laus which were Six, and the Twelve of Hipparchus, all contracted by him into Five Theorems. As for Plutarch, a moft fam'd Philofopher, there are extant his Mathematical Problems. And all know of the learned Commentaries of Eutocius the Af calonite upon Archimedes. By him are recited the Inventions of Philo, Diocles, Nicomedes, Sporus, Heron, as of fo many excellent Mafters in the Mathematicks, concerning Doubling the Cube. Heron's Genius certainly was excellent, as well for Mechanicks as Geometry. The Doubling of the Cube delivered by him is commended by Pappus, Book III. Prop. 7. before all other. The admirable Works of Ctefibius the Alexandrian, to whom we owe our Pumps, are celebrated by Vitruvius, Proclus, Pliny, and Athenæus. The Name alfo of Geminus is not in the lowest Place amongst Mathematicians, whom Proclus has preferr'd in many Things before Euclid himself.

Diophantus, and he also an Alexandrian, was as great in Arithmetick as Archimedes, Apollonius, or Euclid in Geometry; he was certainly a Master of all Subtilty relating to Numbers: by him was found out that admirable Art, which we call Algebra; which in thefe Times has been rendered more perfect and univerfal by Francis Vieta, and Renatus Cartefius. There are

others

others who are celebrated amongst the Antients alfo; as Nicomachus, famous for Arithmetical, Geometrical, and Musical Monuments; Serenus well known to Geometricians for his Two Books, concerning the Section of a Cylinder; Proclus, Pappus, Theon. How great a Mathematician Proclus was, is manifeft from his learned Commentaries on Euclid, and other Writings. And this is he, I fuppofe, who, as Zonaras reports, and from him Ramus, and Baronius, about the Year of Chrift 514, with Optic Artifice, and the Glaffes which he ufed, burnt the Fleet of Vitalian, who was befieging Conftantinople. The Praises of Theon, which truly are deservedly great, Peter Ramus wonderfully exaggerates; infomuch that even the Books which hitherto all have afcribed to Euclid, ought, as he thinks, to be attributed to Theon. But Ramus, who every where is ready to detract from Euclid, and this without grounding himself upon any folid Foundation, is not to be hearken'd to here. To come at length to a Conclufion, let Pappus bring up the Rear, the laft in Time among the Antients, as being one who liv'd about the Year 400; but in Reputation, and all Mathematical Commendation, to be reckon'd a mongst the first. Alexandria, that City fo fruitful of great Men, which before had brought forth Hypficles, Ctefibius

and

and Diophantus, produced him alfo, to the great Advantage of the Mathematicks. He wrote Seven Books of Mathematical Collections, of which the Two First are loft. The Five other do abound with fo many, and fuch various most noble Inventions in almoft all Parts of the Mathematicks, that they are esteemed amongst the chief Monuments of the Antients which are extant.

And thus you have a fhort Hiftory of the Origin and Progrefs of the Mathematicks. From which appears the Antiquity, Excellency, and Dignity of this Sci

ence.

And truly the fame eminent Perfons in the Commonwealth of Learning, who discover'd Philofophy, discover'd alfo the Mathematicks, like two Sifters born at one Birth; whom if any one would violently feparate from each other, he certainly attempts to break off their native Concord, with most notable Injury, and as it were Cruelty to both; feeing, as it is wont to fall out in the Cafe of Twins, where they are remov'd from one another, in Place or by Death, fo it will be like to happen here, that Mathematicks being plucked away from her, Philofophy muft needs languifh and pine away.

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Aftronomical Lectures, read in the publick Schools at Cambridge, first published in Latin for the Ufe of young Students in the University, and now done into English. 8vo. Price 6 s. Sir Ifaac Newton's Mathematical Philofophy, more easily demonftrated; and Dr. Halley's Account of Comets Illuftra

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