the nonfenfical, unintelligible Stuff that the common Writers on these Subject have fill'd their Books with, on the other, are fufficient Inftances to fhew how neceffary Geometry is in fuch Speculations. The only Organ of an Animal Body, whofe Structure and Manner of Operation is fully understood, has been the only one, which the Geometers have taken to their Share to confider.

It is incredible, how fillily the greatest and ablest Physicians talked of the Parts of the Eye, and their Ufe, and of the Modus Vifionis, before Kepler by his Geometry found it out, and put it paft difpute, tho' they apply'd themselves par ticularly to this, and valued themselves on it: And Galen pretended a particular Divine Commiffion to treat of it. Nay, notwithstanding the full Discovery of it, fome go on in copying their Predeceffors, and talk as much Ungeometrically as ever. It's true, we cannot reafon fo clearly of the internal Motions of an Animal Body, as of the external, wanting fufficient data, and decifive Experiments: But what relates to the latter (as the Articulation, Structure, Infertion, and Vires of the Muscles) is as Subject to strict Mathematical Difquifition, as any thing whatsoever: And even in the Theory of Diseases, and their Cures, thofe who talk Mechanically, talk moft Intelligibly; which may be the Reafon for the Opinion of the ancient Phyficians, that Mathematics are neceffary for the Study of Medicine itself, for which I could bring long Quotations out of their Works. Among the Letters that are afcrib'd to Hippocrates, there is one to his Son Theffalus, recommending to him the Study of Arithmetic, and Geometry, as neceffary to Medicine. Galen

in his Book entituled ὅτι ἂς ἰατρὸς καὶ Φιλόσοφο begins thus.

Οἷόν τι πεπόνθασιν οἱ πολλοὶ 7 αθλητῶν ἐπιθυμένες με Ολυμπιονίκαι γενέθαι, μηδὲν ἢ πράττειν ὡς τότε τυχῶν Επιτηδεύοντες, τοιῦτόν τι καὶ τοῖς πολλοῖς τῶν ἰατρῶν συμ βέβηκεν· ἐπαινῖσι με 38 Ιπποκράτίω καὶ πρῶτον ἁπάντων ἡγονται γενέθαι ἢ αὐτὲς ἐν ὁμοίοις ἐκείνῳ πάνα μᾶλλον ἤ τῖτο πράτζεσι. οἱ μὺ δὲ μικρὰν μοῖραν εἰς ἰατρικί φησὶ συμβάλλεθαι ἢ ἀςρονομίαν, καὶ δηλονότι των ταύτης ἦγε μείνω ἐξ ἀνάγκης Γεωμετείαν. οἱ δ ̓ ἐ μόνον αὐτοὶ μετέρ χονται τέτων ἐδέτερον, ἀλλὰ καὶ τοῖς μετιᾶσι μέμφονται.

If one of the Reasons of the Ancients for this be now somewhat unfashionable, viz. because they thought a Physician fhould be able to know the Situation and Afpects of the Stars, which they believed had Influence upon Men and their Dif eafes (and pofitively to deny it, and fay, that they have none at all, is the effect of want of Obfervation) we have a much better and undoubted one in the Room, viz. That Mathematics are found to be the best Inftrument of promoting natural Knowledge. Secondly, If we confider, not only the animal Economy in general, but likewife the wonderful Structure of the different forts of Animals, according to the different purposes for which they were defign'd, the various Elements they inhabit, the feveral ways of procuring their Nourishment, and pro pagating their Species, the different Enemies they have, and Accidents they are fubject to, here is ftill a greater need of Geometry. It is pity, that the Qualities of an expert Anatomift and skilful Geometer, have feldom met in the fame Perfon. When fuch a One fhall appear, there is a whole

Terra

Terra incognita of delightful Knowledge to employ his Time, and reward his Induftry.

As for the other two Kingdoms; Borelli and other Mathematical Men, feem to have talked very clearly of Vegetation: And Steno, another Mathematician, in his excellent Treatife de Solido in tra Solidum naturaliter contento, has applied this part of Learning very handfomely to Fofils, and fome other Parts of Natural History. I shall add only one thing more, that if we confider Motion itself, the great Inftrument of the Actions of Bodies upon one another; the Theory of it is entirely owing to the Geometers, who have demonftrated its Laws both in hard and elastic Bodies; hew'd how to measure its Quantity, how to compound and refolve the feveral Forces, by which Bodies are agitated, and to determine the Lines which thofe compound Forces make them describe; of fuch Forces, Gravity, being the most constant and uniform, affords a great va riety of useful Knowledge, in confidering several Motions that happen upon the Earth, viz. As to the free Descent of heavy Bodies, the Curve of Projectiles; the Defcent and Weight of the heavy Bodies when they lye on inclined Planes; the Theory of the Motion of Pendulous Bodies, &c. all which are very ingenioufly and methodically treated of by the imcomparable Mathematician Mr. Thomas Simpson, who has exceeded all Men (in Mathematical Sciences) fince Sir Isaac Newton.

From what I have faid, I fhall draw but one Corollary, that a natural Philofopher without Mathematics is a very odd fort of a Perfon, that reasons about things that have Bulk, Figure, Motion, Number, Weight, &c. without Arithme

tic, Geometry, Mechanics, Statics, &c. I muft needs fay I have the last Contempt for thofe Gentlemen, that pretend to explain how the Earth was framed, and yet can hardly Measure an Acre of Ground upon the Surface of it. And as the Philofopher fpeaks, Qui repente pedibus illotis ad Philofophos divertunt, non hoc eft fatis, quod fint omnino αθεώρητοι, ἄμεσοι, γεωμέτρητοι, fed legem etiam dant, quâ philofophari difcant..

The Usefulness of Mathematics in feveral other Arts and Sciences is fully as plain. They were look'd upon by the antient Philofophers, as the Key to all Knowledge. Therefore Plato wrote upon his School, viz.

Οὐδεὶς αγεωμέτρητ©· εἰσίτω. i. ε.

Let none unskilled in Geometry enter.

And Xenocrates told one ignorant in Mathematics, who defired to be his Scholar, that he was fitter to card Wool, λαβάς γδ ἐκ ἔχεις Φιλοσοφίας, you want the bandle of Philofophy, viz. Geometry. There is no understanding the Works without it. Theo Smyrnus has wrote a Book entituled, an Explanation of those things in Mathematics, that are neceffary for the reading of Plato. Ariftotle illuftrates his Precepts and other Thoughts by Mathematical Examples, and that not only in Logic, &c. but even in Ethics, where he makes ufe of Geome trical, and Arithmetical Proportion, to explain Commutative and Diftributive Juftice.

Every Body knows, that Chronology and Geography are indifpenfable Preparations for Hiftory; A relation of Matter of Fact, being a very lifelefs infipid thing without the Circumstances of Time and Place. Nor is it fufficient for one,"

that

that would understand things thoroughly, that he knows the Topography, where fuch a Place lies, with those of the near adjacent Places, and how these lie in refpect of one another, but it will become him likewife to understand the Scientifical Principles of the Art; that is, to have a true Idea of a Place, we ought to know the relation it has to any other Place, as to the Distance and Bearing, its Climate, Heat, Cold, Length of Days, &c. which things do much enliven the Reader's Notion of the very Art itself. Juft fo it is neceffary to know the Technical or Doctrinal Part of Chronology, if a Man would be throughly skill'd in Hiftory, it being impoffible, without it, to unravel the Confufion of Hiftorians. I remember the late Dr. Halley has determined the Day and Hour of Julius Cæfar's landing in Britain, from the Circumftances of his Relation. And every Body knows how great ufe Mr. Dodwell has made of the calculated Times of Eclipfes, for fettling the Times of great Events, which before were, as to this effential Circumstance, almoft fabulous.

Both Chronology and Geography, and also the Knowledge of the Sun and Moon's Motions, fo far as they relate to the Constitution of the Kalendar and Year, are neceffary to a Divine, and how fadly fome otherwife Eminent have blundered, when they meddled with things that relate to thefe, and border on them, is too apparent.

Nobody, I think, will question the Intereft, that Mathematics have in Painting, Mufic and Architecture, which are all founded on Numbers. Perspective, and the Rules of Light and Shadows are owing to Geometry and Optics: And I think those two comprehend pretty near the whole Art

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