(Εὐκλείδης). (1) A native of Megara, founder of the Megaric, or Eristic sect. Endowed by nature with a subtle and penetrating genius, he early applied himself to the study of philosophy. The writings of Parmenides first taught him the art of disputation. Hearing of the fame of Socrates, Euclid determined to attend upon his instructions, and for this purpose removed from Megara to Athens. Here he long remained a constant hearer and zealous disciple of the moral philosopher; and when, in consequence of the enmity which subsisted between the Athenians and Megareans, a decree was passed by the former that any inhabitant of Megara who should be seen in Athens should forfeit his life, he frequently came to Athens by night, from the distance of about twenty miles, concealed in a long female cloak and veil, to visit his master (Aul. Gell. vii. 10). Not finding his propensity to disputation sufficiently gratified in the tranquil method of philosophizing adopted by Socrates, he frequently engaged in the business and the disputes of the civil courts. Socrates, who despised forensic contests, expressed some dissatisfaction with his pupil for indulging a fondness for controversy ( Diog. Laert.ii. 30). This cir cumstance probably proved the occasion of a separation between Euclid and his master; for we find him, after this time, at the head of a school in Megara ( Diog. Laert.iii. 6), in which his chief employment was to teach the art of disputation. Debates were conducted with so much vehemence among his pupils that Timon said of Euclid that he had carried the madness of contention from Athens to Megara. That he was, however, capable of commanding his temper appears from his reply to his brother, who, in a quarrel, had said, Let me perish if I be not revenged on you. And let me perish, returned Euclid, if I do not subdue your resentment by forbearance and make you love me as much as ever.
In argument Euclid was averse to the analogical method of reasoning, and judged that legitimate argument consists in deducing fair conclusions from acknowledged premises. He held that there is one supreme good, which he called by the different names of Intelligence, Providence, God; and that evil, considered as an opposite principle to the sovereign good, has no existence. The supreme good, according to Cicero, he defined to be that which is always the same. In this doctrine, in which he followed the subtlety of Parmenides rather than the simplicity of Socrates, he seems to have considered good abstractly as residing in the Deity, and to have maintained that all things which exist are good by their participation of the first good, and, consequently, that there is, in the nature of things, no real evil. It is said that when Euclid was asked his opinion concerning the gods, he replied, I know nothing more of them than this: that they hate inquisitive persons.
(2) A celebrated mathematician of Alexandria, considered by some to have been a native of that city, though the more received opinion makes the place of his birth to have been unknown. He flourished B.C. 280, in the reign of Ptolemy Lagus, and was professor of mathematics in the capital of Egypt. His scholars were numerous, and among them was Ptolemy himself. It is related that the monarch having inquired of Euclid if there was not some mode of learning mathematics less barbarous and requiring less attention than the ordinary one, Euclid, though otherwise of an affable disposition, dryly answered that there was no royal road to geometry (μὴ εἶναι βασιλικὴν ἄτραπον πρὸς γεωμετρίαν). Euclid was the first person who established a mathematical school at Alexandria, and it existed and maintained its reputation till the Mohammedan conquest of Egypt. Many of the fundamental principles of the pure mathematics had been discovered by Thales, Pythagoras, and other predecessors of Euclid; but to him is due the merit of having given a systematic form to the science, especially to that part of it which relates to geometry. He likewise studied the cognate sciences of Astronomy and Optics; and, according to Proclus, he was the author of Elements (Στοιχεῖα), Data (Δεδομένα), An Introduction to Harmony (Εἰσαγωγὴ Ἁρμονική), Phaenomena (Φαινόμενα), Optics (Ὀπτικά), Catoptrics (Κατοπτρικά), On the Division of the Scale (Κατατομὴ Κανόνος), and other works now lost. His most valuable work, The Elements of Geometry, in thirteen books, with two additional books by Hypsicles, has been repeatedly published the first edition at Venice (1482) in a Latin translation from the Arabic. [p. 631] The first Greek text appeared at Basle in 1533. The edition of Peyrard is among the best. It appeared at Paris in 1814- 16-18, in 3 vols. This edition is accompanied with a double translationone in Latin and the other in French. M. Peyrard consulted a manuscript of the latter part of the ninth century, which had belonged to the Vatican library, and was at that time in the French capital. By the aid of this he was enabled to fill various lacunae, and to reestablish various passages which had been altered in all the other manuscripts and in all the editions anterior to his own. The best recent edition is that of Heiberg, 5 vols. (1883-88). The only English edition of all the works ascribed to Euclid is that of Gregory (Oxford, 1703). See Dodgson, Euclid and his Modern Rivals (1879); Allman, Greek Geometry from Thales to Euclid (1889); and Ball, Short Hist. of Mathematics, pp. 48-57 (1888).