This friendly mixture and alliance of Phyfics and Mathematics, from which fo much honour and advantage are derived to the cause of phyfical truth, is a piece of fine philofophy, which, whether it was fpeculately understood by the great Newton, whose labours, founded on the connection, produced fo many fplendid discoveries, is well explained by Ariftotle, whofe Phyfics are little better than a heap of vain hypotheses an illuftrious proof, that the perfection of science is never to be raised from its foundation by the exertions of a fingle genius, however powerful and extenfive; but muft advance, through several stages of improvement, on the labours of many at the fame time that it is a pointed admonition to every later philofopher, to avail himself of the difcoveries of his predeceffors. αἱ φύσεις, περὶ ποτέρας τῇ φυσικοῦ, ἢ περὶ τᾶ ἐξ ἀμφοῖν· ἀλλ ̓ εἰ περὶ τᾶ ἐξ ἀμφοῖν, δὲ περὶ ἐκατέρας. Πότερον οὖν τῆς αὐτῆς, ἢ ἄλλης, ἑκατέραν γνωρίζειν. Ariftot. Aufcult, Natural. lib. ii. cap. 2. See Nat. Aufcult. lib. ii. cap. 2, : It is, however, a truth to be acknowledged and lamented, that the genius of one philofopher being either infenfibly warped or voluntarily enslaved by the authority of another, is a circumftance which has often thwarted the advancement of knowledge, and always proved an infurmountable obftacle to the progress and success of learning and one of the most difficult and important tasks under which every improver of fcience has to labour, however independent in his fpirit and ingenuous in his views, is to know, what of the works of his predeceffors to adopt, and what to reject. This is a field which it is neceffary to cultivate, but which is of moft critical and important determination; which judgment is often embarraffed, and genius perplexed; and in which memory and prejudice too often ufurp their place and, fince he put in execution the precepts, and followed the directions of the organum of an abler logician, we may have cause to rejoice upon the whole, that our great English philofopher was no more converfant in the works of the Peripatetic. in It was neither from the Principles nor Reafoning, neither from the Logic or Practice of Aristotle, (which two last seldom, if ever, coincided in effect,) that Newton aftonished the world with fuch a brilliant train of Aftronomical discoveries and calculations; which, in addition to the other philofophical inventions and improvements of that extraordinary genius, whilft they reflect the highest honour on the country which gave him birth and education, have immortalized his name and memory. The Logic, which directed his phyfical researches, pointed out to him a more humble and laborious, but a more honourable and fuccefsful, road to truth. From the ingenious fictions and plaufible inventions of the Stagyrite, and from the formal but feeble difputations of his weaker followers, it brought him down to the labour of experiment and actual observation. Out of the wilds of imagination, it led him to cultivate the field of nature and from mental fpeculations, it drew down his attention to manual operations. By By Experiments ingeniously made and accurately observed, he took the true phænomena alatt of Motion as generated by the powers of Gravity, Elafticity, the Refiftence of fluids and the like; and analysed the Forces by which it is produced, and of which it is compounded.h To thefe Forces be applied his fublime Geometry, which fcience he advanced much beyond the fartheft reach of all former mathematicians, and by which he demonstrated the phænomena of all the Curves described, and Motions performed by Projectiles, in every hypotheses that could be framed. From the astronomical Obfervations of Copernicus and the Rules and conjectures of Kepler, two of the ableft aftronomers before him, he found the Planets revolving round their respective centres in Curves and Motions All improvement in learning is progressive; and philofophers are never difhonoured by availing themselves of the inventions of their predeceffors or contemporaries. Galilæo obferved the velocity of falling bodies to increase in the duplicate ratio of the time; and that Projectiles move in a Parabola and Sir Chriftopher Wren found the equability of motion by experiments on pendulums. See the Scholium at the end of the fixth Corollary of Newton's Principia. exactly exactly SIMILAR or the SAME; and by a bold and fublime ANALOGY,' which made him the first aftronomer in the world, from his theory of Projectiles, experimentally founded and geometrically confirmed, he raised his philosophy to the celestial Bodies,* i Non a Naturæ Analogia recedendum eft, cum ea fimplex effe foleat, et fibi confona,-et hoc eft fundamentum Philofophiæ totius. Newtoni Regula Philosophandi, lib, iii. Princip. Conclufiones precedentes huic innituntur Axiomati • Effectuum fcilicet ejufdem generis, quorum nempe quæ cognofcuntur proprietates eædem funt, eafdem effe caufas et eafdem effe proprietates quæ nondum cognofcuntur ' &c.-In hac regula fundatur omnis philofophia, quippe, qua fublata, nihil affirmare poffemus de univerfis. Cotefii Præf. in Newtoni Princip. * Eadem ratione qua Projectile vi gravitatis in orbem flecti poffet et terram totam circumire, poteft et Luna vel vi gravitatis, fi modo gravis fit, vel alia quacunque vi qua in terram urgeatur, retrahi femper a curfu rectilineo terram verfus et in orbem fuum flecti: et abfque tali vi Luna in orbe fuo reteneri non poteft. Hæc vis, fi jufto minor esset, non fatis flecteret Lunam a curfu rectilineo: fi jufto major, plus fatis flecteret, ac de orbe terram verfus deduceret. Requiritur quippe ut fit jufte magnitudinis: et Mathematicorum eft invenire Vim, qua corpus in dato quovis orbe data cum velocitate accurate retineri poffit; et viciffim invenire Viam curvilineam, in quam corpus e dato quovis loco data cum velocitate egreffum data vi flectatur. New toni Principio Mathem. Def. v. Without |