the main points in which they agreed with, or differed from, each other. The earliest of them was _Thales_, who was born at Miletus, about 640 B.C. He was a man of great political sagacity and influence; but we have to consider him here as the earliest philosopher who appears to have been convinced of the necessity of scientific proof of whatever was put forward to be believed, and as the originator of mathematics and geometry. He was also a great astronomer; for we read in Herodotus (i. 74) that he predicted the eclipse of the sun which happened in the reign of Alyattes, king of Lydia, B.C. 609. He asserted that water is the origin of all things; that everything is produced out of it, and everything is resolved into it. He also asserted that it is the soul which originates all motion, so much so, that he attributes a soul to the magnet. Aristotle also represents him as saying that everything is full of Gods. He does not appear to have left any written treatises behind him: we are uncertain when or where he died, but he is said to have lived to a great age—to 78, or, according to some writers, to 90 years of age. _Anaximander_, a countryman of Thales, was also born at Miletus, about 30 years later; he is said to have been a pupil of the former, and deserves especial mention as the oldest philosophical writer among the Greeks. He did not devote himself to the mathematical studies of Thales, but rather to speculations concerning the generation and origin of the world; as to which his opinions are involved in some obscurity. He appears, however, to have considered that all things were formed of a sort of matter, which he called τὸ ἄπειρον, or The Infinite; which was something everlasting and divine, though not invested with any spiritual or intelligent nature. His own works have not come down to us; but, according to Aristotle, he considered this “Infinite” as consisting of a mixture of simple, unchangeable elements, from which all things were produced by the concurrence of homogeneous particles already existing in it,—a process which he attributed to the constant conflict between heat and cold, and to affinities of the particles: in this he was opposed to the doctrine of Thales, Anaximenes, and Diogenes of Apollonia, who agreed in deriving all things from a single, not _changeable_, principle. Anaximander further held that the earth was of a cylindrical form, suspended in the middle of the universe, and surrounded by water, air, and fire, like the coats of an onion; but that the interior stratum of fire was broken up and collected into masses, from which originated the sun, moon, and stars; which he thought were carried round by the three spheres in which they were respectively fixed. He believed that the moon had a light of her own, not a borrowed light; that she was nineteen times as large as the earth, and the sun twenty-eight. He thought that all animals, including man, were originally produced in water, and proceeded gradually to become land animals. According to Diogenes Laertius, he was the inventor of the gnomon, and of geographical maps; at all events, he was the first person who introduced the use of the gnomon into Greece. He died about 547 B.C. _Anaximenes_ was also a Milesian, and a contemporary of Thales and Anaximander. We do not exactly know when he was born, or when he died; but he must have lived to a very great age, for he was in high repute...