THE GREAT AND NEW ART OF WEIGHING VANITY: OR A Discovery of the Ignorance and Arro­gance of the great and new Artist, in his Pseudo-Philosophical Writings. By M. Patrick Mathers, Arch-Bedal to the Ʋniversity of S. Andrews. To which are annexed some Tentamina d [...] motu penduli & projectorum.

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GLASGOW, By ROBERT SANDERS, Printer to the City, and University, 1672.

THE PREFACE TO THE READER.

READER,

I doubt not but thou art surprised to find me in print: and I assure you, that it is not more above your hope and expecta­tion, then it is contrair to my former de­signs and resolutions: But as Atis his dumbness from the womb could not keep him from brusting into speech against those souldiers whom he saw ready to have killed his father; so my general in­sufficiency in all things else, cannot keep my natural affection in longer silence, when [Page] I see my bountiful Mother, this ancient and famous University, and all her beauti­ful Daughters, the other Universities of this Kingdom, in hazard to be murdered by one of their unnatural children.

And finding that he with whom I have to do, hath given but a very lame and par­tial account of the occasion of our debate, I judge it both thy interest and mine, that I correct it by a more full, perfect and impartial one: For as [...]he Magicians feigned miracles found greater belief with the Egyptians, then the true ones of Mo­ses; so a false information having nothing to contradict it, oft times prevails as true with us.

Thus then it is. My adversary having published his Tyrocinia Math. and his Ars. Magna & Nova, &c. one here who well understands those things, intending to oblige the Author, and redeem his Countrey from further injury by his wri­tings, friendly represented to him some of his failings in them. And another, whose judgement he ought to have esteemed much, with the same intention, expressed to one of his nearest friends, his dislike of [Page] those Books, and his regrate for the loss which the Author put himself and his Countrey to by them. But this was not sufficient to convince him of his weakness; for he proceeds to give the world another instance of his folly, in printing his Hy­drostaticks; and notwithstanding what had past, he yet fancies that the Masters of this University have as high an esteem of his sufficiency, as he himself: And therefore not doubting of their encouragement to so noble a work, he confidently fends his petitory letters to some of them, intreating their own concurrence, and their assistunce for procuring the encouragement of others thereto.

With his Letters, he sent this following Edict.

Forasmuch as there is a Book of Natural and Experimental Philosophy in English, to be printed within these four moneths, or there­about; Wherein are contained many excellent and new purposes: As first, Thirty Theorems, the most part whereof were never so much as heard of before: in which are proposed briefly the chiefest and most useful principles of that new Doctrine, anent the wonderful weight, force, [Page] and pressure of the water in its own Element. There are next, twenty Experiments in order to that Doctrine, not only most pleasant, and most easie to all capacities, but most useful likewise, which are set down after this method. First, each particular Experiment is briefly and clear­ly described, by its own distinct Schematism and Figure. Secondly, the curious Opera­tions, and natural effects of it are shewed. Thirdly, the true causes of these natural effects are searched into, and most evidently explicated, and demonstrated; not only by the force of reason, but by the evidence of sense also. And lastly, at the close of each Experiment, you will find most naturally deduced from the preceeding De­monstrations, many excellent and new Conclu­sions (hitherto unknown) and these for the ad­vancement of natural knowledge, and practice; among which, mention is made of a new and more commodious way of Dyving. After all which, there is a number of Miscellany Obser­vations; some whereof are Experiments made in Coal-sincks, for knowing the power of Damps, and ill Air, by killing of Animals. Some made for knowing the variation of the Compass here: and an excellent way for knowing, by the eye, the Sun or Moons motion in a second of time, which [Page] is the 3600. part of an hour, and many others of different kinds, useful and pleasant.

These are therefore to give notice to all inge­nious Persons, who are lovers of Learning, that if they shal be pleased to advance to Gedeon Shaw Stationer, at the foot of the Ladies steps, three pound Scots, for defraying the present charges of the said Book, they shal have from him, betwixt the date hereof and April next to come, one of the Copies: And for their further security in the interim, the Authors obligation for performing the same. Edinburgh the 14. of December 1671.

Which so exposed to my Masters the vanity of that confident man, that they were forced plainly to let him know their mind, as is expressed in the first Letter of his Postscript.

To this he returned an answer, which, though it as little deserved his superlative commendation, as their censure, was abun­dantly discreet for obliging them to si­lence, until his Book should come to light. But to show how contrair to his nature this was, it quickly repented him of his discre­tion; and a little after, without any such provocation, as he alledges, he alarmed [Page] this place with a flood of his fury, whereof he dischargeth himself in the second letter of his Postscript.

My Masters thought it unworthy of them to give any reply to this, lest by en­gaging themselves in a debate with one who had nothing wherewith to entertain them, except railing and calumnies, they had stained their reputation, and gained to themselves nothing but the name of foo­lish persons, for speaking to a fool in his folly: but I (to be ingenuous) having no much greater reputation for learning then himself, was content to hazard it against him: and knowing well his bragging hu­mor to be such, as would make him insult and erect Trophies, if nothing were re­plyed, I sent to him a Letter, which, to my best remembrance, was in the words follo­wing.

Sir, I admire ex [...]eedingly the forwardness of your humor (I will call it no worse) in your last to—: he is a person not concerned in you or in your books, neither will he ignorantly commend any thing, as it seems ye expected he should have done, when ye sent him these papers. Ye might have known long ago, that he had no [Page] veneration for what ye had formerly published▪ for he made no secret of his mind, when he was put to it. Ye may mistake him, if ye think that any by-end will cause him speak what he thinks not: nevertheless he delivered your commission, and was willing to be inconcerned, expecting their answer. They pressed him to know his judge­ment of your last piece: he told ingenuously the truth, that there was none of them had less esteem for it then himself. He hopes ye are so much a Christian, that ye will not be offended with him for speaking what he thought, when he had a call to it; and yet, albeit ye seem to favor him more then others, he hath ground to look upon himself as one of the Sophistical rable, for they only are such who condemn any thing ye do, the rest of the Ʋniversity continuing always learned persons. It is to no purpose to apologize for themselves, ye take all for granted, which ye have heard: I shal not put you to the pains of proving it; yet it seems ye would hardly have believed it so easily, had not your conscience told you, that they had some reason for their judgement, which really was this following: That they see nothing in your last piece, new and great, (albeit it be Ars nova & magna) save errors and non-sense; as your demonstrations of the [Page] Pendulum, your Nihil spatiale, your Gravi­tas circularis & horizontalis; your question, Whether or no a body may be condensed in a point? &c. too many to fill several let­ters: for ye must not call experiments new inventions, otherwise we are all making new inventions every day; neither must ye call different explications new inventions, else the same thing might be invented by almost every Writer. I admire how ye que­stion the R. Society; for I desire to know one point of doctrine, which ye or they either pre­tend to, concerning the weight of the air, the spring of it, or any thing else in your book, save mistakes, which was not received by all Mathe­maticians, and the most learned of Philoso­phers, many years before any of you put pen to paper. Ye have been at much pains to prove that by experiment, which all the learned alrea­dy grant, and some have demonstrat à priori from the principles of Geometry and Staticks, and many à posteriori from experience, if sense may be called a demonstration: Yet ye are the only man who produceth the Ars nova & mag­na, when all others are out of fashion. But more to your commendation, it seems ye do all these wonders by Magick; for ye have the ordinair [Page] principles of none of these Sciences: Euclid is as much a stranger, as reason in all your Books: and for this, Perue Mathematicos semper celebrabere fastus! At last ye come to prove a new doctrine, which before now was near 2000. years old, with thirty new Theorems, which must not be named, because they are of such a tender and delicat complexion, that the very naming of them will make them old. There are also many other excellent things, which will be all new when they were printed but yesterday. It is like, some of these dayes, we may have an Ars nova & magna, to prove that a piece of lead is heavier then so much cork. I know not wherefore ye undervalue any man, because he hath not as great esteem for your notions as your self: Have not we as much freedom to speak our mind of you, as ye have to write yours of the R. Society, and the University of Glas­gow? The greatest hurt ye can do us, is to make Dromo famulus one of our Principals. I think it not strange that ye using only demon­strations of sense, should admire the force of our imagination, in affirming no method of Dyving so good as that of Melgim. I am sure that the man dyving for a continual time, if he be not also of your invention, must breath of the air; and [Page] this air must either be kept close by it self, as in Melgims way, or communicat with the air above. If the latter be your invention, I doubt ye must also have some Chirurgical invention to apply to your Dyver at his return, if he go to any great deepness: If the former, it is the same with Melgims; and you cannot, neither any man else help it, but in circumstances (which alters not the method) and perchance to little purpose. As for Archimedes, I am sure he wanted no necessary requisit to prove the weight of water in its own Element. I know not what else ye in­tend to prove: always I am as sure that he had two great requisits, which ye want; to wit, Geo­metry, and a sound head. As to what ye write concerning the imperfections of Scien­ces; the scientisical part of Geography is so perfected, that there is nothing required for the projection, description and situation of a place, which cannot be done and demonstrat. The scien­tifical part of Opticks is so perfected, that no­thing can be required for the perfection of sight, which is not demonstrat, albeit mens hands can­not reach it; and these being the objects of the fore-said Sciences, your authority shal not per­swade me, that it is altogether improper to call them perfect. In the Hydrostaticks, it were [Page] no hard matter to branch out all the Experi­ments that can be made, into several Classes, of which the event and reason might presently be deduced, as consectaries (I speak not here of long deductions, as ye seem to rant) to some­thing already published: if it be noticed but rudely (as ye, not understanding what niceties of proportion means, must do) only considering motion and rest: And I believe there is none igno­rant of this, who understands what is written in this Science. Upon this account writing to you, I might call it perfect; albeit I know there are many things relating to the proportion and acceleration of the motions of fluids, which are yet unknown, and may perchance still be. Ye shal not think that I speak of you without ground; for in your Ars magna & nova, ye bring in your great attempts for a perpe­tual motion; all which a novice of eight days stan­ding in Hydrostaticks would laugh at. I do not que­stion that this age hath many advantages beyond for­mer ages; but I know not any of them, it is be­holden to you for: only I admire your simplicity in this. Astronomers seek always to have the greatest intervals betwixt observations, and ye talk that ye will give an excellent way for observing the Sun or Moons motion for a second of time; that is to say, as if it were a great matter that there is but a second of time betwixt your observations. I wonder ye tell me the eye should be added; for the invention had been much greater, had that been away, I do confess [Page] that a good History of nature is absolutly the most requisit thing for learning; but it is not like that you are sit for that purpose, who so surely believe the Mi­racles of the West, as to put them in print; and re­cord the simple meridian altitudes of Comets, and that only to halfs of degrees, or little more, as worth noticing. However, if ye do this last part concer­ning Coal-sinks well, and all the rest be but an Ars magna & nova, ye may come to have the repute of being more fit to be a Collier then a Scholar. Ye might have let alone the precarious principles and imaginary wordles of Des Cartes, until your new inventions had made them so: For I must tell you, Des Cartes valued the History of Nature, as much as any experimental Philosopher ever did, and per­fected it more with judicious experiments, then ye will by all appearance do in ten ages. Ye are exceedingly misinformed, if ye have heard that any here have pre­judice or envy against you; for there is none here speaks of you but with pity and commiseration: nei­ther heard I ever of any man who commended you for what he understood. As for your Latin Senten­ces, if they be not applyed to your self. I under­stand them not; for here we are printing no Books, we are not sending tickets through the Countrey to tell the wonders we can do: We are going about the imployments we are called to, and strive to give a reason for what we say. Where then are our doli & fallaciae, tabulae & testes, sapientia ad quam pu­tamus nos pervenisse? &c. In these things ye pub­lish, ye know there is no Sophistry, but clear evi­dence: [Page] If ye had done such great matters in Univer­sale & ens rationis, ye might have had a shift; but here ye must either particularize your inventions, or otherwise demonstrat your self derogatory to the cre­dit of the Nation: For what else is it to confound R. Societies and Universities with an Ars magna & nova; and yet when ye were put to it in print, to show your inventions, all ye could say was, that the publisher should have reflected upon the wisdom of the Creator, &c. so that the Poet said well of Demo­crites, &c. of which I understand not the sense, ex­cept ye make your self the summus vir, and us all the Verveces. I suppose this may be the great cre­dit that ye say ye have labored to gain to your Nation; to wit, to get us all the hornable title of Wedders. No more at present, but hoping this free and ingenuous Letter shal have a good effect upon you (for I am half perswaded, that the flattery of scorners and ig­norants, hath brought you to this height of imagina­ry learning) and that when ye come to your self, ye will thank me for my pains. I rest,

Your humble servant.

After this I had no notice of him or his Book, until a copy of it came to my hands: which, when I had opened it, I found dedi­cat to a Noble Person; whose very name being there, did creat in me a greater re­spect for the Book, then I thought my self capable of for any of the Authors works; and made me fear some finer things in this, [Page] then any other of his Books would suffer me to expect. For having known his Lord­ship an ornament to this Place, when his Vertue was but in blossom, I have easily gi­ven credit to that universal testimony, which reports him to have gained to him­self an high esteem among Strangers, by those excellencies, which are the glory of his Family and Name; and therefore I could not but apprehend this present, of­fered to his Lordship on so solemn a day, to be something extraordinar.

But having read over his Theorems, I ad­mired the presumptuous arrogance of the Author, in concerning the authority of so Noble a Name in so worthless a trifflle: And having returned to the Dedication, to see what he said for himself, I justified his first application for Pardon, that he had prefixed his Lordships Name to the bastle and abuse of a Noble subject. Then I consi­dered the motives of the Dedication, and found them great; yea so great, that I won­der they did not fright him from so daring an attempt: For his Lordship, I hope, hath not given security to Strangers abroad, that he might draw upon himself injury from [Page] his Countrey-men at home; his vertues have not made an Italian shelter under his Patro­ciny, that this bold Scribler might be en­couraged to send his Lordship through the world, as a Protector of falshood, and coun­tenancer of such as cannot handle truth without corrupting and defiling it. Could not his Lordships Heroick vertues, and under­standing mind; could not the learning and other excellent endowments of his Lord­ships Father, Grand-father, and Great-Grand-father; could not the Dignity of their fa­mous Ancestors, and the Antiquity of their Illustrious Family, preserve him from the importunity of this impudent man, who will needs enlighten his dark ignorance with the splendor of his Lordships Name? Was not his Lordships being an encourage­ment to learning, sufficient to have kept this arrogant pretender there o, from so­liciting his Lordships authority, to his folly and infirmity? Surely, when he adressed this Book, he either little considered his Lordships abilities to judge thereof, or else he intended to court his friendship and af­fection, for a defence against the power of his understanding; & if he gain his design, [Page] he hath reason to say, that his Lordships goodness is proportioned to his other ac­complishments.

After this view of the Dedication, I went through the rest of the Book unto the Post­script, where I find mention made of the Letter which I sent to the Author, who was wiser then to print it, lest thereby he had published his own shame; but he lets it not pass without a cast of his craft: For finding that by it his ignorance is discovered, he foams and rages, he is troubled in spirit, because he is disturbed in the exercise of his Art; that is, because he is not permitted to call other mens truths, his own, and his own falshoods and follies, rare and useful truths, and obtrude them upon the world as such; and being fettered with that reason which opposeth him, he, in the bitterness of his spi­rit, vomits out his spight against her, calling her Sophistry, Non-sense, and whatever his anger suggests to him: and breathing no­thing but revenge, he calls together his choisest vertues Fury, Malice, and Bold­ness; and having got them to joyn with his Ignorance, he endeavors by these united for­ces, to uphold his cause: Nor was any of [Page] them wanting to him, as may appear from their particular atchievements, which are remarkable in that review of my Letter, which summeth up his Postscript; and in sum, equally betrayes his Insufficiency and Insincerity. For therein he treateth the Masters of this Ʋniversity so unworthily, (as he had done in the second Letter of his Postscript, in answer to that Gentle-man, who, by direction, wrote unto him their mind) that I know nothing like it, except the spirit of its Author, and that entertain­ment which he in the Preface to his Ars magna, and pag. 472. gives to the late Arch-Bishop of Glasgow (who had been most kind to him) and Masters of the Colledge there, in which some then were, & yet are, who may be his teachers in any thing he pretends to.

But this Postscript doth not sufficiently discover the Authors vortues, and therefore he spends a part of his first Epistle to the Reader, in such flat and vulgar railings, as prove him fitter for nothing, then to hold the principality among the Street-scolders. And moreover, that the provocation may be compleat, he gives a formal appeal to any who dare state himself his adversary: and [Page] makes such ostentation of his strength and courage, that, rather then want a comba­tant, he will purchase one with gold; for he offers a Guiny for every Theorem which shal be everted, either in this, or his last Book. And such is his generosity, that I cannot doubt, but he will also be as noble in requiting the labor of any, who shal give him some Tyrocinia, whereby he may cor­rect his discovered errours.

Sure I am, there may be as much gained here as would tempt my Adversary once again, to blot a great many sheets of paper, if to boot, he could be assured of a Crown, or Rix-dolar, or (rather then lose his market) a Legged-dolar, for every Book that should stand himself no more then two Merks.

Now, Reader, I am confident thou thinks me further engaged after all these provocations, then that I can retreat with ho­nour; and so think I my self: And therefore I have accepted my Adversaries Challenge. I have examined all his Books: I have wei­ghed them in the ballance of reason, and have found them so light, that they deserve no better name then Vanity. I have dis­played the Authors infirmity and folly in every [Page] one of them, without other design then to protect my Countrey, and particularly all such as he endeavours to concern in his Writings, from the mean thoughts and misap­prehensions of those who have no other cha­racter of both, then they receive from them.

Yet in this Review I have not displayed all the enormities of this Arrogant pretender to Knowledge; for this should have made my Book swel as far above a just measure, as his Arrogance and Insolence is above eve­ry thing, except his Ignorance; seeing, every period of his Writings is either pregnant with falshood; or if it contain a truth, which he hath taken from some other, his pro­bation thereof is either from false princi­ples, or management so silly and childish, as makes it appear ridiculous. Neither have I taken notice of all the impertinencies where­of he is guilty, lest thereby I had hazarded the reputation of my good nature: But I have only exposed some of his grosser fai­lings, to let the world know, that he hath not so much wit, as himself presumes; and discovered his inveterat malice, to undeceive those who think him a man of much since­rity.

[Page] And this I have done with so much evi­dence and demonstration, that I fear not thy censure, if thou be intelligent: Not have I sent this book to your hands, under any other Patricony, then that of Reason; for she is able to recōmend it to the favour of my Friends, and protect it from the Fury and Malice of my enemies. But if it were not, that the meanness of my person and sta­tion should have made my adress as inde­cent, as the naughtiness of my Adversaries Present made his, I would have offered it (as a testimony of my humble duty, and sincere respect) to that Noble Person, to whom he hath dedicat his Hydrostaticks; and as ear­nestly have solicited his Ʋnderstanding to judge of my Truths, as my Adversary hath done his Lordships Friendship to accept, his Favour to protect, and his Name and Autho­rity to convoy his Falshoods through the world. Nor should I either have precipi­tated or suspended my adress for finding so craving an opportunity, as the day of his Lordships Birth and Majority.

THE GREAT AND NEW ART OF WEIGHING VANITY.

AS in combating, each party first intends his own defence, and in the second place only prepares an assault for his Antagonist: So I, before I make any attempt on my Ad­versaries other Writings, shal endeavour to wipe off that durt which he hath thrown upon me, in the Postscript and Preface to his Hydrostatics.

I think it no wonder that my Adversary hath suppressed that Letter of mine, which he mentioneth in his Postscript, and I have printed in my Preface; for this gives him [Page 2] the greater liberty to belie it; which he doth most splendidly, when he saith, that it is full of barbarous railings, passing all bounds of civility against himself, friends, and works: (whereas there is not a word of his friends in it: and what is therein said of his Works, the following Treatise will manifest, if it deserve the name of barba­rous railings.) Nor is it strange to see one who wants truth on his side, make lies his refuge: But he may henceforth look for the common infelicity of liars, not to be be­lieved, if he shal chance to stumble upon truth.

I had reason to fall upon his Ars mag­na, &c. because I judge ex ungue Leonem, or rather, ex cauda Catum. Nor should the bare title have been past by, because it is arrogant and false, as shal be made to appear in its own place. I am unjustly in this com­pared to blind Vejento; for he had the beast but at one hand; but to whatever hand I turn me, I find the beast there. And because my Adversary complains, that I have only snarled at the horse heels, I shal henceforth endeavour to pull the Ass from the sadle.

I excuse my Adversary for not inter­preting [Page 3] his Latin verses, because they were sent him from—without interpre­tation.

I am obliged to his esteem, in supposing me a Master in an Ʋniversity. He was ne­ver judged worthy of that dignity here: and by his ingratitude to Glasgow, he hath proven himself unworthy ever to have had it there, or any where else. And I wonder, that judging me a Master here, he should think strange that I am not so Pedantick, as (in imitation of him) to stuff my Letter with Latin Sentences altogether impertinent to our debate; and which in his Letter, and his review of mine, serve for nothing so much as to express his malice and virulency. Yea, there be two things which I think more then strange inconsideratness in him. The first is, that he accuseth me for not writing pertinent language in my Mother tongue; whereas in the very next page he writes, He hath done as the Ape did, that thrust the Cats foot into the fire, because he durst not do it himself; whereof, if he or—make good sense and Grammar, I shal give him back one of those Guinies which I am to have for everting his Theorems.

[Page 4] The other is, that he should challenge an Ʋniversity-man for writing a Letter with­out a Latin Sentence, whereas he hath writ­ten Volums of Mathematicks, without ever (for any thing I have yet seen) citing a Classick Mathematician, except once Euclid Prop. 24. lib. 1. El. Geom. in the 265. page of his Hydrostaticks, and that erro­neously. For Euclid hath two sides in one triangle equal to two in another, and our Author hath only one side in each triangle. This is like the Tarsel of a Mathema­tician.

I had reason to ask, Where are our doli & fallaciae, tabulae & testes, sapientia ad quam putamus nos pervenisse? For, first, none here being further concerned then in answering his importunat Letter, desiring the Ʋni­versities encouragement for printing his Hydrostaticks; how could any so much as dream, that a man in his right wits, should provoke others to overthrow the title of a Book Tabulis & testibus, after he had once refused to let them know any part of what was contained in the Book? And yet this Author hath done it, as he himself testifies in the 310. page. Sure no other would, for [Page 5] this dexterous wit is peculiar to him. But good Sir Sciole, let me tell you, it had been as great wisdom, either still to have concealed your great knowledge, or else to have kept up your provocations, whereby you should have saved me from the trouble of producing proof & witness against you, and your self from the shame of being con­victed guilty of both Ignorance and Inso­lence by them: For I assure you, that be­fore your Indiscreet Challenges, I had no de­sign to expose the folly of your arrogant pretences, and the contemptible infirmity of your acquittances, otherwise I might have drawn very lucky instances of both from your Ars magna & nova, &c.

Secondly, before he charged upon the Masters here his doli & fallaciae, there was nothing which could be a ground for it, seeing all that had past, was his Letter de­siring their concurrence to the printing of his Book, and their answer, wherein they declare their mind with much candour and calmness. And he tacitly acknowledgeth the injustice of his challenge, in answering my question from that Letter in which the question it self is contained: For it is [Page 6] against both Reason and Religion, first to calumniat, and then to justifie the calumny from something posterior thereto; and it is yet the worse in him, that he doth it by an untruth, in alledging my letter to have another design, then any, except himself, can discern; nor would he see it, if any other thing could be found to excuse his malicious reflexions upon persons of known integrity.

Thirdly, there are none among those whom he reproacheth, who have been so long at his School, as to learn either arro­gantly to pretend to the knowledge of those things to which they are strangers; or vainly to fancy themselves knowing in that whereof they are ignorant.

After this, my Author proceeds in such a strain as would almost proyoke Meekness her self to make a Satyr. But it is so pitiful, that it cannot excuse a serious answer from being impertinent; and therefore I pass it, without suffering my self to digress into Satyrick reflexions upon his vanity therein. Only I beg his liberty, that since he hath made me the Cat, I may henceforth, with­out offending him, catch the Rat as oft as he comes in my way.

[Page 7] Now my Adversary susficiently animat with rage, prepares himself for making a furious assault upon some passages of my letter, about perfection of Sciences, and be­gins it very learnedly, by bringing in the Historical part of Geography, as a part of the Science of Geography; which is as good Lo­gick, as if he had said, that black is a part of white, because they are both colours. But that he may the better understand this, I tell him, that Geography simpliciter is not a Science: for a great part of it is only Hi­story: and I cannot suppose him so igno­rant, as not to know that Science and Hi­story (albeit all learning, as almost all things else, receive their denomination from the most noble part) are very different: Espe­ccially in Mathematicks, where the scien­tifical part is firm and Geometrical, and the Historical part subject to the weakness of our senses; the one consisting in Me­thods and Demonstrations, the other in Pra­ctises and Observations. All these things he here mentioneth, and thousands more, can be done by sure and Scientifick Methods, and therefore are perfected in so far as they are a Science; except only the measuring [Page 8] the height of the Sea above the Earth; and this I think can only be done by himself, to whom it is easie to make Rivers run up­wards, and so to work many wonders in Hydrostaticks. I am sure that any person who understands Logick, will find by these, that my Adversary hath triumphed before the victory, and hath unjustly called my argument a Fallacy, while he had only rea­son to call it a Caption, since he was catcht thereby.

He next falls upon the Opticks, where after he hath vapored a little, to no other purpose then to display his Pedantry, and discover his dislike of modest expressions, he asketh a question which proves him a stranger to this part of learning. But that he may reap some instruction from this de­bate, let him know that the Opticks hath scientifically so far perfected the sight, that it demonstrateth this Theorem: In all Te­lescops, as the focus from the eye glass is to the distance of the focus from the object glass, so is the simple appearance of the object to the appea­rance of the same through the Telescope. And therefore if the distance from the focus to the eye glass be one inch, and the distance [Page 9] of the focus from the object glass 100000, the object will appear 100000. times lon­ger or broader by help of the Telescope, then to the simple eye: Or with this Te­lescope you may see as well at 100000. miles distance, as with the simple eye at one: If the glasses (or rather mirrours, because they lose no rays, and have caeteris partibus, all one determinat reflexion) be sufficiently large, and of the true Geome­trical figure. By the same method, the de­monstrative, or scientifick part, teacheth us to see at any finit distance, as if it were three foot or less. The like consideratis con­siderandis, is true in Microscops and Scoto­scops also. If our Author do question this rule, he shal find it in Escinardi Optica, and in the Philosophical Transactions, page 4005. as also in others before them both. It is like if he had known it, he had spoken bet­ter sense in his New Optical experiment.

He is mistaken in saying, that it is not known how the sight is made; for it is done by bringing all the rays coming from one point of the visible alwayes to one point of the retina. It was never motioned by any learned man (since the Opticks came to this [Page 10] perfection) that any brutes yet known, should see otherwise then men: Fishes in­deed, because of the dense medium they live in, have their crystalline rounder; and night­beasts, such as Cats and Owles, their uvea larger: yea, many other particulars there are, of which the Opticks do evidently de­monstrat the reason.

Our Author might have remembred since he was a Professor of Philosophy, that lights and colours are qualities, at least ac­cording to him; and therefore not the ob­ject of any Mathematical Science, which is always quantity.

Reflexion and Refraction were fully han­dled by Des Cartes; for it is out of doubt, That the angle of incidence is equal to the angle of reslexion, and the sines of the angles of inci­dence proportional to the sines of the refracted angles. Infraction, is the same with Refra­ction, and therefore impertinently re­peated.

It is no wonder the Lord Verulam was not of my mind; for he died before the time of Des Cartes, who brought the Op­ticks to this perfection. But it is no smal wonder to find a man pretending so highly [Page 11] to learning, as our Author doth, and yet print himself a stranger to the progress thereof.

It is true indeed that M. Newtown hath discovered an inconvenience in Refractions, which was not formerly known, and that therefore Metallin Mirrours are more proper then glasses: but this hath not ad­ded any thing to that universal rule I pre­sently mentioned, which scientifically brin­geth the sight to any degree of perfection, and holdeth in these Telescops, as well as in all others: yea, these Telescops were known before, only their advantage above others was not known.

What he saith of M. Hook, is most im­proper: seeing there he only promiseth to accomplish or bring to practise what hitherto hath been attempted, or by all most desired; not at all mentioning the Science, which our Author questions.

Let any man consider the vast extent of that rule, and think what can be more large. I do not question that there may be many excellent and subtil inventions for promoting sight, as to practise: but I am sure the scientifick part cannot make the [Page 12] sight infinitly perfect, and it hath alrea­dy brought it to any degree of finit perfe­ction.

He flatters himself that he hath gained the victory, as to the Hydrostaticks: but upon what account, may be seen in my Let­ter; which being written in privat, only for disswading him from making himself ridiculous, and for curing him of his blind presumption, was framed to his capacity, and not for the learned world. And seing it was necessar, because of the importu­nity of his Letters, to signifie to him, that this Science was already perfected, as to all these things whereof he is capable; it was more civily and respectfully spoken, to say, that the Hydrostaticks were already perfected, then to say, that they were fur­ther perfected then he could reach.

Our Author should know that all mixed Mathematical Sciences, are nothing else but Geometrical Demonstrations, founded upon some Physical Experiment: So that Geome­try, to speak properly, is the only Science in Mathematicks, and their only store­house for rules, methods, reasons and in­ventions: It is certainly defective in several [Page 13] things; but these are far above our Authors conception.

He next strives to perswade the unlear­ned, that he hath first taught Astronomers the use of Telescops and Pendulum clocks; but I leave this to the examination of his experiments. Yet I must not pass that which he desires the Reader to mark; to wit, my non-sense, in saying, That the invention of representing the Sun or Moons motion in a se­cond of time, had been greater, if the eye had been away. And I intreat the Reader to mark as well, how M. Sinclars dulness ma­keth him impute his own non-sense to me: for in his printed Letter Feb. 22. he chal­lenged as a great neglect, that the Eye is not added in an expression of a former Let­ter; as if any could have dreamed that the observation might be without the eye; to which I answered, That the invention had been greater, if the eye had been away: and surely so it had: Nor could this have escaped M. Sinclar, if he had not wanted his eyes; but his blindness hath made him stumble upon my expression: and because he could not bruise it with his fall, he hath lashed me for his own fault. Surely this discipline [Page 14] is very near in kind to his doctrine, for they are both unreasonable.

I have nothing to say against his mira­cles in the West, especially that grand one of the Sun seen in Winter for an hour about midnight, eight degrees above the Hori­zon: except, that it is only mentioned in his Book; no man, I ever spoke to, having heard of it; altho I know many who have been in the place mentioned, and very in­quisitive concerning it. Besides, that lay­ing one aside, it far surpasseth all miracles of the heavenly bodies, recorded in facred History.

If our Author think that he was well exercised, when he was making his obser­vations of the Comet, he should judge a part of his time well spent, in letting the world know for what they served: but he seems to intend no more; then to make men believe, that he is not ignorant of a degree or a minut, altho he reckons the Suns mo­tion by inches.

I question not, that a Coal-hewer is more useful to the Countrey then he and I both: and therefore he is obliged to me, for gi­ving him a more useful trade, then he now [Page 15] driveth. Nor can I deny, but he justly de­served it; for a Coal-hewer is one who ma­keth gain by digging in another mans mine; and so hath he done; for that Histo­ry of Coal which he hath printed, is none of his, altho he hath made advantage by the publishing and sale thereof. But this is no great wonder, since the most part of the truths contained in his writings, are dig­ged out of other mens works. And that the Author of this History may not escape the fate of others with whom he maketh so bold, he mixeth with his doctrine, some mistakes of his own, and particularly that erroneous application of Euclid above mentioned in page 4. of this Book.

Now my Lords and Gentle-men, who are Coal-masters, I pray you consider how un­justly M. Sinclar inferrs, that I design for you no better name then I have given to him; and how maliciously he thereby en­devours to creat in you a prejudice a­gainst me. I highly esteem and honour all such whose knowledge and vertue maketh useful, and ornaments to their Countrey. But pardon me, that I suffer not M. Sinclar to usurp to himself the name of a Phi­losopher [Page 16] for writing this History, (altho it were his own) since he wants the Science of Coal; for it is not History, but Science, that makes the Philosopher.

I need not concern my self much in his censure of Des Cartes; for he is as far exal­ted above my commendation, as he is with­out the reach of M. Sinclars detracting tongue.

He may well say, that he is not afraid I shal come the length of his labours in Glasgow Colledge, about Ʋniversale, and Ensrationis; for in his last Logick Notes, he hath thirty sheets of paper upon Genus and Ob­jectum Logicae, Ʋniversale and the Praedica­bles; which falsifies the first sentence of the Epistle to the Reader of his Ars Magna.

He might have holden his peace of Rhe­torical and Algebraical composition and reso­lution; for he knows no more of either but the name. If he had read this part of my Letter right, he would have had some other fansies, then he here expresseth; as I should show, were not this too sheepish a subject to be insisted upon.

It is true that a Letter was sent to M. Sin­clar, containing the words which he [Page 17] printeth; but it is as true, that the same Letter contained the condition of that pro­mise which he there mentioneth; to wit, If he made it appear that his Book were an­swerable to his Edict. The concealing of this is so great a proof of his candour and ingenuity, that infallibly it will procure credit to any thing he affirms.

Now this Good Man having spent ma­ny of his spirits in this tempestuous con­flict, is opprest with drowsiness; and having fallen asleep, he dreams all the rest of his Postscript. For I am sure there is not one in this Ʋniversity, who ever either had his name in an Almanack, or craved any man pardon upon such an account.

I have seen the Pamphlet he speaks of with the Advertisement to the Reader, and found nothing in it of any ingenious Gentle­man Artist, set upon inhumanely as by two Mastives; but some Printer checked for playing the Astronomer unhandsomly, and that under a borrowed name, for to make his Prognostication the more vendible; a practise too ordinar. Our Author here tal­king of two, judgeth this business to be of the same difficulty with that of D. Mores [Page 18] butter Scon, which could not be sufficiently fenced from the violence of the Air, by less then the Syllogistical force of two bold brethren.

However, if there be any errours in that Almanack, he bewrays his ignorance in passing them; while he lets a fling at the mistake of a Table, and at some Chronologi­cal Rhymes, things of no importance. For the first, it may be imputed to a piece of rashness, occasioned perhaps by the obscu­rity of that Tables explication, but not to ig­norance; seeing such triffles, as Tobacco-box­tables, and Pocket instruments, which pro­duce nothing, but what can be better done without them, conduce not to knowledge: And therefore no reproach for a man to be ignorant of them, being contrived only for Mechanicks, and such sensible Demon­strators as my Adversary is. As for the Rhymes, I suppose there is as little necessity of thinking the Author of them, and of the Almanack, to be the same, as of judging the new and unheard-of Hydrostatical Theo­rems, and the bundle of Latin Sentences in the reply to my Letter, to have been tursed by the same hand▪

[Page 19] I have no regard for Rhymes, and yet for recreation, I must take notice of our Au­thors two Criticisms; whereof one is, the two last lines exceed the former in a foot, con­trare to that of Horace, ‘Primum ne medio, &c.’

Consult our English Poëts, Sir, what weight this authority hath with them. The other is: It should not have been said, Since that of nought the Lord created man. But, Since that of dust, &c. Pray you, Sir, is this sound Philosophy; and if it be, how taught you your Scholars, Cap. 7. de Causalitatib. Caus. Prim. Creatio est actio causae primae, quâres primo ex nihilo producuntur? But who then can this Prognosticor be? It is very proba­ble, from the rable of Astrology, (for there is none of that profession among us) that he is my Antagonists Apocalyptical Astro­logue, who Lib. 6. Dial. Phys. 3. Sect. 1. be­sides his Astrological Predictions, and Pro­phesies out of the Old Testament, did from the Revelation of S. John, with great zeal declare many, and these even wonderful things, concerning the number of the Beast 666. and the Alphabetical letters A. B. I. S. of great affinity with it. The mystery of [Page 20] these must not be revealed, lest it occasion the discovery of that divine Astrologue.

There is little heat here about Ens ratio­nis; that crack-brain'd knave hath evani­shed, together with his Cousin-germain M. Sinclars dearly beloved Forma sub­stantialis materialis. For ought I know, they have got in to his Nihil spatiale, to erect a Colledge of Fanatick Philosophers.

I Am now to examine his Epistle to the Reader, where he complaineth excee­dingly of Envy, because the Masters of this Ʋniversity would not take his word for the novelty of his inventions: Neverthe­less he must grant (if he will be ingenuous) that they have done him a courtesie, in cau­sing him prefix a more modest Title to his Book, then his Edict carryes.

He wrongs M. Boyl egregiously, in cau­sing him say generally, that Archimedes's Demonstrations have more of Geometrical subtility then usefulness; whereas he saith only (in the Preface to his Hydrostatical Paradoxes) that many of his Hydrostatical Propositions have more of Geometrical sub­tility then usefulness. It were non-sense to [Page 21] speak so of Demonstrations, seeing their only use is to prove the thing in question: which if they do, they cannot be called useless; and if they do it not, they cannot be called Demonstrations.

Our Author now compares his method with that of Archimedes's forsooth. He is more speculative, our Author is more pra­ctical. So may a Trone-lord say: Archi­medes was more speculative in his Staticks, and he more practical. Next Archimedes's Demonstrations are Geometrical, and his Phy­sical. That is to say, Archimedes's reasons are sure and solid, and his are conjectures: And then Archimedes's Demonstrations are but for the use of a few, and these for the use of all. He might truly have added, And for all uses, except to convince; which is the proper use of a Demonstration. As for his last comparison, Archimedes was more wise then to illustrat that in his Book, which any mean man might do, and was already demonstrated. But our Author needs not imagine, that a rational man will venture any surprising Demonstration to the world, without practising it, if he can: yet there was no necessity that he should [Page 22] swel his Book with it. I say the like of Stevinus, in whose Demonstrations, I am not afraid our Philosopher show any defect, ne­vertheless that he be pleased to speak at random.

He beginneth now to tell the strange things he hath invented. And first, he saith, that he considereth the pressure of the wa­ter with the pressure of the air joyntly. Can our Author be so ignorant, that he knows not the arise of the Toricellian expe­riment? Was it not from the considera­tion of Pumps and other Hydrostatical ma­chines, that they had no effect above 33. or 34. foot? Was it not considered here by Galilaeus, that water pressed water no fur­ther then its own level; and it was proba­ble, the weight of the Air might press it up the rest of the way (seeing it was not much) which it ascended in the Pump? Upon this account, he projected the expe­riment first in water, (where was conside­red the pressure of Water and Air joyntly) and afterwards Toricellius perfected it in Quick-silver, judging rationally, that the great weight of the fluid by shortning the tube, would facilitat the experiment. In [Page 23] M. Boyls continuation of Physico-Mechanical Experiments, Exper. 13. 14. 15. Doth he not consider the pressure of both together? Yea, is there any intelligent man who now speaks of a Pump, or any Hydrostatical en­gine, without considering both these pres­sures together?

All these counterposings, which he speaks of, have been tryed by M. Boyl, and also many more; to wit, oyl of Turpen­tine, and oyl of Tartar, &c. but if our Au­thor please, he may try it yet with Ale, Beer, Urine, &c. and all these shal be new Experiments. He should have been more general in these tryals, and more particu­lar in the mysteries and secrets of the Art which he hath discovered, and none else can get notice of. Archimedes asserts the weights of all fluids in general, and conse­quently of the Air, if it be a fluid, which the Learned never yet denyed: Yea, Ar­chimedes's Cōmentator Rivaltus (who died long before the Toricellian experiment) mentioneth the Air and its weight.

That assertion of M. Boyl is true at present, and will constantly be so, suppose every man alive print such Volums as our [Page 24] Author hath done. However, the learned Doctor Wallace hath published a Book not long ago, notwithstanding all our Authors invention; in which he deduceth more then ever our Author shal know of the Hy­drostaticks, as consectaries from one pro­position.

Now, Reader, I stay no longer here to consider my Adversaries indiscreet railings and provocations; for this were unworthy both of you and me: But that you may know, that I am a man of my word, I pro­ceed to the survey of his works, as I promi­sed in my Preface. And I am not a little in­couraged to this, by the hope of gaining as many Guinies, as may help that pitiful poverty, wherewith he upbraideth me.

But lest he think that the Probleme which his Brother proposeth concerning the bringing up from the bottom of the Sea, any weight that can be sunk therein, hath bougled me, I think fit to give thee here three several answers thereto.

First then, for effectuating that which is there proposed, you shal take the new in­vention, called, The Dyving Ark, one so large that it requires a greater weight to [Page 25] sink it down, then the Pondera demersa: which being sunk down near to the Pon­dera demersa, the Dyver must first bind them to the Dyving Ark, and then loose away the weight which did sink it: Now the Pondera demersa, being ex hypothesi, lighter then the weight which was suffi­cient to keep the Ark at the bottom, must of necessity be pressed up with the Ark by the water: and the nearer it cometh to the brim, the motion will be the swifter, not only for the acceleration of the motion, but also because the Air dilateth it self, and (as I determinat in my Examination of this dyvink Ark) the Ark is pressed upward with as much force, as the quantity of wa­ter equaling the included Air, would cause by its weight in the Air. But if the Inventer will take my word upon it, his Ark must be stronger then a Wine glass, and without holes in the bottom: nay, it must not have a Glass window of a foot in square, at least not near the bottom. And if the Pondera demersa be great, when he hath done his utmost, in case the bottom of the new Invention get out, you may have sup­ply from the old Hydrostaticks: Thus,

[Page 26] You shal take at a low water, some great strong tuns banded with iron, so many of them, that being all full of water, they are heavier then the Pondera demersa in the wa­ter; that is to say, that the weight of all these tuns full of water, may weigh more then the Pondera demersa, having rebated from their weight, the weight of their quantity of water. These tuns being all emptied and exactly closed, and iron chains or strong ropes tyed to their iron bands, let the Dyver go down in his Bell, and bind these chains or ropes (all the tuns may be fastened to one chain) to the Pondera de­mersa, as near as may be; and the rising wa­ter shal lift the Pondera demersa from the ground; which being once done, they are easily drawn any where. If the Pondera strike on the ground, at the next low wa­ter stent the chains as much as ye can.

I suppose any man who tryeth these ways, will be best pleased with this, which hath been known these many ages: seeing it is far easier to multiply tuns, then to make a vast bulk of an Ark, with a bottom proportionably strong, to resist the pres­sure of the water, and to be troubled with [Page 27] a weight sufficient to demerge the same. These two Answers I have got from my two brethren the inferior Bedals, who are as fertil in affording satisfactory answers, as my Adversaries Brother is in starting subtil questions. If it be objected against the last of these two Methods, that it can only be practised where the sea ebbeth and flo­weth, I give you a third.

Take two ships (any of which is suffi­cient to raise the Pondera demersa) the one deep loadned with stones, or any such thing, the other altogether empty. Bind the loadned ship as near as may be to the Pondera demersa (which may be easily done by the help of the Dyving Bell) and then liver her into the other which was empty: This livered ship shal raise the Pondera de­mersa from the ground, which afterwards may be easily drawn any where. And if perchance they strike on the ground in the drawing, let them be bound again to the new loadned vessel, doing as formerly. This method, I suppose, you will find in Vitruvius, who is a very old Writer; and yet if M. Sinclar had given it, it is like, he would have listed it amongst his new [Page 28] Inventions, as he did Riccioli's erroneous argument against the motion of the Earth.

Hitherto I have been employed in parreing those thrusts which M. Sinclar gives in at me, through all the Postscript, & part of the Preface to his Hydrostaticks: It is now high time for me to prepare an assault for him, this being a part of my Province: and in forming it, I shal make use of no wea­pon, but Reason: hoping from it, better suc­cess, then my Adversary hath had; & the ra­ther, because he is so great a stranger to it.

The first shal be upon his Hydrostaticks, because that began the debate. The second upon his Ars nova & magna, because of the reproaches my Masters have sustained for their just censure of it. And the last assault shal be upon his Tyrocinia, which indeed is more blameless then the rest, being freest from errours, and more consonant to its title; yet albeit it had no name prefixed, it could not but sufficiently discover the Tyro and the Great and New Artist, to be all one. All this shal be done in the proper language of each Book, that every work, & its exa­mination, may be understood by the same Reader: And so I begin with the Hydrosta­ticks.

AN EXAMINA­TION OF M. SINCLAR'S Hydrostaticks.

Non equidem hoc fludeo, bullatis ut mea nugi [...]
Pagina turgescat, dare pondus idonea fumo.
Secreti loquimur:—
Pers.

THat I had sufficient reason to quarrel the offer of thirty new and unheard-of Hydro­statical Theorems, shal appear from the examination of this Treatise; whereof all that is true, (for a considerable part of it is false and ridiculous) is the same with the do­ctrine of Archimedes and Stevinus, in the following Propositions: only our Authors doctrine is more loose, and less precise.

As for what he hath written concerning the Bensil of fluids, generally applyed, is [Page 30] false; seing no Bensil hath hitherto been perceived in any fluid, except Air. And seing the doctrine of the spring of the Air, is called by most of Authors, and par­ticularly by M. Sinclar himself, Aërosta­ticks: I think not my self obliged to re­duce it to the writings of Archimedes and Stevinus, who wrote only Hydrostaticks pro­perly so called: yet in that subject also, (where he speaks truth) I shal in its due place trace him in Aërostatical Writers ex­tant before him.

In the review of this Tractat, I shal, for my hires sake, begin with the Theorems; and afterward take notice of a few things in the Observations and Experiments.

§. 1. The Theorems reviewed, whereof a great part are proven false, others ridiculous, and the rest not new.

I Shal here at once discover the falsity and ridiculousness of a considerable part of our Authors Theorems, and reduce the rest to these following Propositions of Archi­medes and Stevinus.

Archimedis Positio 1.

Ponatur humidi eam esse naturam, ut, parti­bus ipsius aequaliter jacentibus & continuatis in­ter sese, minus pressa à magis pressa expellatur. Ʋnaquae (que) autem pars ejus premitur humido supra ipsam existente ad perpendiculum, si hu­midum sit descendens in aliquo aut ab alio aliquo pressum.

Prop. 2.

Omnis humidi consistentis atque manentis superficies Sphaerica est, cujus centrum est idem quod centrum terrae.

Prop. 5.

Solidarum magnitudinum quaecunque levior humido fuerit demissa in humidum manens, us (que) eò demergetur, ut tanta moles humidi, quanta est partis demersae, eandem quam tota magni­tudo gravitatem habeat.

Prop. 6.

Solidae magnitudines humido leviores in hu­midum impulsae, sursum feruntur tanta vi, quantò humidum molem habens magnitudini aequalem, gravius est ipsâ magnitudine.

Prop. 7.

Solidae magnitudines humido graviores de­missae in humidum, ferentur deorsum, donec descendant: Et erunt in humido tantò leviores, [Page 32] quanta est gravitas humidi molem habentis so­lidae magnitudini aequalem.

Stevini Postul. 3.

Pondus à quo vas minus altè deprimitur, le­vius; quò altiùs, gravius; quò aeque altè, aequi­pondium esse.

Prop. 5.

Corpus solidum materiae levioris quàm aqu [...] cui innatat, pondere aequale est tantae aquae moli, quanta suae parti demergitur.

Prop. 8.

Corpus solidum in aqua levius est quàm in aëre, pondere aquae magnitudine sibi aequalis.

Prop. 10.

Aquae fundo horizonti parallelo tantum in­sidet pondus, quantum est aquae columnae cujus basis fundo, altitudo perpendiculari ab aquae su­perficie summa ad imam demissae aequalis sit.

Now, Reader, consider well these Pro­positions: my Authors Theorems; and my Censure, which is this.

His first two are no Theorems; but only Suppositions. And the third, a sort of a definition, or rather, aliquid gratis dictum.

The fourth, as he wordeth it, is false: for a broad fluid counterpoyseth more then a narrower; seing a cylinder of Mercury [Page 33] one inch thick and twenty-nine inches high, counterpoyseth a cylinder of Air of the same thickness, and of the altitude of the Atmosphere: and one two inches thick with the former height, counterpoyseth four times as much Air. As he explicateth it, it is true, and the same with Archimedes's second Proposition; for the Demonstra­tion holds, suppose ye divide the fluid by several pipes, if they have entercourse.

Here he maketh a mystery of a very easie thing: for one pillar of water being ten times thicker then another of the same height, and consequently an hundred times heavier, hath no more effect then the other; for because of its base, it hath an hundred times as much resistance. And it is most clear, that if the resistance be pro­portional to the pressure, the effect must constantly be the same.

His fift, is a part of Archimedes's first position.

His sixt also; for Archimedes's expulsion hindered with equal resistance on all sides, he calleth, Pressure on every side. I suppose he will hardly affirm, that this lateral pres­sure was not known before him; seeing [Page 34] Stevinus doth demonstrat, how much it is upon any plain howsoever inclining, in his Prop. 11. 12. 13. which our Author can­not do yet; at least, there is nothing in his Book either so subtil or useful.

His seventh is the same with the last part of Stevinus's third Postulatum.

The eight is manifestly false, (if fluids have a Bensil, as he supposeth, Prop. 17. 19.) which I demonstrat from his own fi­gure thus. The first foot E having one de­gree of weight, and the second foot I ha­ving equal quantity or dimension, and be­ing lower then E, must have more weight; (according to his 17.) let it therefore have 1½ degrees of weight: then the weight of both these must be 2½. Now the third foot N, being of equal quantity with I, and lower, must (according to his 17.) have more gravity then it hath; (to wit, 1½) let it therefore have 2. degrees; and then the weight of all three is 4½ degrees: but 1. 2½, 4½, are not in Arithmetical progression; and therefore the Theorem is false.

I must take notice, that if our Author had understood so much as the terms of [Page 35] Art; he would have said, The pressures of fluids are in direct proportion with their profun­dities. His inference there concerning a Geometrical progression is false; for there are many Geometrical progressions more then 1, 2, 4, 8, &c. And it may be in many several progressions, albeit it nei­ther be in Arithmetical nor Geometrical progression. And, suppose he had not con­tradicted himself, his Theorem is evident from the 10. of Stevinus: For, according to it, the weights or pressures of fluids are equal to the weights of respective Cylin­ders upon the same, or equal bases; but the weights of such Cylinders are in pro­portion with their quantities, which is the same with the proportion of their alti­tudes.

The ninth and tenth (as he explicateth himself) are only this, That fluids press up­on bodies within themselves, and press up bodies lighter then themselves in specie; which is the same with his 6. and 13. The first of which we have examined already: and the o­ther we leave to its own place. But what ground he hath for his sensible and insensible gravity, I shal discuss in the examination [Page 36] of his Ars magna & nova, which is all built upon this wild notion.

His eleventh is manifestly false, as I shal afterward demonstrat from his own prin­ciples: for the Cylinder acquireth only a greater base, (our Author must under­stand that an Horizontal surface is the base, and sustains the pressure) and con­sequently a greater resistance, which ma­keth the same weight of less effect. It is e­vident that a weight of lead cannot press two foot in square, so much as one: yea the pressures of the same weight are al­wayes caeteris paribus in reciprocal propor­tion with the surfaces they press; as it is known by all Mathematicians, except on­ly such pitiful ones, as our Author.

The twelfth is evidently false; for, if ye take a bladder, or any tender vessel half full of water, and put the sides of it toge­ther, the fluid shal be moved from the un­equal pressure of the vertical surface.

The one half of the thirteenth is a part, but a very smal one, of Archimedes's se­venth, and eigth: The other half is also a smal parcel of Archimedes's sixth.

His fourteenth is so much as he under­stands [Page 37] of Archimedes's fifth, and Stevinus's fifth.

The fifteenth, seventeenth and nine­teenth are false; unless the fluid have a spring, or be heterogeneous; none of which he hath made out: but if it were made out, the thing is obious, and noticed by M. Boyl in the thirty-sixth Experiment; yet only in the Air, which is known to have a spring.

His sixteenth is ridiculous; seing we see daily fishes, little particles of earth, horse hairs, and many other such bodies betwixt the surface and bottom of the wa­ter. Yea by adding a sufficient quantity of lead to a body lighter in specie then water, it may be made practicable: and is demon­strat both by Archimedes and Stevinus, sup­posing the water homogeneous; the con­trair of which, our Author hath not yet made out. And more, even a bodie consi­derably heavier in specie then water, beaten out thin and broad, especiallie if it be con­cave below, may be suspended for a consi­derable time betwixt the surface and bot­tom of the water, providing it be laid pa­rallel to the Horizon. But passing by all [Page 36] [...] [Page 37] [...] [Page 38] this, his method is unpracticable, and sup­poseth, without proving any thing, that wa­ter can suffer any degree of compression; and stones, lead, with other bodies, none at all.

His eighteenth is the same with Archi­mede's seventh, and Stevinus's eighth.

His twentieth is the same with his se­venth, otherwayes he grants it not exactly true.

His twentyone (as he wordeth it) is most manifest from that Statical demonstration I mentioned: For seing pressures of the same weight are in reciprocal proportion with their resistances, and the resistances or resisting surfaces can be diminished in infinitum; it is evident that the least weight can produce any pressure, whether the hea­vy body be fluid or solid. But he explica­teth himself otherwayes, relating to the spring of fluids, which is not yet proven in any fluid, save Air; and besides this, the Theorem is ridiculous, seing the spring of any part (where all are equally pressed) is equal to the spring of the whole: for one pound weight presseth one foot as much, as two pound presseth two; and even so in any spring.

[Page 39] His 22. and 23. are made manifest by Pecquet in his fourth Experiment, and M. Boyl in his 19. Physico-Mechanical Expe­riment, yea throughout all that book and many others, constantly calling the weight and spring of the Air diverse, and yet brin­ging them both in for that same effect.

The 24. is ridiculous; seing it is true and obvious in all things, if there be no pe­netration of bodies.

The 25. is evidently false, seing wa­ters upon the tops of hills support less, and in valleys more. Yea Doctor Wallace sho­weth in his Mechanicks, pag. 728. that the Mercury both in M. Boyls Baroscop, and his, fell sometimes at Oxford below 28. inches, and other times above thirty, and in the page 740. he mentioneth unquestio­nable experiments of 34. 52. and 55. in­ches. The contrair of this Theorem is al­so evident from many of our Authors own experiments, if any man think them wor­thy the looking over. And suppose he had hit right, this is nothing but the old To­ricellian Experiment.

His 26. is imperfect; first, seing he speaketh only of fluids to be pressed up, it [Page 40] being also true in all other bodies. Se­condly, he doth not determine how far the sphere of activity reaches; and yet all this is easily done and demonstrat from Stevinus his 10. For the body is pressed up, till it together with the fluid betwixt it and the bottom (not regarding what else inter­veen, but reckoning all for fluid) be equal in weight with a column of fluid, whose height is the same with the height of the fluid, and its base the same with the base of the former fluids portion, or equal to it: and besides all these, this is not different from M. Boyls eleventh Paradox.

His 27. is to say, that a pound of wool weigheth as much, as a pound of lead.

His 28. is the same with that which he would say in the 4. and is true also in so­lids; if ye speak only of columns: For two unequal columns of the same hight and matter press equally, seing their re­sistances are proportional with their weights. In fluids (as I said alreadie) it is the same with Archimedes's Second.

His 29. might have been more general, to wit, That there can be no motion in fluids, without an unequal pressure: And then it [Page 41] had been the same with Archimedes's first position.

His 30. is also a part of Archimedes's first position. For seing pressure is jud­ged only by expulsion the effect of it; and the expulsion is always caused where the least resistance is, which may be in a croo­ked line: wherefore then is not pressure also in crooked lines?

His 31. is the 10 of Stevinus. Here again he justleth with that great difficulty, which I discussed in the 4. and telleth there is no way to answer, but his.

In his 32. the Pondus & Potentia, are to say in plain Scots, a pressure and a resistance. He hath told in his 5. that in all fluids there was a pressure; but now it comes in his head, that a man may fancy a pressure with­out a resistance; & therefore he must guard against that. I suppose here, that his defini­tion of the Staticks is new; otherwise the Tron-lords are the greatest professors of it.

His 33. is to say, that there must be a motion, when the pressure is greater then the resistance; which is yet a part of Archi­medes's first position, and never doubted of by the greatest ignorants.

§. II. The Authors last Theorem, for its good ser­vice, examined by it self.

NOw let us examine his last Theorem, which certainly should be the utmost reach of his wit; and therefore I will exa­mine it more narrowly.

First, let his two fluids in aquilibrio be, Water the one, and Quick-silver the other, The natural weight of Water being 1. the natural weight of Quick-silver is 14. Therefore according to his Theorem; as 1. the weight of the one is to 14. the weight of the other, so is the height of the one, to wit, Water, to the height of the other, to wit, Quick-silver: and therefore the Quick-silver should be 14. times higher then Water, which I leave to be determi­ned by experience. He should have said, as the natural weight of the second, is to the natural weight of the first: Or rather, that their altitudes are in reciprocal pro­portion with their weights, or in direct proportion with their levities.

Secondly, then in his progress, he saith, [Page 43] That by what proportion the one liquor is naturally heavier or lighter then the other, by that same proportion the one Cylinder is higher or lower then the other: here insinuating, that the weights and levities of two bodies are in the same proportion; and yet their proportions are reciprocal, and that is to say, just contrair: or other­wise, he must take the heights proportio­nal with the weights, and the lowness with the levities; which are both false. At last, when he comes to his example, he makes the heights proportional with the levities, which I grant to be his meaning; but this showeth an intolerably confused wit.

Thirdly, even this being granted, I shal demonstrat, that it doth contradict almost all his Theorems. And to that purpose, I assume these two Postulata.

Post. 1. Fluids which have their weights or pressures proportional to their profundities, can have no Bensil: For if they have a Bensil, their pressure is not proportional to their profundities, (as I did demonstrat at his 8. Theor.) which is against the hypothesis.

Post. 2. Quick-silver or water, have their weights and pressures in proportion with their [Page 44] altitudes. At least, so far as any man yet hath made tryal; as M. Boyl witnesseth in the first Appendix to his Paradoxes: yea, our Author affirmeth it of all fluids, in his 8. Theor. and many places of his Experi­ments. The demonstration follows.

Here upon the surface of the Earth, let the height of a Cylinder of Mercury be A, its weight, or the weight of the Cylinder of Air counterpoysing it B, the height of this Cylinder of Air C. Also let the same Cylinder of Mercury be lifted up some distance from the Earth, and the Mer­cury will fall, so that the Cylinder of Mer­cury is now lower, whose height we call D, and weight, or the weight of its counter­poysing aërial Cylinder E, the weight of this aërial Cylinder F; let the proportion betwixt the weights of Mercury and Air be as G unto H. By our second postulatum, A is unto D, as B is unto E; and by this 34. Theorem, H is unto G, as A is unto C: and also H is unto G, as D is unto F; and there­fore A is unto C, as D is unto F; & permu­tando, A is unto D, as C is unto F; but A is unto D, as B is unto E; And therefore B is unto E, as C is unto F; and consequently (by [Page 45] the first Postulatum) the Air hath no Bensil; which is contrair to many of his Theorems, and all his Experiments.

This destroys all his methods of measu­ring the height of the Air, Clouds, and At­mosphere, both here and in his Ars magna & nova. He might have known this mistake many years ago; for M. Boyl rejecteth this proportion betwixt the altitudes of the Air and of the Quick-silver in his 36. Physico-Mechanical Experiment, upon the same account. This letteth our Author see, that if fluids have no Bensil, his Theorem was obvious, and known to all.

§. III. The Authors great skil in Dioptricks, examined.

IN his third Observation, he maketh him­self exceedingly ridiculous. For, first, he showeth hot how much the Telescop re­quired, should magnifie.

Secondly, he showeth not how far the Telescop should be drawn out for this ef­fect; for that draught which serves for a di­stinct and clear sight, will not serve exactly [Page 46] to project an Image; seing sight requireth always parallel, or diverging rays, and the projection of an Image, converging.

Thirdly, he seemeth to attribute the magnifying of Telescops to their length and goodness of the glasses; and yet there may be the best glasses imaginable placed in their due distance in a tube of 50. foot long, and not do so much as an ordinar tube of 5. inches; and yet both the glasses may do wonders with others which give them their due charge.

Fourthly, he requires both the glasses to be very good, and there is no excellency required but in the object glass.

Fifthly, he speaks of the Image, as if it were both near to the Tube, and far from it; and yet it hath one determinat place, the draught of the Tube never being alte­red, which he never once mentioned.

Sixthly, he speaks of the Image of the Sun, that it is the more distinct, the nearer the glass; and yet this brightness near the glass, is nothing but a confused concurse of rays.

Seventhly, when he hath observed his inches, he reduceth them not to degrees, [Page 47] minuts, or seconds, &c. for the Suns mo­tion is not reckoned in inches.

Lastly, suppose he had done all these things aright; this method hath been ordi­narly practised above these thirty years: Let him look Hevelij Selenographia, Schei­neri Rosa Ʋrsina, and Doctor Wallace in the end of his Arithmetica infinitorum.

It is here to be observed, that these Au­thors by such observations designed not to render the Suns motion sensible to the eye. (which our Author values so much, and by some here was formerly called ridicu­lous) but only to observe its spots toge­ther with their motion, or else its eclipse: noticing only by the way, that swift mo­tion of the Suns Image, which was trouble­some, and constrained them oft to alter the position of their Telescop.

§. IV. Our Authors new Diving Ark, put to tryal.

THere is nothing in which our Author is more mistaken, then in his Diving Ark; for in all his discourse, he not only [Page 48] contradicts himself, (which is ordinar, and no great matter) but also the general do­ctrine of the Hydrostaticks. I shal there­fore, to undeceive his Reader, demonstrat, That his Dyving Ark sustains precisely as much pressure under water, as if it were hung in the Air with as much water in it, as now it hath of Air, rebating only a smal matter which the compressed Air in the Ark weigheth. I do it thus.

In his own figure, pag. 179. let PQ be the sufface of the water within the Ark, PY the distance of that surface from the upper horizontal surface, NY the distance of the top of the Ark from the upper sur­face. According to his 7. Theorem, the pres­sure is equal at P and at 4; and therefore according to his 8. Theor. seing the water hath no sensible spring, the pressure at N without the Ark is to the pressure at P, as YN to YP; therefore the pressure at PQ, overcometh the pressure without the Ark at EH, by the pressure of a column of wa­ter, whose base is PQ, and the altitude HQ; but the pressure at EH within the Ark, wanteth only the weight of the co­lumn of Air PQHE, to make up the [Page 49] pressure at PQ; therefore the pressure within at EH, exceedeth the pressure without at EH, by the weight or pressure of a column of water, whose base is PQ, and altitude QH, abating the weight of the column of Air PQHE; Which wa [...] the conclusion to be demonstrated.

I demonstrat this conclusion, supposing no man within the Ark; but if a man be there, it holds only of the Air about him, taking the man to be equal in weight with so much water. I would gladly know if our Author now would affirm, that, sup­pose the Ark were no stronger in the sides then a wine glass, yet it might go down 40. fathom without hazard, and that it may have a glass window a foot in square, and holes in the top, wherein ye may put your little finger: Yet I shal help him in one particular; There is more hazard in the first three fathoms, for the bursting or lee­king of the Ark, then in the next three hundred, seing the space filled with Air groweth less. Are these the great matters, which our practical Mathematicians in­vent, whilst others are nibling at petty de­monstrations?

§. V. The honourable M. Boyl vindicated from our Authors ignorant censure, in his Exper. 17.

I Resolved only (having considered the extraordinary pains it would take to exa­mine all the non-sense, contradictions, ab­surdities, and superfluities in his Experi­ments and Observations, which almost every page is filled with) to take notice of these he mentioned in his Edict: but seeing him so bold, as (in his 17. Experiment) to insult over that learned Gentle-man M. Boyl, I must, by permission of more learned Pens, which this great mans vindication doth deserve, undertake to demonstrat the truth of what M. Boyl affirmeth: that is to say, That the water REF (see the Authors fig. 24.) weighed in the Air, is of the same weight exact­ly, which it hath weighed in the water, accor­ding to M. Boyls method. I do it thus.

By my former Demonstration, before the water EFR enter the glass, the glass PR, is as much pressed upward in the wa­ter, as it would be pressed downward in the Air by its fill of water, rebating the [Page 51] weight of the Air now within it: There­fore the weight which keepeth the glass PR, in aequilibric in the water, must be the same with the weight of its fill of water in the Air, substracting the said weight of Air. Now when the water EF entereth, the glass PR is as much pressed upward in the water, as it would be pressed downward in the Air by EPF, full of water, rebating the weight of the Air EPF, which is the same with the former: and seing at first the pres­sure of the glass upward, was equal to the weight of all PR, full of water rebating such a weight, and now the pressure is on­ly equivalent to the weight of the water EPF, rebating the same weight; the pres­sure of it is now diminished by the weight of the water ERF: but the pressure is like­wise diminished by the weight put in the scale O; and therefore that weight is equal to the weight of the water ERF, in the Air; Which was the conclusion in question.

All that our Author speaks against this, is to no purpose. First, he saith, that tho lead casteth the ballance; but that cannot be, seing the lead was there, before the bal­lance was casten. He concludeth, That water [Page 52] doth press in water, but not weigh in water: I will not call this non-sense, but only retort, that upon the same account, Air will not weigh in Air; and yet I believe, he thinks, that he hath weighed Air in its self. It is like, he may say, that this is done by the Toricellian tube, where the air is exhausted: so might M. Boyl have said, that is in a glass buble, where the water is exhausted: And I may also say of this whole Hydrosta­tical doctrine, that it is exhausted also, and can be no longer, without prejudice, kept back from its grave.

THis waterish doctrine hath past off with more credit then it deserved, ha­ving gasped out its last by vertue of that noble name, The Honorable Robert Boyl. I doubt not, Reader, but by this time thou art made weary by it; and so am I. Where­fore unwilling to return, and rake up its ashes, to thy further annoyance and mine, I shal go forward to the Ars nova & magna, and quickly show thee what novelty and greatness is there, without any prefacing; having no other testimony for it, then what is due to the rest of its fellow-works.

EXAMEN ARTIS NOVAE ET MAGNAE GEORGII SINCLARI.

CAP. I. Tres primi Libri Dialogorum Philosophi­corum, & duo de Instrumentis Hy­dragogicis examinantur.

§. I. Hic rejicitur Authoris Theorema primum.

LIb. 1. 2. & 3. de Baroscopij phaenomenis agitur: quod Baroscopij vocabulum, sicut & quaedam alia, se primum excogitasse gloriatur Author, Regiamue Societatem plagij accusat, acsi ea è suis Manuscriptis compilaverit; licèt res ipsae jampridem extiterint.

[Page 54] Dial. 1. lib. 1. Varia proponuntur theo­remata, quorum primum (quod tantum­modo divisio est, quam membrorum defi­nitiones sequuntur) sie se habet. Quod cor­porafluida, uti Aqua, Aër & Hydrargyrus, duplicem videantur habere gravitatem, unam Sensibilem, aliam Insensibilem. Eam appello (inquit) gravitatem Sensibilem, quam sentio, dum verbi causa, amphoram aquae plenam, à terra manu allevo & sustollo; quod quidem om­nium aliorum corporum gravium, etiam est pro­prium. Gravitas Insensibilis, fluidorum solum­modo proprium, est illa vis & potentia quâ cor­poraseipsis leviora sursum pellunt, &c. Vir­tute hujus, ait Author sub finem Sect. 2. Cir­cumsusum hunc aërem aequipondium efficere cum Hydrargyro, vel aqua, adminiculo tubi in forman Cylindri redacta. Sed haec definitio nullatenus convenit isti potentiae, quâ aër cum aqua tubi constituit aequipondium, nam virtute ejus, aër aquam (quae est cor­pus gravius) in tubo sursum pellit. Nec convenit aquae; nam haec in tubo, corpus le­vius viz. aërem deorsum premit aut pellit. Sidicatur, quod aqua tubi aërem prius qui­dem deorsum premit, sed sic premendo, eundem etiam necessario sursum pellit in [Page 55] locum cadentis aquae: Respondebitur, Obeandem rationem, lapidi cadenti gravita­tem istam insensibilem similiter compe­tere; quam tamen, supra assertum est, flui­dorum esse propriam.

Theorema tertium Sect. 5. est falsum; nempe, Aqua & id genus alia corpora fluida in libra naturali pendentia, gradatim insensibi­lem deperdunt gravitatem, prout gradatim re­clinatur tubus vel Siphonis crus horizontem ver­sus. Hoc fundamentum est totius doctrinae, lib. 1. & 2. Dialogorum Philosophicorum, & duobus libris de instrumentis Hydrago­gicis, traditae; praeterea, id passim fere praesupponitur in plerisque corporum flui­dorum phaenomenis, per reliqua authoris opera solvendis. Qualis sit illa doctrina, hujus Theorematis eversione apparebit.

§. II. Theorema praedictum fundamentale de sluidorum gravitate Insensibili evertitur.

JUxta nostri authoris doctrinam, praeser­tim lib. 1. de Instr. Hydr. dial. 2. & lib. 2. dial. Philos. Dial. 3. Sect. 2. Hydrargyti [Page 56] cylindrus 29. digitis altus aequiponderat cylindro aëris eandem cum ipso basin ha­benti & altitudinem eandem cum Atmos­phaera. Hinc, in ordine ad sequentis pro­positionis demonstrationem, hoc colligo postulatum.

Postul. 1. Gravitatem insensibilem esse eam, quâ Hydrargyri v. g. Cylindrus dictae aëris columnae aequiponderat: & proinde, quò major est haec aëris columna, eò major est etiam Hydrargyri gravitas insensibilis; ita ut, si una aeris columna, alterius sit dupla, tripla, &c. erunt item cylindrorum hydrargyri illis aequi­ponderantium gravitates insensibiles una alte­rius dupla, tripla, &c.

Alterum postulatum deducitur è lib. 2. dial. 1. Sect. 10. & lib. 2. dial. 2. dial. Phi­los. Sect. 5. ubi praeter alia, haec habet ver­ba. Nam inde inferre licet, si divinâ providen­tiâ aëris altitudo augeretur; cylindri mercuria­lis altitudinem in Baroscopio similiter, servatâ nimirum proportione, majorem evadere. Et si eâdem providentiâ, ejus altitudo minueretur, minorem etiam Hydrargyri altitudinem fore. Hinc inquam colligitur postulatum 2. quod sic se habet.

Postul. 2. Cylindrorum hydrargyri aequales [Page 57] bases habentium, gravitates insensibiles sunt in directa altitudinem proportione. Nam cy­lindrorum hydrargyri aequales bases ha­bentium, duplò altior, aëris aut aquae du­plo aequiponderat, & triplus triplo, &c. Quod etiam patet ex Sect. 8. & 9. Dial. 1. lib. 1. Dialog. Phil.

Nunc sequitur propositio de­monstranda Theoremati praedicto contradictoria.

Sisint duo tubi 29. digitis hydrar­gyri repleti, aequè longi, & aequè cras­si, superiori orificio occlusi, quorum alter sit ad horizontem rectus, viz. tubus DF, & alter ad horizontem Fig. 1. reclinatus; viz. tubus DB; Dico utrumque tubum aequalem habere gravitatem insensibilem.

Producatur cylindrus DB usque ad KH, ut sit ejusdem altitudinis cum DF, ducatur etiam QB ad angulos rectos cum DK, & CH, quae aequalis erit basi DG, propter aequalem cylindrorum crassitudi­nem. His factis.

Est insensibilis gravitas cylindri DF, ad insensibilem gravitatem cylindri DH; ut DG, ad DC, ceu QB, ad AB. Etest [Page 58] insensibilis gravitas cylindri DH, ad in­sensibilem gravitatem cylindri DB; ut DK ad DE, seu, ut AB ad QB. Er­go ex aequalitate ordinatae, Erit insensibilis gravitas cylindri DF, ad insensibilem gra­vitatem cylindri DB; ut QB ad QB: h. e. sunt aequales. Quod erat Dem.

§. III. Causa erroris in praecedenti Theoremate ab Authore commissi detegitur.

QUoniam hoc theoremate fretus, in u­troque volumine, ubicunque de flui­dis fir sermo, passim fere hallucinatur Au­thor; non ab re duxi, erroris in hoc theo­remate fabricando originem detegere, quae est haec. Observavit, quod idem tubus ea­dem mole hydrargyri aut aquae repletus, versus horizontem reclinatus, aequipon­dium cum aëre non cōstituat, sicuti fecerat, dum fuit erectus: inde putavit ille, ejusdem hydrargyri pressuram in subjectum aëra debiliorem esse in situ obliquo, quàm in recto: nequaquam animadvertens eandem vim aut pressuram manere posse aequalem, licet ob incrementum resistentiae de novo [Page 59] adveniens, minus quàm antea efficacem: ut res se habet in hoc casu. Nam hydrar­gyrus tubi dum est erectus, premit in basin cylindri aërei circularem, suae basi circu­lari aequalem: cum verò tubus est reclina­tus, idem hydrargyrus premit in basin cy­lindri aërei Ellipticam basi tubi circulari majorem, ideoque in majorem aëris cylin­drum, quam tubô existente erectô. Ac proinde non mirum, si eadem pressura cy­lindri hydrargyri, tubô existente reclina­tô, non possit adaequare resistentiam majo­ris cylindri aërei ad constituendum aequi­pondium, sicuti resistentiam minoris cy­lindri aërei sibi aequiponderantis adaequa­vit, dum fuit tubus erectus.

Novi objici solere, fluidum magis inni­ti interioribus tubi reclinati partibus, quàm erecti; ac proinde non aequè premere in subjectum aëra, in utroque situ. Sed Re­spondetur, hoc argumentum nihil facere contra praecedentem Demonstrationem; nam quantò magis premuntur pàrtes tubi reclinati interiores circa CB, quàm toti­dem partes erecti; tantò minùs inde pre­muntur partes interiores circa DA, quàm totidem tubi erecti partes: (quae omnes [Page 60] semper in eadem altitudine aequaliter pre­muntur.) Et consequenter, totus tubi mer­curius simul sumptus, aequaliter innititur tubo, in utroque situ: seu quod idem est, quantò debilitatur gravitas, seu vis deorsum pellens cylindri mercurialis, ob reclinatio­nem lateris CB, tantò etiam debilitatur resistentia, seu vis sursum pellens mercurij stagnantis, ob inclinationem lateris DA: ut optimè illustrat D. Wallisius in sua Me­chanica, pag. 717.

Per hydrargyri gravitatem insensibi­lem, nihil aliud quam pressuram, quod ad aequipondium cum aëre externo, nunc ma­gis nunc minùs efficacem, ob resistentiam nunc minorem nunc majorem intellexit hic auctor: sed quia nunc majoris nunc minoris in hac pressura efficaciae rationem ignoravit, quando scilicet tanta sit, quanta ad constituendum aequipondium sufficit, quando non; ideo Gravitatis insensibilis for­midabile nomen commentus est egregius hic vocum non rerum novarum artifex.

§. IV. Septem absurda praeter supra refutatos errores in praedictis Dialogorum Philosophico­rum libris, notantur.

PRaeter duorum librorum Artis novae & magnae ineluctabile fatum, praedicti theorematis ruinâ, labuntur duo libri de instrumentis Hydragogicis, tum quoad theoriam, tum quoad praxes circa non ens, (Gravitatem scilicet insensibilem) plane chi­maericas: quos igitur absque ulteriori exa­mine missos sacio, quibusdam tantummo­do absurdis ibidem obiter notaris.

Primum absurdum committit Author si­bimet contradicendo, dum lib. 1. de instr. hydrarg. Dial. 2. sect. 3. haec verba habet: Tubò situm horizontalem habente; ut ABC, totum mercurij pondus interioribus tubi lateri­bus innititur: proinde (que) nullum potest habere co­natum exeundi apertô orificiô A, —quare nequit hydrargyrus illius tubi, utrumlibet extre­morum A vel O urgere, id est, horizontaliter moveri, sed deorsum solum id (que) juxta lineas à terrae centro rectas ductas. Haec inquam con­tradicunt tum primae Archimedis positioni, tum etiam Authoris theoremati, sect. 7. dial. [Page 62] 1. lib. 1. dial. Philos. viz. Corporafluida, utiaër, aqua & hydrargyrus quaquaversum, uni­formiter, & ex omni parte aequaliter urgent & premunt. Etiam experientiae; nam apertô utroque tubi orificiô, effluet hydrargyrus; quod fieri non posset, nisi utrumque ejus extremum mercurius urgeret.

Secundum absurdum est quod occurrit in fine sect. 10. Dial. 1. lib. 2. de instr. hydrarg. Non improbabile hinc deducimus argumentum ad probandum maris summum, montium verti­ces altitudine adaequare, ubi aquarum fontes re­periuntur. Videtur auctor altissimae rupis Forthdnae Bass dictae (ut nihil de alijs lo­quar) perquàm oblitus, dum haec scribe­ret, in cujus summo vertice plusquam 50. ulnis supra maris summum, Fons aquae du­cis habetur. Simile est illud problema, lib. 2. Dial. Philos. 1. sect. 12. quô docetur, ope Baroscopij investigare montiúmne ca­cumina, an maris summum sit altius, aequa­lémne habeant altitudinem.

Tertium absurdum, est problema illud, lib. 2. dial. 1. Philos. quô ex diversis hydrar­gyri in Baroscopio altitudinibus, & altitu­dine montis aut pyramidis, per regulam Trium, Atmosphaerae altitudinem esse [Page 63] 6876. passuum, totiusue aëris quantita­teni secundum reliquas ejus dimensiones colligit & determinat; nam secundum hanc praxin evidens est, aërem ab imo ad Atmosphaerae summum, aequaliter esse den­sum & gravem; aliàs proportio non tene­bit: Et tamen lib. 6. Dial. Philos. 2. sect. 7. ascribit auctor aëri claterium, item lib. 1. Dial. Philos. 3. sect. 9. asserit partes aëris inferiores multò majori compressioni sub­esse, quàm superiores; & per consequens, quò terrae propiores, eo compressiores.

Quartum absurdum est in sect. 1. Dial. 2. ejusdem libri, viz. determinatio morae co­metarum supra horizontem absque consi­deratione declinationis, per solam à terra distantiam; quasi ratione solius distātiae ma­joris, eo majorem haberet cometa moram supra horizontem, & ratione solius distan­tiae minoris, eo minorē: cum cometa intra octingenta milliaria ad terram, absque ullo occasu, motu primi mobilis, circumvolvi possit, (etiam supposito terrae ambitu, quem ponit Author 21600. milliarium) nempe si existat in axe mundi, vel eò circi­ter: & 1. contra, è stellis fixis quaedam sunt, quae nullam omnino habent moram [Page 64] supra horizontem, & aliae quae non ultra unam, duas, vel tres horas a nobis conspi­ciuntur, etiamsi lunâ sint multo altiores.

Authoris imbccillitatem miseratus, re­gulam sequentem, quâ suorum cometarum supra horizontem sensibilem moras com­putet, construxi.

  • Sinus altitud. pol. bor. = a
  • Sinus altit. aequat. = b
  • Cos. declin. verae = c
  • Ejusdem sin. = d
  • Semidiamet. terrae = e
  • Distant. Cometae = f
  • Sinus totus = r

Reg. Si declinatio sit australis, erit semper cosinus arcus semidiurn [...] supra horizontem sen­sibilem [...]; At si haec radio major sit, nunquam oritur cometa.

Si vero declinatio fuerit borealis, & [...], erit ejusdē arcus semidiurni cosinus [...]: Et si haec radio major sit; non oritur cometa.

At si declinatio sit borealis, & [...]; ar­cus semidiurnus supra horizontem sensibilem superabit quadrantem, erit (que) sinus excessus, quo [Page 65] dictus arcus quadrantem superat [...]; Et si haec radio major sit, cometa non occidit.

Et tandem, si declinatio sit borealis, & [...], erit dictus arous praecise quadrans.

Quintum absurdum, est assertio quam ibi­dem habet, viz. Nos juxta terrae superficiem ad 70. vel 80. milliaria prospicere posse: Cum cuilibet in Elementis, Euclidis versato, ex Prop. 36. lib. 3. & prędicto terrae ambitu, demonstratu facillimum sit, hominis octo pedibus alti prospectum ad quatuor millia­ria non extendi.

Ut ad unguem solvere possit hoc pro­blema vel ipse Dromo, hanc a me habeat re­gulam generalem.

Sit terrae diamet. = a

Hominis altit. =b

Srit semidiam, horiz. sensib. = [...].

Hinc positô terrae ambitu milliarium 21600. & hominis altitudine 8. ped. Erit semidiame­ter horizontis sensibilis, milliar. 3'32. quàm proxime.

Sextum absurdum, est contradictio inter Authoris scripta; nam scribens de lagenae descensu in mare profundum, lib. 2. Dial. [Page 66] Philos. 4. sect. 10. sic ait, Necesse est, quum quò altior est aqua, eò validius & fortius eva­dit ejus elaterium: seu, quod idem est, pressura. FRANC. Fortiúsne similiter evadit incarce­rati aëris elaterium? ALEX. Haud dubiè: semper tamen manet aquae elaterio debilius. Et Dial. 5. sect. 6. ejusd. lib. istis apertè con­tradicit; ubi enim de quodam Barosco­pij intra campanam urinatoriam aquae im­mersam phaenomeno, & accuratissimo in­ter aquam ambientem, incarceratumue, aërem, aequipondio, verba fecisset, addit: Verbô, incarceratus campanae aër, eâ 34. pe­dibus demersa, eidemmet subest elaterij gradui, cui aqua proxima, &c.

Septimum abfurdum, idque peccans ad­versus elementa Geometrica, tale est, lib. 4. Dial. Philos. 1. sect. 8. circa sinem, dum ostendit duo plana aenea rotunda dia­metri 3. digit. pondere praecisè 100. li­brarum, pati separationem, quia cylin­drus aëreus, cujus pressura uniuntur, 100. libris est gravis; addit, Si duplò minoris fo­rent diametri, tum 50. pondo sufficerent: Si duplò majoris forent diametri priore mensura, non minùs 200. libris est appendendum. Hic evidenter supponit noster Author, circulos [Page 67] inter se esse in simplici proportione diame­trorum: quod falsissimum est: nam ex Prop. 2. lib. 12. Elem. Eucl. Circuli inter se sunt, quemadmodum quadrata à diametris, & ex Prop. 20. lib. 6. El. Polygona similia du­plicatam habent: eam inter se rationem, quam latus homologum ad latus homologum: Ergo circuli sunt in duplicata ratione diametro­rum: Consequenter, si corpus aeneum pla­num & rotundum diametri 3. digit. ad se­ipsum à simili separandum, pondus praecisè 100. librarum requirat, tunc planum aec [...]e crassum duplò minoris diametri, requi [...]t tantùm 25. libras; & planum duplò ma­joris diametri requiret 400. libras.

Similiter errat lib. 2. Dial. Philos. 3. sect. 9. dum ait, Cylindrum aereum trium [...] ­guorum in diametro, 100. libris esse gravem-Volam manus totidem supportare. Tergum ho­minis proni, sextuplum. Nam sic facit volam (novem ad minimum digitos quadratos continentem) circulo trium digitorum in diametro aequalem: Et quod ad tergum hominis proni, pedi quadrato seu 144. di­gi [...]is quadratis ad minimum aequale, at­tinet; imo ex suppositione, quod quadra­tum trium digitorum, 100. tantum aërus [Page 68] libras supportet, (quot ipse circulus aequa­lis diametri posse, locis citatis affirmatur) secundum duplicatam laterum rationem, 1600. libras sustentabit; & tamen juxta Authoris nostri praxin Geometricam, 600. tantummodo libras supportat.

CAP. II. Reliqui Dialogorum Philosophicorum li­bri leviter perstringuntur.

LIb. 4. de Vacuitate prolixè satis tractatur, de quo lectorem Philoso­phicum appello, siquid in eo, de va­cui existentia, praesertim in Baroscopio post hydrargyri delapsum, positivè ne­dum solidè determinatum, indial. 2. specia­tim, aut alibi reperiat: Anne sibimet hac de re contradixerit Author, affirmando in hujus libri dial. 3. sect. 8. Aliquod corpus spatium hydrargyri delapsi in Baroscopio occu­pare: & dicendo, sect. 3. Dial. 2. ejusd. lib. Satis improbabile esse supremam tubi par­tem aethere repleri; Cum nihil per Aethera in­telligat Cartesius, quàm corpus aëre subti­lius. Númne etiam rectè assignaverit Au­thor vulgarem opinionem, scil. Naturam [Page 69] penitus ab inanitate abhorrere, pro fundamen­to sententiae aethera astruentis; cum satis constet, talis corporis necessitatem, ex sen­tentia Cartesij, ab identitate Corporis & Spa­tij unicè dependere; nequaquam verò ab ulla naturae Exhorrescentia aut Appetitu, quem solis Viventibus attribuit.

Adhaec, lectorem Philosophicum appel­lo, de rationibus, lib. 2. dial. Philos. 2. pro Vacuo disseminato: quantum ijs insit ponderis. Num etiam Deusingio, spatiola inter partes aeris disseminata probanti esse aliquid, propter ipsorum trinam dimensio­nem, repugnantiam sapiant distinctiones, lib. 4. dial. Philos. 3. sect. 2. adhibitae, scil. Dimensionum, in Reales & Spatiales: Alicu­jus, in Aliquid reale & Spatiale; Nihili, in nihil reale & Spatiale? Númne hinc etiam sequatur, (quod alibi asseritur) Spatium esse nihil; Corpusue esse in spatio, idem esse, ac Corpus esse in Nihilo?

Librum quintum de Antliae Phaenomenis missum facio: Libri etiam sexti tentamina ad Motum perpetuum puerilia; Libros item de Instrumentis Hydrag [...]gicis, quos cap. 1. §. 1. & 2. funditus eversos cuivis est in propatulo.

[Page 70] Sequitur liber de Hygroscopio & Chrono­scopio; de illo, praeter vocabulum, alia non­nulla ab ipso, alium quendam mutuatum esse veretur Author. Et tamen rem ipsam a Baptista Porta, si non etiam ab alijs, se ha­bere fatetur. Ea quae de Chronoscopio, Capi­te sequenti castigabuntur.

CAP. III. Probatur universa Authoris doctrina de Pendulo esse falsa.

DIal. 3. sect. 1. de Pendulo, haec ha­bet verba: Fateor hoc opus eò dif­sicilius & laboriosius fore nobis, quod neminem adhuc viderimus, quorum dicta vel scripta consuleremus, & quorum vestigijs, si opus foret, insisteremus. Ideo sect. 3. Nostrum appellat Chronoscopium, licet non recens excogiratum. Authori credo, artificium enim sapit artificem; nam ne vel unam ve­ritatem de Pendulo demonstratam conti­net, sed merits est elrorum fasciculus; ut in progressu patebit. Interim, quàm maxime observanda est Authoris nostri fiducia ina­nis, qui, absque ope Geometrica, Motus phaenomena aggreditur. Sed ad rem ipsam redeamus.

[Page 71] Normam ex aere vel ferro, multo plus amplitudinis quam crassitudinis parari ju­bet: in cujus altero extremo fiat forami­nulum, per quod ingressus claviculus sus­pensum radium sustentet, ut videre est in figura Sect. 2. Vult etiam normam esse 60. digitis longam, & totidem uncijs gra­vem. Pag. 555. Dein praecognita quae­dam tradit, unde conclusionem quandam deducit, & hinc propositiones suas de Penduli Phaenomenis.

§. I. Praecognita ad propositiones de pendulo, examini subjiciuntur.

DIal. 4. Sect. 3. distinguit Author in pendulo, motum perpendicularem & circularem, & rursus in hoc, sect. 7. mo­tum perpendicularem & horizontalem. Di­vidit etiam gravitatem in perpendicularem & circularem: Ratione illius (inquit) placi­dè quiescit pendulum, finitis vibrationibus in perpendiculo AB, cum appetitu tamen natura­li [...]endendi deorsum sublatô claviculo centrali. (vide Authoris figuram) Circularem gravi­tatem subdividit in circularem descendentem, [Page 72] & ascendentem; virtute prioris, ait pendulum ferri deorsum in semicirculo à puncto H ad B: virtute posterioris sursum ferri à B ad R.

Quod ad distinctiones has, lectorem ad­vertere velim, quomodo ulla gravitas dica­tur ascendens, cum ipse Author, lib. 1. dial. Phil. 1. fect. 6. sic definiat, Gravitas est potentia intrinseca, quâ aptum natum est corpus ferre deorsum. Insuper, si pro qualibet mo­tus determinatione, varias gravitatis spe­cies pro demonstrationum basi essingere li­ceat, novas in infinitum excogitabit qui­libet, v. g. Gravitatem Horizontalem, Spira­lem, Hyperbolicam, Parabolicam, Ellipticam, gravitatem Cissoidalem, &c. nam per istarum figurarum tubos potest aqua deorsum sur­súmve ferri.

En quas ridiculas comminiscitur Gravi­tatis distinctiones, pro qualibet motus de­terminatione, de qua dicturus erat: fig­mentis eum uti necesse est, qui ad proprie­tates motus explicandas se accingit, solidis, praesertim Geometricis principijs nudus: Post haec, in ordine ad propositiones se­quentes, quaedam Scienda, partim absurda, partim sibi repugnantia, pręmittit; quo­rum

[Page 73] Primum habetur Dial. 4. sect. 4. Radium scil. aeneum AB placidè quiescentem, habere solummodo gravitatem perpendicularem.

Secundum est, Radium AB ad H usque elevatum, tum gravitatem perpendicularem, tum circularem habere: priorem, quia extractô claviculo A, positò (que) planô ad terrae centrum inclinante, super quod descenderet, eò indubie progrederetur, quemadmodum lapis de tecto aedificij devolveretur, semel demissus. Poste­riorem habet, quia sublatô digito radium in H supportante, confestim ad perpendiculum AB deorsum ruit.

Tertium, Radium AB ad summam alti­tudinem G elevatum, omnem suam gravitatem perpendicularem amisisse, atque sic solam circu­larem habere. Rationem prioris hanc assig­nat, Quia nullum habet appetitum radius mo­vendi se horizontaliter. Ridiculum & fal­sum est, dicere radium AG non habere ap­petitum rectâ movendi deorsum, quia non habet appetirum movendi horizontaliter: Hinc enim sequeretur, (contra hujus sectio­nis positionem primam) radium AB placidè quiescentem, nullam habere gravitatem perpendicularem; nam non habet appeti­tum se movendi horizontaliter.

[Page 74] Insuper ibidem scribit, Dimidium gra­vitatis radij ejusdem ad summam altitudinem AG elevati, claviculô suspendi: Hinc infero, Extractô claviculo, positoue plano ad ter­rae centrum inclinante, super quod descen­deret, eo indubie progrederetur quemad­modum lapis de tecto aedificij devolvere­tur, semel demissus: (alias claviculus nul­lam supportaret gravitatem) Ergo secun­dum ipsum authorem in Sciendo secundo huj. Sect. Radius AG habet gravitatem per­pendicularem: quod negavit author in Sciendo tertio.

A praecedentibus Sciendis sibi invicem contradicentibus, infert Author Sect. 5. conclusionem hanc: Radium aneum, quò altius elevatur, eò magis gravitatem lucrari circularem: atque ex consequenti, eò magis amittere gravitatem perpendicularem: & è contrario, quò magis deprimitur, eò magis gra­vitatem circularem amittere, & ex consequenti eò magis gravitatem perpendicularem lucrari. Quomodo hoc probatum sit, Authoris verba (etiam admissa ejus distinctione gra­vitatis fictitia) manifestabunt: Inter pro­bandum, hac etiam utitur ratione. Ideo ne­quit pendulum AF (in fig. pag. 555.) plus [Page 75] gravitatis perpendicularis, quantùm ad motum rectà deorsum, habere, quam sunt unciae Radij inter 2 & A, & ratio est, quomam meo digito ejus extremum F: supportanti tot radij unciae in­nituntur, quot sunt digiti inter 2 & C, qui sunt propemodum quatuor, & ex consequenti radius sic elevatus minùs gravat claviculum, quatuor uncijs, quam radius perpendicularis AC; Quid multis? Claviculus supportat uncias radij AF: quinquaginta sex, digitus verò quatuor.

Hinc contra authorem infero. Ergo di­gitus similiter supportabit 60. uncias radij AD, (quia tot sunt digiti inter A & C) & claviculus supportabit nullas, (quia totus radius ex suppositione continet tantum 60) quod est gravissimum absurdum: & etiam contradictorium Sciendo 4. sect. 4. Item isti quod habetur Dial. 5. sect. 1. lin. 9. Quarto, claviculum 30. solum uncias penduli, ad sum­mam altitudinem AD elevati sustinere; & di­gitum, cui alterum radij extremum D innititur, totidem supportare, summatim 60.

§. II. Propositio prima de Pendulo ostenditur ridicula esse, vel falsa.

EX praedictis Dial. 4. sect. 6. propositio­nem hanc primam demonstrare cona­tur; viz. Progressum diminutionis vibrationum penduli, esse juxta sinuum proportionem, id est, singulas vibrationes alternatim se invicem bre­viores esse, eadem proportione, quâ inaequales di­visiones semidiametri AC, sunt se invicem am­pliores. Et Sect. 7. Hinc clarissime ostenditur quomodo penduli vibrationes sunt proportiona­les ad sinus, nam posito, quod à summa alti­tudine demissum, ad S usque vibraret, oportet provehatur horizontaliter inter N & MR, in primâ vibratione. In secundâ ex MR ad O. In tertia ex O ad P. In quarta ex P ad Q, & ita deinceps: sed illarum divisionum decremen­tum est ipsorum sinuum, ut patet, conferendo eas cum semidiametri divisionibus AC. Et ad­dit: Penduli vibrationes diminui cum propor­tione ad sinus, quatenus ejus motus est Hortzon­talis; non autem quatenus est perpendicularts, aliàs forent conformes etiam inaequalibus divi­sionibus semicirculi BCD, cui experientia, teste oculo, contradicit.

[Page 77] Vel hic intelligit author (dum de pro­portione sinuum loquitur) relationem quam habent sinus ar cuum aequidifferen­tium, ut apparet ex ejus figura; vel nihil solidi: cum sinus omnem inter se habere possint proportionem: & si relationem in­telligat jam dictam, erunt arcus decremen­torum omnium vibrationum inter se oequa­les, quod ipse fatetur experientiae contra­dicere: quodue absurdum ipse secutu­rum infert, si vibrationes dicerentur dimi­nui, cum proportione ad sinus, quatenus ejus motus est perpendicularis; cum tamen per easdem vibrationes consideratas ut motus Horizontales, describantur sinus recti, & per easdem consideratas ut motus perpen­diculares, describantur sinus versi: & per easdem prout considerantur distantes à li­nea horizontali, describantur cosinus ar­cuum vibrationum.

§. III. Propositio secunda de Pendulo rejicitur.

PRaecedenti propositioni falsae aut ridi­culae confisus, hanc secundam demon­strare tentat. Scil, Omnes vibrationes penduli [Page 78] esse Synchronicas. Quae quoniam priori ha­ctenus eversae innititur, cum caeteris pariter est rejicienda; observatô obiter unico peti­tionis principij levi vitio, quod in ejus de­monstratione, pro more solito, commit­titur.

Arguit enim author ab incremento gra­vitatis circularis descendentis ad incre­mentum velocitatis: quam Gravitatem, ibi­dem sciendum ait reipsa idem esse, nempe re­spectu penduli motus, cum velocitate: & hinc est, ut quot uncias gravitatis acquirit pendulum ex E ad K elevatum, tot revera gradus veloci­tatis acquirantur; quibus penduli motus effici­tur velocior. Hoc est, (per authoris Sciendum jam dictum) quot uncias velocitatis acquirit pendulum, tot revera gradus velocitatis acquiruntur.

§. IV. Rejicitur reliqua authoris doctrina Dialogo 5. tradita, de hactenus dictis, & caeteris penduli Phaenomenis.

DIal. 5. reliqua Chronoscopij Phae­nomena proponit explicanda: ubi Sect. 1. modum computandi incrementum [Page 79] gravitatis penduli, inter ascendendum, pri­mum aggreditur. Ubi notandum est, quod Dial. 4. sect. 6. lin. 14. ad probandum pro­gressum diminutionis vibrationum penduli esse juxta sinuum proportionem, hoc me­dio usus fuerat: Quia câdem proportione dimi­nuitur radij gravitas ex C ad K; vel L vibran­tis, quâ inaequales divisiones semidiametri CA evadunt se mutuò ampliores. Et ibidem dixe­rat, incrementum illud gravitatis, quod ac­quirit pendulum inter ascendendum, esse proportionale ad sinus. Haec, ut dicebam, ad praxin reducere conatur, Sect. 1. do­cendo methodum supputandi numerum unciarum radij aenei penduli 60. uncijs gravis, quas supportat claviculus centralis, & quas digitus, pro singulis penduli eleva­tionibus. Haec sunt ejus verba. Sed quo­modo definitè nôsti claviculum supportare 35½ uncias penduli AM, & uncias 40. penduli AL? (Vide fig. pag. 564.) ALEX. Extende cir­cini mucrones inter 8 & C, & sumptô hujus di­stantiae dimidio, applicetur alterum circini ex­tremum puncto M, atque oppositum in puncto N terminari invenies. Docet hoc, claviculum tan­tò plus de gravitate penduli AM sustinere, quàm penduli AD, quantò distantia AN [Page 80] est major AX, quae est digitorum 5½.

Quomodo haec cohaereant, judicet le­ctor: locis citatis, indefinitè loquitur de incremento, & etiam de decremento gravitatis Penduli inter ascendendum. Sibi quoque adversatur, nam locô prius citato, dicit incrementum gravitatis inter ascen­dendum esse proportionale ad sinus; & ta­men illud per dimidia sinuum versorum hic loci supputat. Sed si veri penduli, h. e. glo­bi filo appensi gravitatem pro quavis ele­vatione congruè computare velit author, hac regula sequenti utatur.

  • Si sit penduli longitudo = r
  • Gravitas globi dum in li­nea perpendiculari quiescit = b
  • Sinus elevationis penduli = a
  • Erit globi gravitas in elevatione data = [...]

Hanc gravitatis computandę methodum sequuntur praedicta & etiam reliqua pen­duli Phaenomena ab Authore demonstran­da. Scil. sect. 4. Penduli vibrationes juxta sinuum proportionem diminui. Sect. 5. Eas esse Synchronicas. Sect. 6. Incrementum velocita­tis penduli inter descendendum esse ad sinus pro­portionale. Sect. 7. Pendulum tam citò qua­drantem [Page 81] circuli percurrere, quàm corpus ejus­dem gravitatis & figurae semidiametrum. Sect. 8. Incrementum velocitatis penduli esse non tantùm proportionale ad sinus, verùmetiam esse juxta ordinem numerorum quadratorum, ab unitate initorum, in spatijs post aequalia tempora confectis. Sequentibus sectionibus, adducit argumentum Riccioli, quasi suum, ab incre­mento velocitatis corporum descenden­tium, adversus Copernici sententiam de mo­tu Telluris, tanquam invictissimum.

Quod ad primum, pari efficacitate id probat, quâ anteà: atque insuper hic loci novae & falsae nititur Hypothesi, nimirum, Quod nullae aliae possint excogitari divisiones, quibus proportionales dici possunt vibrationes, quàm arcus & sinus; Cum tamen omnes li­neae possunt infinitis diversis rationibus in partes inaequales dividi.

Demonstratio secundi & tertij phaeno­meni, novae & falsae nititur hypothesi: viz. Phaenomeno Sectionis septimae: quam, praeterquam quod quivis experientiae ad­versari comperiat; falsam esse, ex duobus postulatis sequentibus hic demonstrabitur.

Postul. 1. Duos globos ejusdem ponderis & magnitudinis, integram diametrum perpendicu [Page 82] larem AB circuli ADBC, & quamvis ejus­dem circuli chordam diametro perpendi­culari conterminam, aequali tempore per­currere. Fig. 2.

Hoc extra omnem contraversiam est positum, & à Galilaeo notatum, System. Cosm. dial. 4. pag. 335. secundum impres­sionem Lugdunensem.

Postul. 2. Omnes ejusdem penduli vibratio­nes esse Synchronicas. Hoc est ipsius Authoris.

Hinc contra Authorem demonstraturus sum, Duos globos ejusdem magnitudinis & gravitatis, seu (quod idem est) eundem, circu­li semidiametrum GB, & quadrantem DEB, aequali tempore non percurrere. Sumatur arcus EB indefinitè parvus, ita ut non dif­ferat à sua chorda EN, faciendo differen­tiam omni quantitate assignabili minorem: Ergo, cum (per Pôstul. 2.) globus idem quadrantem DEB, & arcum EB, aequa­li tempore percurrat: aequali etiam tem­pore percurret quadrantem DEB, & chordam EN: sed aequali tempore per­currit chordam EN, & Diametrum AB, per Postul. 1. Ergo, aequali tempore per­curret quadrantem DEB, & diametrum AB; sed (juxta hunc Authorem) aequali [Page 83] tempore percurrit quadrantem DEB, & semidiametrum GB; Ergo, aequali tempore percurrit integrum diametrum AB, & se­midiametrum GB. Quod est absurdum. Ergo, globus non percurrit circuli qua­drantem, & semidiametrum, aequali tem­pore. (contra quàm volebat hic author) Quod erat dem.

Demonstratio quinti phaenomeni, viz. Incrementum velocitatis penduli esse juxta or­dinem numerorum quadratorum, est, ut reli­quae, parenti similis; oftendit enim mirabi­lem centralis claviculi influxum in penduli motum, pro singulis momentis ad finem usque; ejusque efficientiam in penduli ve­locitatem cum proportione ad sinus: at hoc leve! Innititur praeterea haec dicta de­monstratio Phaenomeno quarto, quod fal­sum esse jam demonstravimus.

Praeter errores supra refutatos, authoris nostri ignorantiam phaenomeni istius in pendulo, quod jampridem omnibus tritum est ac vulgare, ob nimiam ejus jactantiam & insolentiam, absque nota praetereundam non esse censeo. Phaenomenon est hoc.

Si sunt duo gravia aequalia & similia, B & D, filis AB, & CD appensa: Tempus [Page 84] vibrationis penduli AB est ad tempus vibrationis penduli CD, in subdupli­cata Fig. 3. ratione AB ad CD; seu in ratione AB ad G mediam inter AB & CD Proportiona­lem. Quod in gratiam authoris nostri sic demonstratur.

Sint AB = AE, CD = CF, Tempus vibrationis penduli AB = M, Tempus vi­brationis penduli CD = N. M est tem­pus quô grave B cadit ab E, & N est tem­pus quô grave D vel idem B cadit ab F: & ideo, [...], [...]. Ergo, [...]. Quod erat dem.

Hinc in gratiam authoris, hanc etiam re­gulam construxi.

  • Ʋnius penduli longitudo sit = a
  • Alterius longitudo = b
  • Prioris tempus vibrationis = c
  • Erit alterius tempus vibrationis = [...]

Proprietatem hanc penduli, quod no­strum appellat, eum penitus latuisse, ex dial. 6. de Chronosc. sect. 12. omnibus conspi­cuum est. Si unquam audiverit, ratio cur eam scriptis suis non inseruerit, facile as­signari potest haec; proportionum ignarus [Page 85] subduplicatam rationem non intellexit: quod ex scriptis ejus praesertim Hydro­staticis, ubi proportionem Directam & Reciprocam ubique confundit, clare cerni­tur.

Dialogum quintum claudit argumento, contra Copernici sententiam, ab incremento motus gravium desumpto; de quo quasi in­victissimo Thrasonem agit; & licèt primus omnium eo usus fuerit Ricciolus, ejus tamen nulla facta hic mentio. Dicitur hic, Ne­cessariam esse connexionem inter motum terrae vertiginosum, & incrementum velocitatis de­scendentium apparens solum: Quod incum­bit probandum. Asseritur item, Copernica­nos ad unum omnes, incrementum reale veloci­tatis negare: Quod falsissimum est. Quid ponderis huic argumento insit, extra om­nem contraversiam, adversus Ricciolum non ita pridem posuere Stephanus de Ange­lis, & Andreas Tacquet, uterque licèt Ponti­ficius: quorum rationibus tandem ille suc­cumbere coactus est, ut manifestum est ex Transact. Philos. pag. 870. & alibi; quare actum agere supersedeo.

Nihilominus authorem monitum volo, argumentum hoc falsa suffulciri hypothesi, [Page 86] scil. Lineam curvam in qua descendit grave ca­dens, esse circularem: quam praedictus Ste­phanus quandam esse Spiralem demonstrat, cujus proprietas est haec. Quod rectae (in Riccioli & authoris figura pag. 578.) sump­tae ad libitum, HQ, IR, semper sunt in duplicata ratione angulorum HAD, IAD. Et nunquam ad Circulum appropinquat, ni­si grave ad terrae centrum spatiô sex hora­rum decidat, quod in casu Riccioli & autho­ris nostri fit spatio 21. 53. Imo datâ at non concessâ Riccioli suppositione, quod prae­dicta linea sit circularis, nullatenus tamen inde tollitur incrementum velocitatis rea­le: Quod si hac de re dubitare pergat no­ster author, primo rogatu satisfaciet è Pe­dellis, alter.

Ego intereà, ne caeteris magnis quidem illis artis revera parvae immorando nugis, nimia lectori creetur nausea, ad examen Tyrociniorum Mathematicorum vcrbô ex­pediendum memet accingo: in quo, ut ex cauda catum dignoscat lector, sufficiat se­quentes annotasse errores.

TYROCINIO­RUM MATHEMATI­CORUM EXAMEN.

DIcit itaque (1) noster Tyro (modò hoc sit insigniendus nomine, quem ne vel prima Matheseos elementa primo­ribus degustasse labris certo certius est) pag. 26. Horas planetarias distingui per circulos; quas per lineas mixtas fieri norunt Gnomonici omnes.

(2.) Asserit pag. 50. Sub circulis polari­bus, Gnomonum extremitates in horologijs hori­zontalibus, ut semel ab Aequatore digressus est Sol, Parabolas describere: Cum tamen in ho­rologio horizontali describatur Parabola, solummodo dum Sol est in Tropico proxi­mo: Et extra hunc (nisi in Aequatore) sem­per describantur Hyperbolae.

(3.) Pag. 52. dicit, Gnomones & stylos suis extremitatibus describere Ellipses, in zona [Page 88] frigida. Quod verum tantummodo est, cum Sol non occidit; nam cum occidit, semper describitur Hyperbola, nisi in Aequatore: Et cum mediâ nocte horizontem radit, semper describitur Parabola.

Ne amplius noster hic Tyro, sub Polari­bus aut terrarum alibi, in sectionibus Co­nicis sciaterico horizontali, aut cuivis alij inscribendis erret: has regulas generales observet.

Reg. 1. Ʋbique terrarum, quando Sol occidit, describitur semper Hyperbola in plano horizontali, nisi Sol fuerit in Aequatore, & tunc describitur linea recta.

Reg. 2. Quando Sol non occidit, semper descri­bitur Ellipsis; nisi idem fuerit horizon cum Aequa­tore, & tunc describitur Circulus.

Reg. 3. Quando Sol horizontem lambit, descri­bitur Parabola.

Not. Quod hic dicitur de horizontali, de quovis alio plano super quod Sol occidit, non occidit, aut tantùm lambit, intelligendum esse.

(4.) Pag. 100. Dum distantiam duo­rum locorum, quorum alter sub aequatore sit positus, inquirit; Proportionis termi­nos sic statuit. Ʋt est radius totus ad comple­mentum differentiae longitudinis; ita complemen­tum latitudinis datae ad complementum distantiae [Page 89] quaesitae. Egregiè hallucinatur tum in voca­bulis artis, nam, non radius totus, sed sinus to­tus, vel simpliciter radius dicere debuit: tum in ipsa arte, nam proportio sic se habet. Ʋt radius, ad sinum complementi differentiae longitudinis; ita sinus complementi latitudinis datae, ad sinum complementi distantiae quaesitae.

(5.) Denique ubi loquitur pag. 120. de Echo taciturna, dicit, In quolibet speculi Elliptici puncto non potest exaudiri hujusmodi echo, sed in ipso tantùm puncto concursus. (radiorum scil. soni reflexi) Sed in speculo Elliptico nullum tale punctum concursus agnoscunt Mathematici; nam in Ellipsi duo sunt foci, in quorum uno debet statui cor­pus sonorum, & in altero auris audientis.

Quâ fronte, Methodum suam Echome­tricam, in praefatione, Geometricam desig­narit author, cum non nudae figurae Geo­metricae, verùm demonstrationes metho­dum Geometricam constituant, lectori di­judicandum relinquo.

Atque jam habes, Candide & Erudite Le­ctor, animadversiones hasce leves, in nugivenduli nostri Scioli egregia & erudita opuscula scombris & thuri jure merito aeternum consecranda; quas à me invito, [Page 90] Ardelionis istius insolentia, impudentia & arrogantia extorserunt: quibus virtutibus fretus & inflatus, non tantum in varios ex­teros, viros eruditos & celebres, rixatri­cis & furiosae mulierculae in morem debac­chatus est; sed etiam, ut est os homini os­seum, & frons plusquàm serrea, varijs suis compatriotis, nominatim Professori prima­rio inclytae Academiae Glasguensis, quàm Salgucensem Art. nov. pag. 296. vocat, (viro, quem norunt omnes summô animi candore, vitae integritate, multâ & omnigenâ eruditione, praecipuè verò lin­guarum trium & omnium Orientalium pe­ritiâ praeditum, insignem & ornatum) in­solenter & impunè hucusque in­sultare ausus est Art. nov. pag. 472. Quare nullus dubito, quin meos conatus aequi boniue consulturus, & veniam mihi daturus sis, sicubi tibi visus fuerim paulò acerbiùs adversarium tractasse, cujus insulsa petulantia, & insignis procacitas, vel psam mansuetudinē, satyram scripsisse co­geret. Interea, ut relaxetur tibi animus ab aegritudine, aut indignatione, quam censeo non potuisse non contrahere, modò pensi­culatiùs cogitaverit, quantam & qualem [Page 91] ignominiae notam patriae suae inurere, quem fucum & frandem literato orbi facere co­natus sit famosus meus antagonista, pueri­lium, ridicularum, & trivialium tricarum miseram & miserè consutam farraginem sub adeo amplis & speciosis titulis praelo committendo. Interea, inquam, ut relaxe­tur tuus animus à praedicta aegritudine, ne dedigneris tuos oculos convertere in se­quentia Tentamina Geometrica, quae sat scio, fatebere aeue virum & veram Mathesin sa­pere, ac quae à me ad examinis incudem modò revocata sunt, nauci hominem, supi­nam inscitiam, crassam & stupendam igno­rantiam, tum Matheseos, tum naturalis Philosophiae, altâ & clarâ voce singulis pronunciant & proclamant: Quae denique examini subjicere, modò capiat, aut ad Graecas Calendas capere possit, nostro per me licebit adversario. Interim tu ijs utere, fruere, & Vale.

TENTAMINA QUAEDAM GEOMETRICA DE Motu Penduli & Projectorum.

I. SInt rectae AE, DB, hori­zonti parallelae; situe tem­pus (quo descendit grave in recta CD) Fig. 4. [...], & [...], [...], [...]: Esset tempus (quo descendit idem grave in recta AB) [...].

II. Et positâ [...] in D; foret velocitas in [...]. Haec facile eliciun­tur ex Galilaei, & aliorum de motu demon­strationibus.

III. Sint deinde [...], [...], [...], [...]; ponitur enim AG ipsi FE perpendicularis. Descendat itaque grave per rectam AB, cujus velocitas in B sit [...]: [Page 2] descendat quoque idem grave per rectas AF, FD; erit ejus velocitas in [...]. Hoc ex antecedente nullo negotio deducitur; modo animadvertatur mobilis, quod in diversis rectis movetur, impetum seu velocitatem mutari in recta­rum occursu, ita ut velocitas in prima li­nea sit ad velocitatem in secunda, in ratio­ne radij ad cosinum inclinationis mutuae re­ctarum. Ut in figura, cum motus perfici­tur in diversis rectis AF, FD; velocitas, quam acquirit grave descendens in F, mu­tatur in aliam in FD, quae priore minor est in ratione FG, ad FA: Atque hoc ve­rum est in omni motu, sive aequali, sive quo­vis modo accelerato vel retardato.

IV. Hinc igitur colligimus motuum praescriptas velocitates variari tantum propter linearum inclinationes, in quibus diriguntur. Et proinde si nullae tales sint inclinationes, nullae etiam sunt velocitatum ab ordinatis differentiae: atque in lineis cur­vis nullae tales sunt inclinationes, & ideo in lineis curvis mobilia eâdem velocitate incedunt, qua in lineis rectis. Hisce in gene­re pensitatis, dico grave eâdem velocitate [Page 3] moveri, sive in linea curva, sive in recta descendat; nam eruditis hactenus innotes­cit, grave eâdem velocitate moveri, sive in recta horizonti perpendiculari, sive in re­cta eidem inclinatâ descendat. Non ar­duum foret, hoc in penduli descensu Geo­metrice demonstrare per hujus tertiam, ab exhaustione Archimedea: sed prolixior est haec summi Geometrae methodus, quam permittit instituti brevitas. Novi hanc do­ctrinam Galilaei experimentis non congrue­re, dum asfirmat mobile citius descendere per arcum circuli, quam per ejusdem chor­dam; & citius per duas chordas, quam per unam: Item (quod hinc emergit) brevio­res penduli vibrationes tardius persici, quam ejusdem longiores. Sed vereor Ga­lilaeum deceptum esse à gravium elaterio motum praecipitante, quod hic summo­pere advertendum est, & seorsim conside­randum. Utcunque sit, super hac hypo­thesi, de tempore quo perficitur penduli vibratio inquiramus.

V. Sit igitut AHF circuli quadrans, ex hujus puncto C demittatur pendulum. Du­catur radio & horizonti AH parallela EG, & huic perpendicularis CD: pendulum [Page 4] in G eandem habet velocitatem vel impetum, quam habuisset in D, si ex Fig. 5. C demissum fuisset. Quaestio nunc est quam cito descendit à C in G? Sit [...], [...], [...], [...], [...]. Erit tempus, quo pendulum descendit ex C in [...]

VI. Altitudines penduli vibrationum, seu ipsarum sinus versi, sunt quam proxime in subduplicata ratione quantitatum har­monice continue proportionalium: atque hinc videtur sequi corporis gravis per cen­trum terrae vibrationes esse in eadem ra­tione.

VII. Affirmant non pauci in projecto­rum jactu perpendiculari aequales impetus sub eadem altitudine tam ascendenti quam descendenti mobili inesse: quod mihi ne­quaquam arridet: cum hinc clare sequatur, motum projectorum, exclusa gravitate, esse aequabilem: & gravis vibrationes per [Page 5] centrum terrae omnes inter se esse aequales, atque motum hunc in perpetuum duratu­rum: imo ipsius penduli vibrationes aequa­les & perpetuae forent.

VIII. Motus projectorum, exclusa gravitate, videtur aequaliter retardatus; nam unius medij homogenei, quale hic sup­ponimus nostrum aërem, una semper est resistentia; quod impedimentum de novo semper adveniens motum producit aequa­liter retardatum.

IX. Propositum nunc sit inquirere, qua­lis sit linea à motu projectorum descripta, secundum nostram hypothesin composita ex uno motu aequaliter retardato & altero gravitatis aequaliter accelerato. Sit igitur linea recta VK, in qua perficeretur motus projecti exclusa gravitate, & Fig. 6. recta AK (eidem VK perpendicularis) tempus in quo motus perficitur. Tempore AB sit projecti ob gravitatem descensus BF; ducatur nunc parabola AFI, verti­cem habens A, & compleatur rectangulum AKVX, fiatue parabola XYK, cujus vertex K. Sit tandem curva à motu pro­jecti descripta VTRPL; sintue datae rectae [...], [...], [Page 6] [...], [...]; rectae vero indefinitae sint [...], [...]: sintue [...], latus rectum parabolae [...], latus rectum parabolae [...]. Mani­festum est tempus [...], [...], [...]; & proinde [...], [...], [...] & ideo [...], [...], [...]: Ope ha­rum trium aequationum, ablatis quantitabus r, l, x, fit [...]. Fiat nunc [...], & [...] emergetue sequens aequatio [...] & ad tollenda signa radica­lia, utramque aequationis partem in se mul­tiplicando, & radicem quadratam extra­hendo [...] Unde innotescit curvam VTRL esse pa­rabolam, cujus constructio est satis expe­dita, cum V sit ejusdem vertex, & V β ip­sius diameter, factis [...], & re­ctis V α, α β, ipsis ST, SV, parallelis: hinc [Page 7] innotescit V β (cum detur angulus VOP) quae sit [...]; & proinde parabolae latus re­ctum est [...]. Ex praedictis facile colligitur rectam VK tangere para­bolam in V, & KL eandem tangere in L.

X. Si detur recta [...], ejusque ele­vatio supra horizontem PVL: oportet ita elevare machinam VS, ut projectum deci­dat in P quoniam OP perpendicularis est ad horizontem, datur angulus OPV, cu­jus finus [...], situe anguli ignoti OVP si­nus [...], & anguli VOP sinus [...], sinus totus [...], item [...]; ope harum trium aequationum, & prioris quae quanti­tatis g valorem exhibuit, auferantur quan­titates ignotae x, c, g; & ostendet ultima aequatio restans post ablatas dictas quanti­tates valorem ipsius v sinus quaesiti.

XI. Hinc quoque deducitur. Si gra­ve ascendens perpendiculariter tempore k perficiat z, & tempore s perficiat t, tem­pore n perficere [...] [Page 8] Hac ratione adhuc projectum perpendi­culari jactu in eadem altitudine, tam ascen­dens quam descendens eundem habet im­petum; & praeterea ex una altitudine velo­cius moveretur, & ex alia tardius; quae duo sunt absurda summopere evitanda: at vi­dentur provenire potius à recepto Mathe­maticorum experimento, nimirum, quod gravium descensus sint in duplicata ratione temporum, quam à nostro commento de projectorum motu aequaliter retardato. Sit enim tempus AB, quo projecti ascensus fiat BI; item tempora AC, AK, AD, eorum (que) ascensus respectivi CG, Fig. 7. KM, DO; ita ut generetur curva AGN, cujus vertex G. Satis probabile est AGN esse Geometricam quandam & uniformem curvam, cum accelerationes & retardatio­nes gradatim & successive fiant; at multo­rum experientia testatur GMN esse para­bolam ab axe GC, & propterea GIA esset etiam ejusdem parabolae pars altera; quod tamen non videtur rationi congruere. Nos potius existimamus AGN esse quandam hyperbolam (vel saltem hyperbolifor­mem) ita ut AC sit minor quam CN, cujus diameter ducitur à G ad punctum [Page 9] medium rectae AN: hac enim ratione, GO in parvis descensibus, quales fere hucusque tantum sunt observati, parum differt à curva parabolica; at ex magnis altitudinibus, cum motus acceleratus accedit quàm proximè ad aequabilem, considerabilis forte accedet dissimilitudo; tunc enim hyperbolae curva vix differens ab ejusdem asymptota recta, motum quàm proximè aequabilem reprae­sentabit. Qualiscunque sit curva AGN, haec est una ejus proprietas: exclusa gravitate, sint temporum AB, AC, AK, AD, respe­ctivi ascensus BH, CF, KP, DE; eritue AHFPE parabola: ductâ GQ curvam tangente in puncto G, fiant arbitrariè AB, GL aequales; erit ML aequalis rectae IH, & figura GLM aequalis figurae AIH.

FINIS.

Errata.

Pag. 56. l. 12. pro sit, lege sit. p. 57. l. 2. pro altitu­dinem, lege altitudinum. p. 62. l. 9. pro hydrarg. lege Hydrag. p. 63. l. penult. dele 1. p. 72. l. 9. pro ferre, lege ferri. pag. 75. l. 4. & 9. dele: & l. 12. dele. p. 83. l. 3. pro integrum, lege integram.

[geometric figures]

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