the truth is Chrysaspis says he never read over or rather thorowly so much as Euclide nor ever profest to study Geometry though in that very place he directly affirms he had both study'd it for recreation and attain'd sufficient skill in it to transfer its rigorous proceedings to Metaphysicks All which Querela's Publisher honestly acknowledges in his Translation of the Latin p. 58. and I am glad my Name-sake is the fairer Gamester Nor will I here omit a Passage wherein I confess I have not art enough entirely to justifie either of them Chrysaspis writes mistakably and Querela mistakes him the One might have exprest himself more plainly the Other might have interpreted him more courteously Both in some sense perhaps defendable and in some sense both blameable Chrysaspis says Guldinus was so vain that when he thought he had committed an errour he could by no means be induced to cover it by blotting it out And so far is true for he publisht it or candidly confess the same Yet all 's well enough for whoever reads Guldinus shall see how long he rolls the sweet morsel in his mouth before he can be perswaded to spit it out but goes on framing excuses as if in the very errour he had carried himself gallantly And does not he frame excuses who after a plain Demonstration of his errour and that found out as he says by himself puts down in the very next number a Notandum that what he held was probabilissimum and then proceeds to examin on both sides as if the point were yet doubtful which reasons are the stronger and if any fail how it comes to pass and which are they c. After these Advertisements he immediately advances this Proposition of which already I have given some touch Detegere quomodo Principium c. assumptum subsistat not how it miscarries for still he holds the Maxim that deceiv'd him true though not universally verum est sed non universim which words must be meant in that sense wherein himself misunderstood the notion of Inscrib'd and Circumscrib'd else as all the rest of the World interprets them that Maxim is absolutely and universally true And as to imagin what he call'd Inscrib'd to be less then the Circumscriber was a prety Conjecture and might not want hope to deceive were it in some other Science then slow-believing Mathematicks so to take those lines to be inscrib'd which had but one common term was an intolerable Oversight Now for the hardest task that he bore himself as if he had done gallantly thus much even of that he verifies not onely speaking of his opinion as most probable when he knew it to be false nor onely mincing the business while he says his Principle is true though not universally but maintaining that the ground of what he affirmed was to use his own odd expression Commune quasi in Geometricis assertum generale and so plausible still and dear to the good man was his own invention that at last he sends his Reader once more to review the Demonstration that sustains his so probable Opinion and then thus asks his judgement annon ea intellectum ipsius quodamodo ad assensum si non omnino cogat saltem suaviter pertrahat This is the Crime that amaz'd Querela this the foul and evident untruth against which he exclaims as a most unworthy and false Calumny and maliciously imputed to Guldinus Words of too fierce and rude a sense for so mild a nature as Querela seems to have whose choller sometimes may simber a little but surely never boyl over unless some hotter spirits blow the Coals though perhaps once put into a heat we know not when he may cease but let him carry on the metaphor a line or two farther and it will faithfully give him this seasonable advice that intemperate overflowings both spill themselves and diminish the fire that rais'd 'em And sure he was a little warmer then ordinary else what mean those angry and rash and which I am loath to say untrue expressions pag. 30. Of all that Chrysaspis so maliciously here imputes to Guldin there is not one word to be seen in him nor the least ground or shadow in his writings yea just the contrary to what is here so shamefully avouch 't c. and p. 33. No man that has any worth in him conscience or morall honesty would ever so unworthily have carried himself And why so furious good Querela against your Adversary why so passionate for your friend I 'm sure you had not read over his whole Book when you wrote these undertaking words not the least shadow in his writings You affirm he says just the contrary and 't is acknowledg'd for he says almost just the contrary to himself besides I must tell you what already is sufficiently prov'd there is more then one word to be seen more then the least ground or shadow to justifie Chrysaspis his charge against Guldinus of Vanity unskilfulness c. for I find no pleasure in repeating anothers faults if it were not necessary to the clearing of my Friend and I hope should Querela seek any exception against my proceeding he will find my answer in his own Again why so furious at this time Querela and upon this occasion while your Antagonist oppos'd onely Tenets which you commonly call'd Articles of faith you very neighbourly let him alone while he did but evacuate all Christian Religion and introduce a Pagan Philosophy as others accuse him you patiently held your hands but when he once presum'd to go too far and touch one of your friends then immediately you strike him on the face with malicious shameful nonsence c. then flies out Querela true to his name full of complaints and accusations and bitter resentments And now tell me for love of truth how comes it to be lawful for the Opposers of Chrysaspis to talk and write and act what they list against him and he not permitted who neither talks much nor acts any thing against them to write a little in defence of himself Remember how insolently his Vindicator provokes him with Pagan Fatility Epicurean Philosophy Miscreant Imp of Hell c. Remember how bitterly Querela reviles him with false Calumniator notorious Detracter a man of no worth no conscience nor moral honesty c. Remember how spitefully the ignorant followers of these principal Parties asperse him abridging all the anger their Tutors teach 'em into this compendious calumny HERETICK And when they have done all this and more and every day and every where immediately their rash and froward passion will censure him if he sit not down in a dull stupid indifferency but shew himself sometimes a little sensible of their unreasonableness in his Replies which yet he does both very seldom and onely by occasional touches where the subject invites him not in downright railings and long invectives wherein his envious Adversaries too often excercize both their lungs and spleen against him But enough
CHRYSASPIS TO QUERELA A LETTER publish't By a Friend of CHRYSASPIS Amicus certus in re incertâ cernitur LONDON Printed MCDLX The Publisher THIS then must be the Mode two to two the Authors and the Publishers or rather we I mean my fellow-Publisher and I are onely as Lay-Brothers to the Principal Disputants Chrysaspis and Querela and therefore no more can reasonably be expected of us then to present their Papers stand by and look on or at most if occasion should afterwards require it bear witness how they carried themselves Nor let our lower condition discourage us we may be honest as well as they nay perhaps with far more ease and security their wisdoms still tempting them to be Polititians while our unskilfulness inclines us to plain dealing a Quality which my reason as well as interest engages me to esteem above all the devices of the finest and craftyest wits First then I freely and openly acknowledge my self One far highlyer oblig'd to Chrysaspis under another more fortunate Name then to all the World besides having continually receiv'd from Him so many and so happy satisfactions in the noblest and most important Inquisitions of a Rational Soul yet seriously profess I am not conscious of ever following him one hairs bredth farther then his Reason drew me and this not onely by the humour of my nature whether stubborn or ingenuous I know not that secures me from such a servile spirit but by his express and constant direction never to depend the least jot on him but entirely on the pure force of Truth and Evidence a Lesson I hope the Reader shall see I perfectly observe in my frank relation of this Encounter wherein if I may judge they Both gave too much advantage to one another for Chrysaspis's foot which us'd to stand firm and strong unhappily slipt and Querela instead of dispatching him made at him with such a bungling blow that himself lay open to an easy revenge But to disguise the story no longer in a Metaphor Master White having written many excellent Pieces both in Philosophy and Divinity and endeavour'd not without a good degree of Success to reduce those noblest Sciences to a fair correspondence and orderly connexion undertook to print a little Treatise in Geometry hoping it might invite some apt to be affected with such motives to read his other works not that they needed it but we nor is he so severely to be interpreted that the fate of all his Books should depend on this God forbid so rich a treasure should be so rashly ventur'd but conceiving he had found the Quadrature he consequently argues He has invented in Mathematicks what was thought impossible therefore his other speculations are not to be neglected which you would pervert to a quite contrary sense He has miscarry'd in what was thought impossible therefore he is deceiv'd in every thing else which consequence if we admit we are weak discoursers if we deny 't is a weak Discourse having not the least reason to sustain it 'T is true this his expectation met with the mischance of failing but why should he not be allow'd the benefit of repenting since as soon as he saw his error no lesse friendly then clearly discover'd to him by the Learned and rightly Honourable Lord my Lord Brouncker he immediately retracted it both by word in his thankful Letters to his Lordship and by deed in his quick suppressing the Book when 't was ready to be publish't and what in so short a time could he have done more who knowes how long Guldinus liv'd in a confidence of his error before he retracted it who knowes not how tenaciously all those famous Mathematicians that conceited they had found this Quadrature cleav'd to their opinions read but Guldinus himself lib. 2. pro 4. and you shall see how many he there brings in more glorying in the Invention more obstinate in defending it more dilatory in revoking it then the so clamorously condemn'd Chrysaspis yet every one mistaken as well as he All I can say is 't is the fate alas of Circle-squares and Philosopher-stone finders to boast and to miscarry Instantly after this calling in Chrysaspis out comes Querela not onely disingenuous enough to bewray to the World the secret defects of Chrysaspis after knowledg of its being recal'd but bold enough to confess in print that knowledg nay worse envious enough to do all this in plain English and a stile flat and mean fit for the lowest capacity of the vulgar Certainly a proceeding neither just nor civil not to talk of courteous or charitable But Chrysaspis had wrong'd a friend of Querela's and I willingly commend his undertaking to defend him as one of the worthiest and most generous actions that belong to our nature yet with this Caution he must take heed of injuring Reason while he strives to do right to Friendship Let 's then examine the Cause Querela complains that Chrysaspis had stoln a thing cal'd for really it was not a Demonstration the Accus'd answers the Charge and gives his reasons to clear himself But that they contend about being a plain error in a Science where fallacies get neither credit nor profit I can believe Chrysaspis may possibly fall into the same mistake with Guldinus that was the friend's Name but scarce can imagin he should steal from him a deaf nut or a rotten apple and therefore since 't is at least probable the Casuist that allows so deep a revenge for taking away an Apple meant a sound one which no ways hinders my pretence I desire this Case may be dismist for its under-value You strive indeed to enhance the Crime because 't was Guldinus's proper Invention of which Chrysaspis rob'd him and every one is apt to cherish and tenderly love the issue of their own brain But what if it was no more then one of Guldinus's by blows what if not so much but a meer abortion and therefore I desire again it may be dismist for an error ought never to be made much of whoever is the father If it be said Chrysaspis suddenly took what he thought was sound That would acquit him absolutely of even the least suspition to be conscious of Guldinus's Retractation which is a greater Crime and more severely imputed Yet that 't was possible he might not know it will easily be believ'd by any who know him a Person soon weary of reading flourishes and fine words if they deliver but ordinary sense and such perhaps he judg'd Guldinus's and I doubt he might have some temptation to do so if he did not light on very favourable passages if he red his Dedicatory his Transitionary his Discoursive parts even among his Demonstrations strangely too talkative for a Mathematician And though we agree Guldinus have truly acknowledg'd his error yet not so openly that he that runs may read it he confesses publickly but 't is in the corner of the Church No Title of any the five Propositions lib. 2. c. 3. where
he treats directly of it expressing any mistake but proposing still either to examin something about the Question or to try how the Principle he had rely'd on subsisted c. not where it fail'd so that his Retractation indeed is there in print yet so nicely touch't and in so few words and those mingled and almost lost among many others that easily it might escape a less diligent Reader Not that I mean in this entirely to justifie Chrysaspis but rightly to state his fault which is that as it was free for him at first to think the Book not worth his study yet ought he not censure it without a full perusal But if Chrysaspis judg'd too hastily is that a crime beyond all pardon are we not every one of us sometimes overseen He that 's innocent let him throw the first stone I 'm sure he that threw the fiâ—fr stone at Chrysaspis is not innocent for had be with impartial industry red over Guldinus he might easily have found very many periods not so uncensurable as he imagins He complains that Guldinus is accus'd and calls it unworthy injurious c. and cites places out of his Book to acquit him I ask may not a Writer be modest humble and solid in some parts of his Book and quite contrary in others if I unhappily light upon these am I not excusable in saying I dislike them if your better fortune lead you to those may you not commend as you see cause Querela may exalt Guldinus Chrysaspis may depress him both may have reason and in my conceit all this is not onely possible but true for I see sometimes he discourses ingeniously and modestly sometimes again trivially and vainly This branch I must prove the other Querela will freely grant and two or three Instances I hope will dispatch it Onely here I desire to enter this Protestation that I am really sorry the just defence of my best Friend engages me to look into the faults of others wherein I thank God I take no delight To begin with a short account of the Book in generall whereof first I find a great part very little akin to the Title and of that little very much mechanically not Geometrically treated and this Guldinus freely acknowledges and seems indeed by many passages of his Book to be a good natur'd man He gathers out of others most of his notions of whose names he gives his Reader two fair Catalogues in one of which there are not many above thirty but in the other almost fourscore He professes most to meddle with the practical part but tells you where to find the Demonstrations His Collections are often not pertinent to his end but are many times for all that prety things in themselves The subjects he treats of are some of them indeed hardly reducible to his purpose as Algebra numbers ranging of Troops besides long Tables c. Yet are they all fit for Youth to learn and that was the design of these his Labours as himself professes in his Preface to his third Book though afterwards collected printed in Folio And will you now wonder that one who us'd stil to be the best man in the Company he taught and daily triumpht among his Scholars should be tainted at last with a little Vanity for my part I think it so shrewd a temptation that few in such circumstances are observed to resist it But to come to the particulars this spirit of Vanity may be plainly seen walking up and down his Book I 'm sure I met it often especially in his Epistles and Discourses which generally tast a little strong of the Scoolmaster Turn but to the page 67. and read Ultimum ergo mirabilis illius lineae punctum in quo nimirum vis omnis omneque momentum ac pondus circa Quadraturam Circuli consistit quodque neque antiqui neque moderni interque illos nec nos ipsi omnino geometrice determinant ipsum tamen Centrum esse Gravitatis semiperipheriae circuli nos primùm mundo manifestamus Wherefore of that wonderful line the last Point in which all the force and all the moment and weight in relation to the Quadrature of the Circle consists and which neither the Ancients nor the Moderns nor among them we our selves do altogether Geometrically determin yet that it is the Center of Gravity of the Circles semicircumference we first manifest to the World Will one more content you see then the first Chapter of his third Book where having briefly mention'd what the Ancients and Moderns had taught for measuring of round surfaces and administring their Methods begins thus of his own Nos eam ita tractare constituimus ut eandem ex solis unicis nostris principiis c. pendere ostendamus Quare etiamsi nullius alterius Geometrae exstarent de Dimensione Rotundi lucubrationes eam tamen ex his nostris sine ullo alio alterius auxilio expediemus This is your modest man does he not deserve to be enthron'd on a golden Chariot and great Archimedes with him and so both be led into the Capitol of eternal Honour what else do his own words mean in his long Preface to the fourth Book Quem Archimedem aureo nobiscum sedentem curru in honoris perpetui arcem Capitolinam deducemus Run now over the rest of this great Volume and when you have wondred as you go at the vast variety of forreign subjects he has gathered together pass on to the very end where you shall find a long and pleasant exercise which will both need and perhaps by its jolly humour deserve your Courtesie to forgive a little tediousness The mirth I confess came with some disadvantage to me because I had formerly seen the substance of it elsewhere though not so illustriously manag'd as by this Authour 'T is a curious Arithmetical Problem and begins pag. 351. Where after a short Rhetorical Introduction he entertains his Reader with some prety little flourishes to usher in the grand VVork Firct he proposes the Case of 100 stones so dispos'd at several short distances which so many times repeated unexpectedly exceed five miles and makes that side lose the VVager then puts another of a Horse sold for so much a nail in every shooe though beginning at a very low price but doubling Geometrically till the Buyer come to a dear bargain A third of one that invited 12 to dinner c. at last he arrives at the grand Question How many several Combinations may be made of the 23 letters which notwithstanding some restrictions he reckons up in words at length and figures too to no less a number then seventy thousand two hundred seventy three millions of millions sixty seven thousand three hundred and thirty millions of millions three hundred thirty thousand ninety and eight millions ninety one thousand one hundred fifty five words Then in condescendence to his Auditors he gathers all these words into a Book just like that in his hand counts
how many pages in a leaf how many lines in a page how many letters in a line then sums up the whole into a world of millions of millions c. and all this while the Title of his Book is Of the Center of Gravity But methinks I hear some of you murmur says he that you understand this but a little better then the other To these he offers all imaginable satisfaction first he surveys the bulk of every single Book then proposes the gathering them into one Library whose Model he describes to say the truth most exactly sets down particularly the figure which must be square and is call'd sayes he by Mathematicians Cubical then appoints the height no less then that of St. Stephen's Tower of which he gives you the measure to a foot Then goes to the VValls how high in themselves how distant from one another how many shelves each VVall can hold how many Books each shelf c. then collects the same not forgetting what space the boards and other little necessaries take up and still the Title is Of the Center of Gravity It remains says he that we consider the bredth which he contrives to be filled with several rows each regarding one another like our new Exchange to the very middle yet providently allowing space for two to walk a brest in a Gallery between the shelves besides what 's requisite for Ladder's to take down the Books for both which purposes he judges six foot and a half sufficient then multiplying and dividing he learnedly finds out the number of Libraries capable to contain all these Volumes to be eight thousand millions not to speak of the 52 millions c. as being but an od number I had almost forgot the Cover of the Library which he cares not though it be the Concave of the Moon it self Still they grudg and he heares them mutter that 't were far easier to apprehend so intricate a mystery by the quantity of ground these Libraries must be built on then by their number To these he professes he would willingly give satisfaction But what Province sayes he what Kingdom what Empire of the Chineses of the Turks or of the Christians or rather what World the Old or the New shall we chuse for so vast a foundation To be short he will try it with the whole Globe of the Earth let it be sayes he as big as it will and not to lose time in gathering his Libraries into Cities onely he takes in every inch of dry Land and setting aside one moyety of the Globe for Waters he casts up how many feet square the more diligent Moderns reckon are on the surface of the Earth fifteen hundred millions of millions c. then assigns to every Library its due Plant then sums up what number of them will cover the whole Earth and at last concludes they are two few for his work by more then all our vastest Europe can hold If any have yet a curiosity continues Guldinus to learn whether the said Books being laid one by another and close together can cover the whole Globe wet and dry for he doubts some foul play may be suspected in those large and many Galleries he left for Walks and Ladders that might have held some millions of Books and been perhaps sufficient without building Libraries on the Sea which is little better then Castles in the Air And here he judges it fit for a Complement of the Problem that this suspition be taken away To the triple reason therefore he returns as manifold an answer I could not easily distinguish this triplicity of reasons perhaps if you will bestow so much time you may at the bottom of the page 356 but to proceed and end I hope ere long for I am quite tired Books says he may either stand thus on their ends or on their long edges or so on their flat sides The first way they would overspread above seventeen such Globes as ours the second twice as many the third above a hundred such Worlds as these might so be covered with our Books he meanes those he there speaks of that not the least pins point of Earth should be seen And were not this enough to tempt any who loves a short and close method of writing to note with some sharpness such extravagancies would you think any farther questions should be rais'd about this business and that in a Treatise of the Center of Gravity would you imagin he should ask how many Clarks were necessary and how much time to copy these Books c. Item sayes he whether or no the paper wherein they are written can cover and cloth not the Earth but Heaven it self and the very Firmament call'd by us the seat of the fixt Stars He leaves least he should seem to abuse the patience of their courtesie to be considered by themselves at their leisure Thus ends the famous Center of Gravity and with these pompous words closes up it self Viam ostendimus qua itur ad astra and if any serious Reader can forgive a Quibble I think his Motto true and pertinent since in my conceit his Discourse goes quite away from the Center of Gravity to the utmost bounds or Circumference of Levity Perhaps he may retract all this mirth in another place and I be taken in the same crime with Chrysaspis but I vow I am not guilty of knowing any such correction and if there prove any I am sure it must be in some by corner of the Book else had it been in the open passages I could not possibly have balk't it Besides I doubt he is a little over-hasty too in his Censures especially himself being guilty of the fault he charges on others for having given us as his own new Invention which I easily believe it being not very excellent a little Treatise of the Center of Gravity both of one and more indivisible Points as also of Lines he uses a liberty by supposing Points and Lines to have real Gravity which he flatly denies to Cavalerius and somewhat roundly censures his calling a Surface All the lines and a Solid All the surfaces because no multitude of Mathematical lines can make a surface c. And I pray how many Mathematical points will weigh a pound Why may not Cavalerius as well take up a supposition so advancive of Mathematicks and so approv'd by Mathematicians as Guldinus demand the allowance of One neither beneficial nor admitted for should we comply with what he desires as soon as a Point is considered to have Gravity does it not immediately become of the Nature of a Solid and then how is the World beholden to him for his new Invention should we be froward and deny how will he possibly prove that to have a Center of Gravity which has no Gravity Nor was it injurious for Chrysaspis to tax Guldinus of unskilfulness in Mathematicks when as 't is rightly observed in Chrysaspis Nota quarta he offended against the very Definition of Inscribing