lay the foundations of fo great and extenfive an Art, Non Venus & vinam fublimia pectora fregit, Ovid in Io. Faft. But tho' the induftry of former Ages had difcovered the Periods of the great Bodies of the Universe, and the true System and Order of them, and their Orbits pretty near; yet was there one thing ftill referved for the glory of this Age, and the honour of the English Nation, The grand fecret of the whole Machine; which, now it is difcovered, proves to be (like the other contrivances of Infinite Wisdom) fimple and natural, depending upon the most known and most common property of matter, viz. gravity. From this the incomparable Mr. Newton has demonftrated ftrated the Theories of all the Bodies of the Solar System, of all the primary Planets and their fecondaries, and among others, the Moon, which feemed moft averfe to numbers: and not only of the Planets, the floweft of which compleats its Period in lefs than half the Age of a Man, but likewife of the Comets, fome of which it is probable spend more than 2000 years in one Revolution about the Sun; for whose Theory he has laid fuch a foundation, that after Ages, affifted with more Observations, may be able to Calculate their returns. In a word, the preceffion of the Equinoctial Points, the Tides, the unequal Vibration of Pendulous Bodies in different Latitudes, &c. are no more a Question to those that have Geometry enough to understand what he has delivered on thofe Subjects: a perfection in PhiloSophy, that the boldest Thinker durft hardly have hoped for; and, unless Mankind turn barbarous, will continue the Reputation of this Nation as long as the Fabrick of Nature fhall endure. After this, what is it we may not expect from Geometry joined to Obfervations and Experiments? The next confiderable object of Natural knowledge I take to be Light. How unfuccefsful enquiries are about this Glorious Body without the help of Geometry, may appear from the empty and frivolous difcourfes and difputations of a fort of Men, that call themfelves Philofophers; whom nothing will ferve, perhaps, but the knowledge of the very Nature, and intimate Caufes of every thing; while on the other hand the Geometers, not troubling themfelves with those fruitlefs enquiries about the Nature of Light, have difcovered two remarkable properties of it in the reflexion and refraction of its beams; and from thofe, and their freightnefs in other cafes, have invented the noble Arts of Opticks, Catoptricks, and Dioptricks; teaching us to manage this fubtile A 5 Body Body for the improvement of our knowledge, and ufeful purposes of Life. They have likewife demonftrated the caufes of feveral Coeleftial appearances, that arife from the inflection of its Beams, both in the Heavenly Bodies themselves and other Phoenomena, as Parhelia, the Iris, &c. and by a late Experiment they have difcovered the celerity of its motion. And we fhall know yet more furprizing properties of Light, when Mr. Newton fhall be pleased to gratify the World with his Book of Light and Colours. The Fluids which involve our Earth, viz. Air and Water, are the next great and confpicuous Bodies that Nature prefents to our view: and I think we know little of either, but what is owing to Mechanicks and Geometry. The two chiefeft properties of Air, its Gravity and Elaftick force, have been difcovered by Mechanical Experiments. From thence the decrease of the Air's denfity according to the increase of the distance of the Earth has been demonftrated by Geometers, and confirmed by Experiments of the fubfidence of the Mercury in the Torricellian Experiment. From this likewife, by the affiftance of Geometry, they have determined the height of the Atmosphere, as far as it has any fenfible denfity; which agrees exactly with another Obfervation of the duration of the Twilight. Air and Water make up the object of the Hydrostaticks, tho' denominated only from the latter, of which the principles were long fince fettled and demonftrated by Archimedes, in his Book περὶ τῶν Οχεμένων, where are demonftrated the caufes of feveral furprizing Phoenomena of Nature, depending only on the Equilibrium of Fluids, the relative Gravities of thefe Fluids, and of folids fwimming or finking therein. Here alfo the Mathematicians confider the different Preffures, Refiftances, and Celerities of Solids moved in in Fluids, from whence they explain a great many appearances of Nature, unintelligible to thofe who are ignorant of Geometry. Next, if we defcend to the Animal Kingdom, there we fee the brightest strokes of Divine Mechanicks. And whether we confider first the Animal Oeconomy in general, either in the internal motion and circulation of the Juices forced through the feveral Canals by the motion of the Heart, or their external motions, and the Inftruments wherewith these are performed, we must reduce them to Mechanical Rules, and confefs the neceffity of the knowledge of Mechanicks to understand them, or explain them to others. Borelli in his excellent Treatife de motu Animalium, Steno in his admirable Myologiæ fpecimen, and other Mathematical Men on the one hand, and the nonfenfical, unintelligible ftuff that the common Writers on these Subjects have filled their Books with on the other, are fufficient inftances to shew, how neceffary Geometry is in fuch fpeculations. The only Organ of an Animal Body, whofe ftructure and manner of operation is fully understood, has been the only one which the Geometers have taken to their fhare to confider. It is incredible, how fillily the greatest and ableft Physicians talked of the parts of the Eye and their use, and of the modus vifionis, before Kelper by his Geometry found it out, and put it paft difpute, tho' they applied themfelves particularly to this, and valued themfelves on it; and Galen pretended a particular Divine Commiffion to treat of it. Nay, notwithstanding the full difcovery of it, fome go on in copying their Predeceffors, and talk as Ungeometrically as ever. It is true, we cannot rea fon 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 Mufcles) is as fubject to ftrict Mathematical digeifition, as any thing whatfoever; and even indi the Theory of Difeafes and their Cures, thofe who talk Mechanically talk moft intelligibly; which on may be the reafon for the Opinion of the ancient Phyficians, that Mathematicks are neceffary for the m study of Medicine itself, for which I could bring quotations out of their Works. Among the Letters that are ascribed to Hippocrates, there is one to his Son Theffalus, recommending to him the study of Arithmetick and Geometry, as neceffary to Medicine. Galen in his Book intituled, ὅτι ἄριτος ἰατρὸς καὶ Φιλόσοφ, begins Οἷόν τι πεπόνθασιν οἱ πολλοὶ τῶν ἀθλητῶν, ἐπιθυμέντες μὲν Ὀλυμπιονίκαι γενέσθαι, μηδὲν δὲ πράτλειν, ὥς τέτε τυχεῖν, ἐπιτηδεύοντες, τοῦτόν τι καὶ τοῖς πολλοῖς τῶν ἰατρῶν συμβέβηκεν· ἐπαι νησι· μὴν γὰρ Ἱπποκράτην καὶ πρῶτον ἁπάντων ἡγῆν ται· γενέσθαι δὲ αὐτές ἐν ὁμοίοις εκείνῳ πάντα μάλλον ἤ τότο πράτλεσι. οἱ μὲν γὰρ 8 μικρὰν μοῖραν, εἰς ἰατρικὴν φησὶ συμβάλλεσθαι τὴν ἀτρονομίαν, καὶ δηλο νότι, τὴν ταύτης ἡγεμένην ἐξ ἀνάγκης Γεωμετρίαν. οἱ δὲ ἐ μόνον αὐτοὶ μετέρχονται τετων ἐ δέτερον, ἀλλὰ καὶ τοῖς μετιᾶσι μέμφονται. If one of the reafons of the Ancients for this be now fomewhat unfashionable, to wit, because they thought a Physician fhould be able to know the fituation and afpects of the Stars, which they believed had influence upon Men and their Difeafes (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 its room; viz. That Mathematicks are found to be the best Initrument of promoting natural knowledge. 2dly, If we confider not only the Animal Oeconomy in general, but likewife the wonderful ftructure of the different forts of Animals, according to the different purposes for which they were defigned, the various Elements they inhabit, the feve ral |