, of Megara, a celebrated philosopher and logician; he was a disciple of Socrates, and flourished about 400 years before Christ. The Athenians having prohibited the Megarians from entering their city on pain of death, this philosopher disguised himself in women's clothes to attend the lectures of Socrates. After the death of Socrates, Plato and other philosophers went to Euclid at Megara, to shelter themselves from the tyrants who governed Athens.—This philosopher admitted but one chief good; which he at different times called God, or the Spirit, or Providence.


, the celebrated mathematician, according to the account of Pappus and Proclus, was born at Alexandria, in Egypt, where he flourished and taught mathematics, with great applause, under the reign of Ptolomy 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 Eratosthenes, Archimedes, Apollonius, Ptolomy, Theon, &c, &c. He reduced into regularity and order all the fundamental principles of pure mathematics, which had been delivered down by Thales, Pythagoras, Eudoxus, and other mathematicians before him, and added many others of his own discovering: on which account it is said he was the first who reduced arithmetic and geometry into the form of a science. He likewise applied himself to the study of mixed mathematics, particularly to astronomy and optics.

His works, as we learn from Pappus and Proclus, are the Elements, Data, Introduction to Harmony, Phenomena, Optics, Catoprics, a Treatise of the Division of Supersicies, Porisms, Loci ad Supersiciem, Fallacies, and Four books of Conics. The most celebrated of these, is the sirst work, the Elements of Geometry; of which there have been numberless editions, in all languages; and a fine edition of all his works, now extant, was printed in 1703, by David Gregory, Savilian professor of astronomy at Oxford.

The Elements, as commonly published, consist of 15 books, of which the two last it is suspected are not Euclid's, but a comment of Hypsicles of Alexandria, who lived 200 years after Euclid. They are divided into three parts, viz, the Contemplation of Superficies, Numbers, and Solids: The first 4 books treat of planes only; the 5th of the proportions of magnitudes in general; the 6th of the proportion of plane figures; the 7th, 8th, and 9th give us the fundamental properties of numbers; the 10th contains the theory of commensurable and incommensurable lines and spaces; the 11th, 12th, 13th, 14th, and 15th, treat of the doctrine 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, completed many things in those of Theatetus, and besides strengthened such propositions as before were too slightly, or but superficially established, with the most firm and convincing demonstrations.

History is silent as to the time of Euclid's death, or his age. He is represented as a person of a courteous and agreeable behaviour, and in great esteem and familiarity with king Ptolomy; who once asking him, whether there was any shorter way of coming at geometry than by his Elements, Euclid, as Proclus testifies, made answer, that there was no royal way or path to geometry.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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EULER (Leonard)