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this Knowledge is, which the wisest Men of all Ages have, with incredible Study, labour'd to attain unto, and become poffefs'd of. Moreover, I muft own that Peter Ramus's Labours have been of great Service to me in the compiling of this Account, who in the whole firft Book of his Inftitution, which is not a little one, hath out of Proclus, Laertius, Gellius, Polybius, Tzetzes, and others, compofed a Mathematical History both accurately and copiously.
The Mathematical Sciences were the first of all other amongst Men, if we may believe Jofephus. He, Book I. Chap. 3. writeth, that the Pofterity of Seth obferved the Order of the Heavens, and the Courses of the Stars. And left these Inventions fhould flip out of the Knowledge of Men, Adam having predicted a twofold Destruction of the Earth, by a Deluge, the other by Fire, they rais'd two Columns, one of Bricks, of Stone the other; and infcribed their Inventions upon them, that if the Brick one should happen to be deftroy'd by the Deluge, that of Stone, which would remain, might afford Men an Opportunity of being inftructed, and prefent to their View the Things which it had infcrib'd on it. They fay alfo, that that stone Pillar, which even in our Days is seen
in Syria, was dedicated by them. This -Jofephus fays: whom I leave to vouch for. the Story.
That the Affyrians and Chaldeans were the first after the Flood, who applied themfelves to the Mathematicks, is delivered by the fame Jofephus; as alfo by Pliny, Diodorus, and Cicero. But the Mathematick Arts, which firft fprang amongst the Chaldeans, amongst whom they flourifhed, were afterwards transferr'd out of Chaldea and Affyria unto the Egyptians, by Abraham. For, when, at the Command of Go D, he went forth from his native Soil into Palestine, and from thence into Egypt, and perceiv'd the Egyptians to be taken with the Study of good Arts, and to be of a remarkable Difpofition and Capacity for Learning, (as Jofephus teftifies, Book I Chap. 9.) he communicated to them Arithmetick and Aftronomy; and confequently Geometry, which muft of Neceffity go before Aftronomy. which Studies afterwards the Egyptians fo flourish'd, that Ariftotle, 1 Metaph. Chap. 1. doth affirm, That the Mathematick Arts were first found out in Egypt, by their Priests; who by their Employments were at leifure for thefe Things.
Then these Arts croffing the Sea out of Egypt, came to the Philofophers of Greece: For Thales the Milefian, who A 3
flourish'd 584 Years before Chrift, was the first of the Greeks, who coming into Egypt, transferr'd Geometry from thence into Greece. He it was indeed, who, befides other Things, found out the 5th, 15th, and 26th Propofitions of the first Book. To the fame are alfo owing the 2d, 3d, 4th, 5th, of the fourth Book. The fame Perfon began to obferve the Equinoxes and Solftices, as Laertius teftifies; and he was the first who foretold an Eclipfe of the Sun, as Hippias and Arif totle write; and Tzetzes faith, That he alfo foretold an Eclipfe of the Moon to King Cyrus. For which Things fake he is to be look'd on as the firft Founder and Author of the Mathematical Sciences in Greece.
After him was Pythagoras of Samos: Which most ancient Philofopher, exceedingly improv'd and adorn'd the Mathematick Sciences. And he fo gave himfelf to Arithmetick in particular, that almost his whole Method of Philofophizing was taken from Numbers. And he firft of all, as Laertius relates, abftracted Geometry from Matter; in which Elevation of the Mind, be found out the 32d, 44th, 47th, and 48th Propofitions of the firft Book. But he is especially celebrated for the Invention of Prop. 32, and 47. of that Book; and he conceiv'd fo great Joy
upon this Invention, that, as Apollodorus witneffes in Laertius, on that Account he facrific'd an Hecatomb. The fame Perfon first laid open the Theory of incommenfurable Magnitudes, and the Five regular Bodies. The fame Perfon did both moft diligently teach and exercife the Art of Aftrology and Mufick: For he did not only acutely and fubtily find out many Things himself, but he alfo firft opened a School, in which Youth might learn these honourable and noble Arts.
Pythagoras was follow'd by Anaxagoras of Clazomena, and Oenopides of Chios, of whom Plato makes mention in his Dialogue, The Lovers, where young Men are brought in contending about Anaxagoras and Oenopides in their Defcriptions of Circles. Ariftotle reports, that a certain Treatife of Geometry was written by Anaxagoras; and we have it from Laertius, that it was fhew'd by him that the Sun is greater than Peloponnefus (a notable Inftance of the Infancy of Aftronomy at that Time); and that he made fome Conjectures concerning Habitations in the Moon. As for Oenopides, to him Proclus afcribes the 12 and 23. l. 1. Thefe were followed by Brifo, Antipho, and Hippocrates of Chios, all of them, for attempting the Quadrature of the Circle, reprehended by Ariftotle, and at the fame
time celebrated. But amongst them, Hippocrates was by far the moft Famous; that celebrated Perfon, who of a Merchant growing to be a Philofopher and a Geometrician, befides the Quadrature of the Circle, alfo first attempted the Doubling of the Cube, by two mean Proportionals; which as being an excellent, and indeed the only Way, all that have followed him to this time have embrac'd. 'Tis alfo his peculiar and great Commendation, that he, as Proclus teftifies, firft wrote Elements, and digefted into Order the Discoveries made by others.
Democritus was admirable, not in Philofophy only, but also in the Mathematicks. His Phyfical Monuments, and, if fuch there were, his Mathematical Works alfo, are wholly loft, thro' the Envy (as some report) of Ariftotle, who defired to have no other Writings read but his own.
The Philofophy of Democritus hath been reftored by Peter Gaffendus, in a very Learned Work lately publish'd. Theodorus Cyrenæus, altho' none of his Mathematical Inventions are extant, yet is great upon this Account, if there were no other, that he is reported to have been the Master of Plato.
Unto Plato therefore we are come at length, than whom no one brought grea