770 EUCLID OF MEGARA EUDOCIA known of the treatises of Euclid, after the "Elements," is the "Data." By this name are designated certain known quantities which by means of analysis lead to the discovery of other quantities before unknown. One hun- dred propositions are here collected which are the most curious examples of geometrical an- alysis among the ancients. Newton highly valued them, and Montucla styles them the first step toward transcendental geometry. The history of the works of Euclid is the his- tory of geometry itself, both in Christian and Mohammedan countries, until after the revival of learning. They were commented upon by Theon and Proclus, and became the foundation of mathematical instruction in the school of Alexandria. Of the numerous editions and commentaries among the Orientals, that of Nasir ed-Din, a Persian astronomer of the 13th century, was the best. The "Elements" were restored to Europe by translation from the Arabic, the first European who translated them being Adelard of Bath, who was alive in 1130, and who found his original among the Moors of Spain. Campanus, under whose name this translation was printed, was for a long time thought to be its author. The Greek text was first published in 1533 by Si- mon Grynasus at Basel, and in subsequent edi- tions was corrected by comparison of manu- scripts. Since then the work has been pub- lished in a great variety of editions, and trans- lated into all the European and many oriental languages. The English adaptations by Sim- son and Playfair have been widely received as text books in geometry. EUCLID OF MEGARA, a Greek philosopher, born about 440 B. 0. His first master was Parmenides ; afterward he became a devoted disciple of Socrates, at whose death, according to Plato, he was present. But notwithstand- ing his affection for his second teacher, he re- tained from the Eleatic school an invincible tendency to subtlety, and it was said of him by Socrates that he knew how to live with soph- ists, but not with men. After the death of Socrates, his disciples, fearing for their lives, fled from Athens ; and at Megara, in the house of Euclid, they found an asylum and a new centre for their studies. Plato himself was an ardent attendant upon Euclid, who taught that the essence of good was unity, unity so entire-as to embrace immobility, iden- tity, and permanence. Hence the sensible world has no moral character and no relation to good. He taught also that being consists only in unity, identity, and permanence, and hence the sensible world has no part in ex- istence. Being and good are thus the same thing, namely, unity ; good therefore alone ex- ists, and evil is but the absence of existence. It does not follow, however, that there is but a single being and a single sort of good, for unity may be found contained in various things. Euclid expressly taught that in spite of their unity, being and good clothe themselves in different forms, present themselves under dif- ferent points of view, and receive different names, as wisdom, God, intelligence, and others. Euclid also anticipated Aristotle in distinguishing the act from the power, and re- solved according to his ideas of being the rela- tion between the two. EUDIOMETER (Gr. evdia, pure air, and [itrpov, measure), an instrument invented by Priestley for determining the proportion of oxygen in the air, in the belief that on this depended its salubrity. Many other instruments have since been invented for estimating the amount of oxygen in gaseous mixtures, and the name is retained for these, though it has no longer its original significance. In the application of the instrument for estimating oxygen, the gas is made to unite with some substance, as phos- phorus, introduced into the gaseous mixture, which is contained in the upper end of a graduated glass tube inverted over mercury. The diminution of bulk caused by the absorp- tion of the oxygen indicates its quantity. In other forms a known quantity of hydrogen is introduced, and a mixture fired by an electric spark produced by means of two wires being melted into the sides of the tube and nearly meeting each other within. In this case the tube is made very thick to withstand the ex- plosion. Every two volumes of hydrogen con- sume one of oxygen, whence the quantity of the latter may be estimated. EUDOCIA. I. A Roman empress, born in Athens about A. D. 394, died in Jerusalem about 461. She was instructed by her father, the sophist Leontinus, in the religion, literature, and science of the pagan Greeks, and was as remarkable for beauty as for learning. Leon- tinus at his death left her only 100 pieces of gold, saying that the merits of his daughter, which raised her so much above her sex, would be sufficient for her. Having sought in vain from her brothers a share in the paternal heri- tage, she went with an aunt to Constantinople to solicit the cancelling of the will. She pro- cured an audience of Pulcheria, sister of the young emperor Theodosius II., and regent in his name, who was so charmed by her wit and beauty that she induced her brother to marry her in 421, after her baptism, when she re- ceived the name of Eudocia in place of her original one of Athenais. She received the title of Augusta in 423, and requited the un- kindness of her brothers by making them con- suls and prefects. During the first 20 years after her marriage she took little part in pub- lic affairs, which remained in the hands of Pulcheria. She translated parts of the Old Testament into hexameter verses, and a life of Jesus Christ composed in verses taken from Homer is attributed to her. She also cele- brated in verse the Persian victories of Theo- dosius, and the legends and martyrdom of St. Cyprian. She at length, supplanting Pulche- ria, ruled the empire for several years. Her court was filled with learned men, with one
