EUCLTD, the celebrated mathematician, according to the account of Pappus and Proclus, was born at Alexandria, in Egypt, where lie flourished and taught mathe matics,, with great applause, under the reign of Ptolemy Lagos, about 280 years before Christ. And here, from his time till the conquest of 'Alexandria by the Saracens, all the eminent mathematicians were either born or studied ; and it is to Euclid, and his scholars, we are beholden for Eradtosthenes, Achimedes, Apollo nius, Ptolemy, Theon, &c. &e. He re duced into regularity and order all the fundamental principles of pure mathe matics, which had been delivered down by Thales, Pythagoras, Eudoxus, and other mathematicians before him, and ad ded many others of his own discovering : on which account it is said he was the first who reduced arithmetic and geome try into the form of a science. He like wise applied himself to the study of mix ed mathematics, particularly to astrono my and optics.
His works, as we learn from Pappus and Proclus, are, the Elements, Data, in troduction to Harmony, Phenomena, Op tics, Catoptrics, a Treatise of the Division of Superficies, Porisms, Loci ad Super ficiem, Fallacies, and four books of Co nics.
The most celebrated of these is the first work, the " Elements of Geometry ;" of which there have been numberless edi tions, in all languages ; and a fine edition of all his works, now extant, was printed in 1703, by David Gregory, Savilian Pro fessor of Astronmy at Oxford.
The " Elements," as commonly pub lished, consist of fifteen books, of which the two last, it is suspected, are not Eu clid's, but a comment of Hypsicles of Alexandria, who lived 200 years after Eu clid. They are divided into three parts,
viz. The contemplation of Superficies, Numbers, and Solids ; the first four books treat of planes only; the fifth of the pro portions of magnitudes in general ; the sixth of the proportion of plane figures; the seventh, eight, and ninth, give us the fundamental properties of numbers ; the tenth contains the theory of commensura ble and incommensurable lines and spa ces ; the eleventh, twelfth, thirteenth, fourteenth, and fifteenth, treat of the doc trine of solids.
There is no doubt but, before Euclid, elements of geometry were compiled by Hippocrates of Chius, Eudoxus, Leon, and many others, mentioned by Proclus, in the beginning of his second book ; for he affirms, that Euclid new ordered many things in the Elements of Eudoxus, com pleted many things in those of Theatettts, and besides strengthened such proposi tions as before were too slightly, or but superficially, established, with the most firm and convincing demonstrations.
History is silent as to the time of Eu clid's death, or his age. He is represent ed as a person of a courteous and agreea ble behaviour, and in great esteem and familiarity with King Ptolemy ; who once asking him whether there was any short er way of coming at geometry than by his Elements, Euclid, as Proclus testifies, made answer, that there was no other royal way or path to geometry.