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this Knowledge is, which the wiseft Men of all Ages have, with incredible Study, labour'd attain unto, and become possess’d_of. Moreover, I must own that Peter Ramus's Labours have been of great Service to me in the compiling of this Account, who in the whole first Book of his Institution, which is not a little one, hath out of Proclus, Laertius, Gellius; Polybius, Tzetzes, and others, composed á Mathematical History both accurately and copiously.




The Mathematical Sciences were the first of all other amongst Men, if we may believe Josephus. He, Book I. Chap. 3. writerh, that the Posterity of Seth observed the Order of the Heavens, and the Courses of the Stars. And left these Inventions should 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 inscribed their Inventions upon them, that if the Brick one should happen to be destroy'd by the Deluge, that of Stone, which would remain, might afford Men an Opportunity of being instructed, and present to their View the Things which it had inscrib'd on it.

They say also, that that stone Pillar, which even in our Days is seen


in Syria, was dedicated by them. This
Jofephus says: whom I leave to vouch for.
the Story

That the Allyrians and Chaldeans were the first after the Flood, who applied them. selves to the Mathematicks, is delivered by the fame Jofephus ; as also by Pliny, Diodorus, and Cicero. But the Mathemarick Arts, which first sprang, amongst 'the Chaldeans,' amongst whom they flourished, were afrerwards transferr'd out of Chaldea and Asyria unto the Egyptians, by Abraham. For, when, at the Command of God, 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 Disposition and Capacity for Learning. (as Jofephus' testifies, Book I. Chap. 9.) he communicated to them Arithmetick and Astronomy; and consequently Geometry, which must of Necessity go before Astronomy. In which Studies afterwards the Egyptians so flourish’d, i that Aristotle, 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 leisure for these Things.

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Then these Arts crossing the Sea out of Egypt, came to the Philosophers of Greece: For Thales the Milesian, who


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flourish'd 584 Years before Christ, was
the first of the Greeks, who coming in-
to Egypt, transferr’d Geometry from thence
into Greece. He it was indeed, who, be-
sides other Things, found out the 5th,
15th, and 26th Propositions of the first
Book. To the same are also owing the
2d, 3d, 4th, sth, of the fourth Book.
The same Person began to observe the E-
quinoxes and Solstices, as Laertius testi-
fies; and he was the first who foretold an
Eclipse of the Sun, as Hippias and Arif
totle write ; and Tzetzes faith, That
he also foretold an Eclipse of the Moon
to King. Cyrus, For which Things fake he
is to be look'd on as the first Founder
and Author of the Mathematical Sciences
in Greece.

After him was Pythagoras of Samos:
Which most ancient Philosopher, exceed-
ingly improv'd and adorn'd the Mathe-
matick Sciences. And he fo gave him-
self to Arithmetick in particular, that al-
most his whole Method of Philosophizing
was taken from Numbers. And he first of
all, as Laertius relates, abstracted Geo-
metry from Matter ; in which Elevation
of the Mind, be found out the 32d, 44th,
47th, and 48th Propositions of the first

But he is especially celebrated for
the Invention of Prop. 32,


that Book; and he conceird so great Joy



upon this Invention, that, as Apollodorus witnesses in Laertius, on that Account he sacrific'd an Hecatomb. The same Perfon first laid open the Theory of incommensurable Magnitudes, and the Five regular Bodies. The same Person did both most diligently teach and exercise the Art of Astrology and Musick : For he did not only acutely and fubtily find out many Things himself, but he also first 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 Descriptions of Circles. Aristotle reports, that a certain Treatise of Geometry was writ. ten by Anaxagoras ; and we have it from Laertius, that it was fhew'd by him that the Sun is greater than Peloponnesus (a notable Instance of the Infancy of Astronomy at that Time); and that he made fome Conjectures concerning Habitations in the Moon. As for Oenopides, to him Proclus ascribes the 12 and 23.1. i. These were followed by Briso, Antipho, and Hippocrates of Chios, all of them, for ace tempting the Quadrature of the Circle, reprehended by Aristotle, and at the same


A 4.

time celebrated. But amongst them, Hippocrates was by far the most famous; that celebrated Perfon, who of a Merchant

· growing to be a Philosopher and a Geometrician, besides the Quadrature of the Circle, also 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 also his peculiar and great Commendation, that he, as Proclus testifies, first wrote Elements, and digested into Order the Discoveries made by others.


Democritus was admirable, not in Phi. lofophy only, but also in the Mathematicks. His Physical Monuments, and, if such there were, his Mathematical Works also, are wholly lost, thro' the Envy (as fome report) of Aristotle, who desired to have no other Writings read but his own. The Philosophy of Democritus hath been restored by Peter Gasendus, 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


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