EUCHOLOGIUM, Εὐχαλογίον, a Greek term, signifying literally a discourse on prayer. The word is formed of εὐχα, prayer, and λογίον, discourse.
The Euchologium is properly the Greek ritual, wherein are prescribed the order and manner of every thing
Euclid
Eudoxia.
thing relating to the order and administration of their ceremonies, sacraments, ordinations, &c.
F. GOAR has given us an edition of the Greek Eudologium in Greek and Latin, with notes, at Paris.
EUCLID of MEGARA, a celebrated philosopher and logician, flourished about 400 B. C. The Athenians having prohibited the Megareans 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. Euclid admitted but one chief good; which he sometimes called God, sometimes Spirit, and sometimes Providence.
EUCLID of ALEXANDRIA, the celebrated mathematician, flourished in the reign of Ptolemy Lagus, about 277 B. C. He reduced all the fundamental principles of pure mathematics, which had been delivered down by Thales, Pythagoras, Eudoxus, and other mathematicians before him, into regularity and order, and added many others of his own discovering; on which account he is said to be the first who reduced arithmetic and geometry into the form of a science. He likewise applied himself to the study of mixed mathematics, and especially to astronomy, in which he also excelled. The most celebrated of his works is his Elements of Geometry, of which there have been a great number of editions in all languages; and a fine edition of all his works was printed in 1703, by David Gregory, Savilian professor of astronomy at Oxford.