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ter Luftre to the Mathematical Sciences.
Out of Plato's Academy, almost innumerable Mathematicians came forth. Thirteen of Plato's familiar Acquaintance are commemorated by Proclus, as Men by whofe Studies the Mathematicks were improv'd. From hence were Leodamus the Thafian, Archytas the Tarentine, Theatetus the Athenian, by whom the Mathematicks were notably enlarged. Leodamus practifed the Analyfis received from Plato,
and is faid by Laertius to have found out many things by the Help of it. As for Theatetus, both his own Inventions, amongst which are the Elements written by him, and the Infcription of regular Bodies; and Plato's Encomiums, who also infcribed a Dialogue to his Name, do make him fa
Archytas alfo wrote Elements himself; and his Doubling of the Cube is mentioned by Eutocius; whofe fingular Commendation it likewife was, that he was almost the First that brought down the Mathematicks to humane Ufes; by whofe Contrivance alfo a wooden Pigeon was made to fly, as Gellius reports; he being followed by Dedalus, and other Artificers, yielded Matter for the Fables of the Poets. Moreover, Archytas was both a Mathematician and General of an Army: He five times commanded the Forces of his own Citizens, in the Wars of his Country, and five times overcame their Enemies. The meer Name of Neoclides is only Famous, he being more illuftrious for his Scholar Leon perhaps, than for his own Inventions. Leon certainly wrote Elements of all the Mathematicks, improv'd them, and made them more fit for Ufe. Wherefore he is deservedly to be reckon'd amongst the chief Compilers of Elements.
Eudoxus of Cnidos was not inferior to Leon: A Man great in Arithmetick, and to him (if we may believe the Greek Scholiaft) we owe the whole fifth Book. likewife wrote Elements, and made them more general, and increased the Sections begun by Plato; over and above this he was the first Framer of Aftronomical Hypothefes, and derived down the Springs of Geometry, as Archytas had done before, to Mechanicks. Amyclas the Heracleot, and Menæchmus, and his Brother Dinoftratus, Helicon of Cyzium, Theudius, Her motimus the Colophonian, Philippus the Medmaan, all Platonifts, rendered Geome-try much more perfect. Menæchmus allo found out the Conick Sections, and by the help of them, two mean Proportionals; whofe Invention in this Cafe is preferr'd by Eutocius before any other. Theudius
and Hermotimus made the Elements more univerfal and full. And all thefe, who were of Plato's Academy, brought Mathematick -Philofophy to Perfection, as Proclus faith. Xenocrates alfo, one of Plato's Auditors, and Master of Ariftotle, as well as Arif totle himself, were famous for the Knowledge of the Mathematicks. When a certain Perfon, who knew nothing of Geometry, was defirous to be his Auditor, Go thy way, faith he, for thou wanteft the very Handles of Philofophy.
But of Ariftotle, what can I fay? All his Books are filled with Mathematical Arguments, from a Collection of which Blancane hath made a Book. Two of Arif totle's School are especially celebrated, Eudemus and Theophraftus: This latter wrote two Books of Numbers, four of Geometry, and one of indivifible Lines: The other, compofed a Mathematical History; and from him Proclus, and others have borrowed theirs. To Arifteus, Ifidore, Hypficles, moft fubtle Geometricians, we are especially indebted for the Books of Solids. Euclid gathered together the Inventions of others, difpofed them into Order, improv'd them, and demonftrated them more accurately, and left to us thofe Elements, by which Youth is every where instructed in the Mathematicks. He died in the Year before Chrift 284. There follow'd Euclid almost an 100 Years afterwards Eratofthenes The Name of Eratof thenes was very famous, but his Writings are loft. Many Remains we have of Archimedes, and many we have loft.
But when I name Archimedes, I conceive
my Mind the very Top of humane Subtilty, and the Perfection of the whole Mathematical Sciences. His wonderful Inventions have been delivered to us by Polybius, Plutarch, Tzetzes, and others. Conon was Contemporary to Archimedes,
one who was both a Geometrician and an Aftronomer, whofe Death Archimedes laments in his Book of the Quadrature of the Parabola. There followed Archimedes and Conon, and that at no great Distance, Apollonius of Perga, another Prince in Geometry, who was called by way of high Encomium, The Great Geometrician. There are extant Four [now Seven] moft fubtle Books of his Conicks. To the fame Perfon are afcribed, the 14 and 15 Books of Euclid, which were contracted by Hypficles. Hipparchus and Menelaus wrote, this latter 6, the other 12 Books of Subtenfes in a Circle; for which Invention, fo very profitable and neceffary, great Commendations and Thanks are due to both. There are alfo extant three Books of Menelaus concerning Spherical Triangles. Three most useful Books of Sphericks of Theodofi us the Tripolite are alfo in the Hands of all. And these indeed, if you except Menelaus, lived all of them before Christ.
In the Year after Chrift peared in the World Claudius Ptolemæus, the Prince of Aftronomers, a Man certainly wonderful, and (as Pliny faith) above the Nature of Mortals. But he was not only moft skilful in Aftronomy, but in Geometry alfo; which as many other Things written by him do witnefs, fo efpecially do the Books of Subtenfes: Thofe of Menelaus