one by returning back should with a contrary motion begin the same Voyage anew but this would be an interrupted and no continued motion SALV Very true But the Navigation from the Strait of Magalanes by the Pacifick Ocean the Moluccha's the Cape di buona Speranza and from thence by the same Strait and then again by the Pacifick Ocean c. do you believe that it may be perpetuated SIMPL. It may for this being a circumgyration which returneth about its self with infinite replications it may be perpetuated without any interruption SALV A Ship then may in this Voyage continue sailing eternally SIMPL. It may in case the Ship were incorruptible but the Ship decaying the Navigation must of necessity come to an end SALV But in the Mediterrane though the Vessel were incorruptible yet could she not sail perpetually towards Palestina that Voyage being determined Two things then are required to the end a moveable may without intermission move perpetually the one is that the motion may of its own nature be indeterminate and infinite the other that the moveable be likewise incorruptible and eternal SIMPL. All this is necessary SALV Therefore you may see how of your own accord you have confessed it impossible that any moveable should move eternally in a right line in regard that right motion whether it be upwards or downwards is by you your self bounded by the circumference and centre so that if a Moveable as suppose the Earth be eternal yet forasmuch as the right motion is not of its own nature eternall but most terminate it cannot naturally suit with the Earth Nay as was said yesterday Aristotle himself is constrained to make the Terrestrial Globe eternally immoveable When again you say that the parts of the Earth evermore move downwards all impediments being removed you egregiously equivocate for then on the other side they must be impeded contraried and forced if you would have them move for when they are once fallen to the ground they must be violently thrown upwards that they may a second time fall and as to the impediments these only hinder its arrival at the centre but if there were a Well that did passe thorow and beyond the centre yet would not a cold of Earth passe beyond it unlesse inasmuch as being transported by its impetus it should passe the same to return thither again and in the end there to rest As therefore to the defending that the motion by a right line doth or can agree naturally neither to the Earth nor to any other moveable whil'st the Universe retaineth its perfect order I would have you take no further paines about it but unlesse you will grant them the circular motion your best way will be to defend and maintain their immobility SIMPL. As to their immoveablenesse the arguments of Aristotle and moreover those alledged by your self seem in my opinion necessarily to conclude the same as yet and I conceive it will be a hard matter to refute them SALV Come we therefore to the second Argument which was That those bodies which we are assured do move circularly have more than one motion
its peculiar right motion If therefore in the circumference CD certain equal parts CF FG GH HL be marked and from the points F G H L right lines be drawn towards the centre A the parts of them intercepted between the two circumferences CD and BI shall represent unto us the same Tower CB transported by the Terrestrial Globe towards DI in which lines the points where they come to be intersected by the arch of the semicircle CI are the places by which from time to time the falling stone doth passe which points go continually with greater and greater proportion receding from the top of the Tower And this is the cause vvhy the right motion made along the side of the Tower apeareth to us more and more accelerate It appeareth also how by reason of the infinite acutenesse of the contact of those two circles DC CI the recession of the cadent moveable from the circumference CFD namely from the top of the Tower is towards the beginning extream small which is as much as if one said its motion downwards is very slow and more and more slow in infinitum according to its vicinity to the term C that is to the state of rest And lastly it is seen how in the end this same motion goeth to terminate in the centre of the Earth A. SAGR. I understand all this very well nor can I perswade my self that the falling moveable doth describe with the centre of its gravity any other line but such an one as this SALV But stay a little Sagredus for I am to acquaint you also with three Observations of mine that its possible will not displease you The first of which is that if we do well consider the moveable moveth not really with any more than onely one motion simply circular as when being placed upon the Tower it moved with one single and circular motion The second is yet more pleasant for it moveth neither more nor lesse then if it had staid continually upon the Tower being that to the arches CF FG GH c. that it would have passed continuing alwayes upon the Tower the arches of the circumference CI are exactly equal answering under the same CF FG GH c. Whence followeth the third wonder That the true and real motion of the stone is never accelerated but alwayes even and uniforme since that all the equal arches noted in the circumference CD and their respondent ones marked in the circumference CI are past in equal times so that we are left at liberty to seek new causes of acceleration or of other motions seeing that the moveable as well standing upon the Tower as descending thence alwayes moveth in the same fashion that is circularly with the same velocity and with the same uniformity Now tell me what you think of this my fantastical conjecture SAGR. I must tell you that I cannot with words sufficiently expresse how admirable it seemeth to me and for vvhat at present offereth it self to my understanding I cannot think that the business happeneth otherwise and vvould to God that all the demonstrations of Philosophers were but half so probable as this However for my perfect satisfaction I would gladly hear how you prove those arches to be equal SALV The demonstration is most easie Suppose to your self a line drawn from I to E. And the Semidiameter of the circle CD that is the line CA being double the Semidiameter CE of the circle CI the circumference shall be double to the circumference and every arch of the greater circle double to every like arch of the lesser and consequently the half of the arch of the greater circle equal to the whole arch of the lesse And because the angle CEI made in the centre E of the lesser circle and which insisteth upon the arch CI is double the angle CAD made in the centre A of the greater circle to which the arch CD subtendeth therefore the arch CD is half of the arch of the greater circle like to the arch CI and therefore the two arches CD and CI are equal and in the same manner we may demonstrate of all their parts But that the business as to the motion of descending grave bodies proceedeth exactly thus I will not at this time affirm but this I will say that if the line described by the cadent moveable be not exactly the same with this it doth extream neerly resemble the same SAGR. But I Salviatus am just now considering another particular very admirable and this it is That admitting these considerations the right motion doth go wholly mounting and that Nature never makes use thereof since that even that that use which was from the beginning granted to it which was of reducing the parts of integral bodies to their place when they were separated from their whole and therefore constituted in a depraved disposition is taken from it and assigned to the circular motion SALV This would necessarily follow if it were concluded that the Terrestrial Globe moveth circularly a thing which I pretend not to be done but have onely hitherto attempted as I shall still to examine the strength of those reasons which have been alledged by Philosophers to prove the immobility of the Earth of which this first taken from things falling perpendicularly hath begat the doubts that have been mentioned which I know not of what force they may have seemed to Simplicius and therefore before I passe to the examination of the remaining arguments it would be convenient that he produce what he hath to reply to the contrary SIMP As to this first I confesse indeed that I have heard sundry pretty notions which I never thought upon before and in regard they are new unto me I cannot have answers so ready for them but this argument taken â—rom things falling perpendicularly I esteem it not one of the strongest proofs of the mobility of the Earth and I know not what may happen touching the shots of great Guns especially those aimed contrary to the diurnal motion SAGR. The flying of the birds as much puzzleth me as the objection of the Gun-shot and all the other experiments above alledged For these birds which at their pleasure flie forwards and backwards and wind to and again in a thousand fashions and which more importeth lie whole hours upon the wing these I say do not a little pose me nor do I see how amongst so many circumgyrations they should not lose the motion of the Earth and how they should be able to keep pace with so great a velocity as that which they so far exceed with their flight SALV To speak the truth your scruple is not without reason and its possible Copernicus himself could not find an answer for it that was to himself entirely satisfactory and therefore haply past it over in silence albeit he was indeed very brief in examining the other allegations of his adversaries I believe through his height of wit placed on greater aud sublimer
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
farther and farther off the distance always encreaseth with a greater proportion so that in a circle that should have v. g. ten yards of diameter a point of the Tangent that was distant from the contact but two palms would be three or four times as far distant from the circumference of the circle as a point that was distant from the contaction one palm and the point that was distant half a palm I likewise believe would fearse recede the fourth part of the distance of the second so that within an inch or two of the contact the separation of the Tangent from the circumference is scarse discernable SALV So that the recession of the project from the circumference of the precedent circular motion is very small in the begining SIMP Almost insensible SALV Now tell me a little the project which from the motion of the projicient receiveth an impetus of moving along the Tangent in a right line and that would keep unto the same did not its own weight depress it downwards how long is it after the separation ere it begin to decline downwards SIMP I believe that it beginneth presently for it not having any thing to uphold it its proper gravity cannot but operate SALV So that if that same stone which being extruded from that wheel turn'd about very fast had as great a natural propension of moving towards the centre of the said wheel as it hath to move towards the centre of the Earth it would be an easie matter for it to return unto the wheel or rather not to depart from it in regard that upon the begining of the separation the recession being so small by reason of the infinite acuteness of the angle of contact every very little of inclination that draweth it back towards the centre of the wheel would be sufficient to retain it upon the rim or circumference SIMP I question not but that if one suppose that which neither is nor can be to wit that the inclination of those grave bodies was to go towards the centre of the wheel they would never come to be extruded or shaken off SALV But I neither do nor need to suppose that which is not for I will not deny but that the stones are extruded Yet I speak this by way of supposition to the end that you might grant me the rest Now fancy to your self that the Earth is that great wheel which moved with so great velocity is to extrude the stones You could tell me very well even now that the motion of projection ought to be by that right line which toucheth the Earth in the point of separation and this Tangent how doth it notably recede from the superficies of the Terrestrial Globe SIMP I believe that in a thousand yards it will not recede from the Earth an inch SALV And did you not say that the project being drawn by its own weight declineth from the Tangent towards the centre of the Earth SIMP I said so and also confesse the rest and do now plainly understand that the stone will not separate from the Earth for that its recession in the beginning would be such and so small that it is a thousand times exceeded by the inclination which the stone hath to move towards the centre of the Earth which centre in this case is also the centre of the wheel And indeed it must be confessed that the stones the living creatures and the other grave bodies cannot be extruded but here again the lighter things beget in me a new doubt they having but a very weak propension of descent towards the centre so that there being wanting in them that faculty of withdrawing from the superficies I see not but that they may be extruded and you know the rule that ad destruendum sufficit unum SAVL We will also give you satisfaction in this Tell me therefore in the first place what you understand by light matters that is whether you thereby mean things really so light as that they go upvvards or else not absolutely light but of so small gravity that though they descend downwards it is but very slowly for if you mean the absolutely light I will be readier than your self to admit their extrusion SIMP I speak of the other sort such as are feathers wool cotton and the like to lift up which every small force sufficeth yet neverthelesse we see they rest on the Earth very quietly SALV This pen as it hath a natural propension to descend towards the superficies of the Earth though it be very small yet I must tell you that it sufficeth to keep it from mounting upwards and this again is not unknown to you your self therefore tell me if the pen were extruded by the Vertigo of the Earth by what line would it move SIMP By the tangent in the point of separation SALV And when it should be to return and re-unite it self to the Earth by what line would it then move SIMP By that which goeth from it to the centre of the Earth SALV So then here falls under our consideration two motions one the motion of projection which beginneth from the point of contact and proceedeth along the tangent and the other the motion of inclination downwards which beginneth from the project it self and goeth by the secant towards the centre and if you desire that the projection follow it is necessary that the impetus by the tangent overcome the inclination by the secant is it not so SIMP So it seemeth to me SALV But what is it that you think necessary in the motion of the projicient to make that it may prevail over that inclination from which ensueth the separation and elongation of the pen from the Earth SIMP I cannot tell SALV How do you not know that The moveable is here the same that is the same pen now how can the same moveable superate and exceed it self in motion SIMP I do not see how it can overcome or yield to it self in motion unlesse by moving one while faster and another while slower SALV You see then that you do know it If therefore the projection of the pen ought to follow and its motion by the tangent be to overcome its motion by the secant what is it requisite that their velocities should be SIMP It is requisite that the motion by the tangent be greater than that other by the secant But wretch that I am Is it not only many thousand times greater than the descending motion of the pen but than that of the stone And yet like a simple fellow I had suffered my self to be perswaded that stones could not be extruded by the revolution of the Earth I do therefore revoke my former sentence and say that if the Earth should move stones Elephants Towers and whole Cities would of necessity be tost up into the Air and because that that doth not evene I conclude that the Earth doth not move SALV Softly Simplicius you go on so fast that
weak threads which I speak of saying that the Parallaxes come to be lessened by means of the refractions which opperating contrarily sublimate the Phaenomenon whereas the Parallaxes abase it Now of what little stead this lamentable refuge is judge by this that in case that effect of the refractions were of such an efficacy as that which not long time since some Astronomers have introduced the most that they could work touching the elevating a Phaeuomenon above the Horizon more than truth when it is before hand 23. or 24. Degrees high would be the lessening its Parallax about 3. minutes the which abatement is too small to pull down the Star below the Moon and in some cases is lesse than the advantage given him by us in admitting that the excesse of the inferiour distance from the Pole above the Superiour is all Parallax the which advantage is far more clear and palpable than the effect of Refracton of the greatnesse of which I stand in doubt and not without reason But besides I demand of the Author whether he thinks that those Astronomers of whose observations he maketh use had knowledge of these effects of Refractions and considered the same or no if they did know and consider them it is reasonable to think that the kept account of them in assigning the true Elevation of the Star making in those degrees of Attitude discovered with the Instruments such abatements as were convenient on the account of the alterations made by the Refractions insomuch that the distances by them delivered were in the end those corrected and exact and not the apparent and false ones But if he think that those Authors made no reflection upon the said Refractions it must be confessed that they had in like manner erred in determining all those things which cannot be perfectly adjusted without allowance for the Refractions amongst which things one is the precise investigation of the Polar Altitudes which are commonly taken from the two Meridian Altitudes of some of the fixed Stars that are constantly visible which Altitudes will come to be altered by Refraction in the same manner just as those of the new Star so that the Polar Altitude that is deduced from them will prove to be defective and to partake of the self same want which this Author assigns to the Altitudes ascribed to the new Star to wit both that and these will be with equal falshood placed higher than really they are But any such errour as far as concerns our present businesse doth no prejudce at all For we not needing to know any more but onely the difference between the two distances of the new Star from the Pole at such time as it was inferiour and superiour it is evident that such distances would be the same taking the alteration of Refraction commonly for the Star and for the Pole or for them when commonly amended The Authors Argument would indeed have had some strength though very small if he had assured us that the Altitude of the Pole had been once precisely assigned and corrected from the errour depending on refraction from which again the Astronomers had not kept themselves in assigning the altitudes of the new Star but he hath not ascertained us of that nor perhaps could he have done nor haply and this is more probable was that caution wanting in the Observators SAGR. This argument is in my judgment sufficiently answered therefore tell me how he dis-ingageth himself in the next place from that particular of the Stars having constantly kept the same distance from the fixed Stars circumjacent to it SALV He betakes himself in like manner to two threads yet more unable to uphold him than the former one of which is likewise fastened to refraction but so much less firmly in that he saith that refraction operating upon the new Star and sublimating it higher than its true situation maketh the seeming distances untain to be distinguished from the true when compared to the circumposed fixed Stars that environ it Nor can I sufficiently admire how he can dissemble his knowing how that the same refraction will work alike upon the new Star as upon the antient one its neighbour elevating both equally so as that such a like accident altereth not the space betwixt them His other subterfuge is yet more unhappy and carryeth with it much of ridiculous it being founded upon the errour that may arise in the instrumental operation it self whilst that the Observator not being able to constitute the centre of the eyes pupil in the centre of the Sextant an Instrument imployed in observing the distance between two Stars but holding it elevated above that centre as much as the said pupil is distant from I know not what bone of the cheek against which the end of the Instrument resteth there is formed in the eye an angle more acute than that which is made by the sides of the Instrument which angle of rayes differeth also from it self at such time as a man looketh upon Stars not much elevated above the Horizon and the same being afterwards placed at a great height that angle saith he is made different while the Instrument goeth ascending the head standing still but if in mounting the Instrument the neck should bend backwards and the head go rising together with the Instrument the angle would then continue the same So that the Authours answer supposeth that the Observators in using the Instrument have not raised the head as they ought to have done a thing which hath nothing of likelihood in it But granting that so it had been I leave you to judge what difference can be between two acute angles of two equicrural triangles the sides of one of which triangles are each four Italian Braces i. e. about three English yards and those of the other four braces within the quantity of the diameter of a Pea for the differences cannot be absolutely greater between the length of the two visive rayes whilst the line is drawn perpendicularly from the centre of the pupil upon the plain of the Rule of the Sextant which line is no bigger than the breath of the thumb and the length of the same rayes whilst elevating the Sextant without raising the head together with it that same line no longer falleth perpendicularly upon the said plane but inclineth making the angle towards the circumference something acute But wholly to free this Authour from these unhappy lies let him know in regard it appears that he is not very skilful in the use of Astronomicall Instruments that in the sides of the Sextant or Quadrant there are placed two Sights one in the centre and the other at the other at the opposite end which are raised an inch or more above the plane of the Rule and through the tops of those sights the ray of the eye is made to passe which eye likewise is held an hands breadth or two or it may be more from the Instrument so that neither the pupil nor any bone
a very exact observation and of great consequence we are advertized to make the observation of that concourse in the act of the same or just such another operation but in this our case wherein we are to shew the errour of Astronomers this accuratenesse is not necessary for though we should in favour of the contrary party suppose the said concourse to be made upon the pupil it self it would import little their mistake being so great I am not certain Sagredus that this would have been your objection SAGR. It is the very same and I am glad that it was not altogether without reason as your concurrence in the same assureth me but yet upon this occasion I would willingly hear what way may be taken to finde out the distance of the concourse of the visual rayes SALV The method is very easie and this it is I take two long labels of paper one black and the other white and make the black half as broad as the white then I stick up the white against a wall and far from that I place the other upon a stick or other support at a distance of fifteen or twenty yards and receding from this second another such a space in the same right line it is very manifest that at the said distance the right lines will concur that departing from the termes of the breadth of the white piece shall passe close by the edges of the other label placed in the mid-way whence it followeth that in case the eye were placed in the point of the said concourse or intersection the black slip of paper in the midst would precisely hide the opposite blank if the sight were made in one onely point but if we should find that the edges of the white cartel appear discovered it shall be a necessary argument that the visual rayes do not issue from one sole point And to make the white label to be hid by the black it will be requisite to draw neerer with the eye Therefore having approached so neer that the intermediate label covereth the other and noted how much the required approximation was the quantity of that approach shall be the certain measure how much the true concourse of the visive rayes is remote from the eye in the said operation and we shall moreover have the diameter of the pupil or of that circlet from whence the visive rayes proceed for it shall be to the breadth of the black paper as is the distance from the concourse of the lines that are produced by the edges of the papers to the place where the eye standeth when it first seeth the remote paper to be hid by the intermediate one as that distance is I say to the distance that is between those two papers And therefore when we would with exactnesse measure the apparent diameter of a Star having made the observation in manner as aforesaid it would be necessary to compare the diameter of the rope to the diameter of the pupil and having found v. g. the diameter of the rope to be quadruple to that of the pupil and the distance of the eye from the rope to be for example thirty yards we would say that the true concourse of the lines produced from the ends or extremities of the diameter of the star by the extremities of the diameter of the rope doth fall out to be fourty yards remote from the said rope for so we shall have observed as we ought the proportion between the distance of the rope from the concourse of the said lines and the distance from the said concourse to the place of the eye which ought to be the same that is between the diameter of the rope and diameter of the pupil SAGR. I have perfectly understood the whole businesse and therefore let us hear what Simplicius hath to alledge in defence of the Anti-Copernicans SIMP Albeit that grand and altogether incredible inconvenience insisted upon by these adversaries of Copernicus be much moderated and abated by the discourse of Salviatus yet do I not think it weakened so as that it hath not strength enough left to foil this same opinion For if I have rightly apprehended the chief and ultimate conclusion in case the stars of the sixth magnitude were supposed to be as big as the Sun which yet I can hardly think yet it would still be true that the grand Orb or Ecliptick would occasion a mutation and variation in the starry Sphere like to that which the semidiameter of the Earth produceth in the Sun which yet is observable so that neither that no nor a lesse mutation being discerned in the fixed Stars methinks that by this means the annual motion of the Earth is destroyed and overthrown SALV You might very well so conclude Simplicius if we had nothing else to say in behalf of Copernicus but we have many things to alledge that yet have not been mentioned and as to that your reply nothing hindereth but that we may suppose the distance of the fixed Stars to be yet much greater than that which hath been allowed them and you your self and whoever else will not derogate from the propositions admitted by Piolomy's sectators must needs grant it as a thing most requisite to suppose the Starry Sphere to be very much bigger yet than that which even now we said that it ought to be esteemed For all Astronomers agreeing in this that the cause of the greater tardity of the Revolutions of the Planets is the majority of their Spheres and that therefore Saturn is more slow than Jupiter and Jupiter than the Sun for that the first is to describe a greater circle than the second and that than this later c. confidering that Saturn v. g. the altitude of whose Orb is nine times higher than that of the Sun and that for that cause the time of one Revolution of Saturn is thirty times longer than that of a conversion of the Sun in regard that according to the Doctrine of Ptolomy one conversion of the starry Sphere is finished in 36000. years whereas that of Saturn is consummate in thirty and that of the Sun in one arguing with a like proportion and saying if the Orb of Saturn by reason it is nine times bigger than that of the Sun revolves in a time thirty times longer by conversion how great ought that Orb to be which revolves 36000. times more slowly it shall be found that the distance of the starry Sphere ought to be 10800 semidiameters of the grand Orb which should be full five times bigger than that which even now we computed it to be in case that a fixed Star of the sixth magnitude were equal to the Sun Now see how much lesser yet upon this account the variation occasioned in the said Stars by the annual motion of the Earth ought to appear And if at the same rate we would argue the distance of the starry Sphere from Jupiter and from Mars that would give it us
to be 15000. and this 27000 semidiameters of the grand Orb to wit the first seven and the second twelve times bigger than what the magnitude of the fixed Star supposed equal to the Sun did make it SIMP Methinks that to this might be answered that the motion of the starry Sphere hath since Ptolomy been observed not to be so slow as he accounted it yea if I mistake not I have heard that Copernicus himself made the Observation SALV You say very well but you alledge nothing in that which may favour the cause of the Ptolomaeans in the least who did never yet reject the motion of 36000. years in the starry Sphere for that the said tardity would make it too vast and immense For if that the said immensity was not to be supposed in Nature they ought before now to to have denied a conversion so slow as that it could not with good proportion adapt it self save onely to a Sphere of monstrous magnitude SAGR. Pray you Salviatus let us lose no more time in proceeding by the way of these proportions with people that are apt to admit things most dis-proportionate so that its impossible to win any thing upon them this way and what more disproportionate proportion can be imagined than that which these men swallow down and admit in that writing that there cannot be a more convenient way to dispose the Coelestial Spheres in order than to regulate them by the differences of the times of their periods placing from one degree to another the more slow above the more swift when they have constituted the Starry Sphere higher than the rest as being the slowest they frame another higher still than that and consequently greater and make it revolve in twenty four hours whilst the next below it moves not round under 36000. years SALV I could wish Simplicius that suspending for a time the affection rhat you bear to the followers of your opinion you would sincerely tell me whether you think that they do in their minds comprehend that magnitude which they reject afterwards as uncapable for its immensity to be ascribed to the Universe For I as to my own part think that they do not But believe that like as in the apprehension of numbers when once a man begins to passe those millions of millions the imagination is confounded and can no longer form a conceipt of the same so it happens also in comprehending immense magnitudes and distances so that there intervenes to the comprehension an effect like to that which befalleth the sense For whilest that in a serene night I look towards the Stars I judge according to sense that their distance is but a few miles and that the fixed Stars are not a jot more remote than Jupiter or Saturn nay than the Moon But without more ado consider the controversies that have past between the Astronomers and Peripatetick Philosophers upon occasion of the new Stars of Cassiopeia and of Sagittary the Astronomers placing them amongst the fixed Stars and the Philosophers believing them to be below the Moon So unable is our sense to distinguish great distances from the greatest though these be in reality many thousand times greater than those In a word I ask of thee O foolish man Doth thy imagination comprehend that vast magnitude of the Universe whâ—ch thou afterwards judgest to be too immense If thou comprehendest it wilt thou hold that thy apprehension extendeth it self farther than the Divine Power wilt thou say that thou canst imagine greater things than those which God can bring to passe But if thou apprehendest it not why wilt thou passe thy verdict upon things beyond thy comprehension SIMP All this is very well nor can it be denied but that Heaven may in greatnesse surpasse our imagination as also that God might have created it thousands of times vaster than now it is but we ought not to grant any thing to have been made in vain and to be idle in the Universe Now in that we see this admirable order of the Planets disposed about the Earth in distances proportionate for producing their effects for our advantage to what purpose is it to interpose afterwards between the sublime Orb of Saturn and the starry Sphere a vast vacancy without any star that is superfluous and to no purpose To what end For whose profit and advantage SALV Methinks we arrogate too much to our selves Simplicius whilst we will have it that the onely care of us is the adaequate work and bound beyond which the Divine Wisdome and Power doth or disposeth of nothing But I will not consent that we should so much shorten its hand but desire that we may content our selves with an assurance that God and Nature are so imployed in the governing of humane affairs that they could not more apply themselves thereto although they had no other care than onely that of mankind and this I think I am able to make out by a most pertinent and most noble example taken from the operation of the Suns light which whilest it attracteth these vapours or scorcheth that plant it attracteth it scorcheth them as if it had no more to do yea in ripening that bunch of grapes nay that one single grape it doth apply it self so that it could not be more intense if the sum of all its business had been the only maturation of that grape Now if this grape receiveth all that it is possible for it to receive from the Sun not suffering the least injury by the Suns production of a thousand other effects at the same time it would be either envy or folly to blame that grape if it should think or wish that the Sun would onely appropriate its rayes to its advantage I am confident that nothing is omitted by the Divine Providence of what concernes the government of humane affairs but that there may not be other things in the Universe that depend upon the same infinite Wisdome I cannot of my self by what my reason holds forth to me bring my self to believe However if it were not so yet should I not forbear to believe the reasons laid before me by some more sublime intelligence In the mean time if one should tell me that an immense space interposed between the Orbs of the Planets and the Starry Sphere deprived of stars and idle would be vain and uselesse as likewise that so great an immensity for receipt of the fixed stars as exceeds our utmost comprehension would be superfluous I would reply that it is rashnesse to go about to make our shallow reason judg of the Works of God and to call vain and superfluous whatsoever thing in the Universe is not subservient to us SAGR. Say rather and I believe you would say better that we know not what is subservient to us and I hold it one of the greatest vanities yea follies that can be in the World to say because I know not of what use Jupiter or Saturn are to me that