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DEM states. Demochares especially distinguished himself in the raising and administration of the public finances. The last recorded act of his life was the proposing and carrying of the decree in honour of his great uncle. Only a few fragments of his works remain.—R. M., A.  DEMOCRITUS, the main founder of the atomistic philosophy, was born at Abdera in Thrace, 460. His father was a citizen of that town, in the possession of a fortune so considerable, that he is said to have entertained the army of Xerxes on its route towards Greece. Democritus inherited this fortune, and consumed the greater portion of it in a long course of extensive travels. The same thirst for knowledge led him in its pursuit over climates and countries as many and various as those traversed about the same period by the historian Herodotus; and, in some of his fragments which have been preserved, he declares ore rotunda how much he had seen and known. After visiting Egypt and Asia, and penetrating, according to some accounts, as far as India, he returned, rich in the results of his research, to devote himself in his native land to the study of natural history and philosophy. He had a high character for modesty and simplicity, as well as integrity of life; and seems to have attained a cheerful wisdom and a complacent view of men and things, which won for him the name of the Laughing Philosopher. His countrymen regarded him as a sort of oracle: things happened, they said, as Democritus foretold to them. He died at a great age, leaving no fortune behind him but renown. His love of knowledge remained intense throughout his life; he would rather, he declared, discover one new truth, than rule over all the Persians. His fame in the generation which succeeded him surpassed that of Empedocles or Heraclitus. He was regarded as one of the most learned of philosophers before Aristotle; and the list of his books preserved by Diogenes Laertius, bears testimony to an industry at least equal to that of the Stagyrite. These works were written in Ionic-Greek, in a style which Cicero praises as rivalling that of Plato himself. "Urguentur longa nocte," only a few scattered fragments remain, and we have to form our notions of his philosophy from the reports and adaptations of his successors. The atomistic philosophy, first advanced by Leucippus, adopted and developed by Democritus, formed in after times the theoretical basis of the system of Epicurus. In common with most of the earlier schemes of nature, it originated in a desire to reduce to some primal unity the multiplex phenomena of the universe. A rudimentary analysis of nature showed that a variety of appearances resulted from different combinations of the same elements. The question naturally arose, might not those elements themselves be further reduced? Modern chemistry laboriously seeks for a demonstration of the same proposition which ancient philosophy guessed at and prematurely asserted. Nature it said, is One, a Unity manifesting itself in various forms. The early Ionic philosophers differed as to the nature of this unity. They asserted in turn that all things might be analyzed into water, into air, into fire. The atomists, rejecting these solutions, assumed, as the ground of existence, an infinite number of Primæval Atoms, invisible, impenetrable, and indestructible. To such atoms they assigned certain powers of motion and combination, rendered possible by the postulate of a Void or empty space, in which, revolving and meeting and cohering, they made up the various visible forms of the universe. All apparent varieties of quality, were thus reduced to varieties of quantity and form. Bodies differ according as the atoms composing them are loosely—as in fire and water—or densely packed together, as in stone and metal; or according as those atoms themselves were sharp or blunt, hooked or round. All differences of taste, colour, smell, were referred to the same source of variation. In asserting that mind was merely a fine form of matter, the atomists only followed out consistently the train of thought suggested by the Ionic school. Their reasoning is merely repeated in all systems of materialism. The soul was with them a body within the body, made of more delicate atoms, and endowed with subtler senses. Thought, giving a knowledge more true than ordinary sensation, was itself but a more refined and pure sensation. All force was matter in motion. Democritus disclosed the weak point of his system in meeting the question as to the origin of this motion. He could not, without going beyond his hypothesis, attribute it to the impulse of an ultimate reason acting on the atoms, and had to rest in the final ground of an ultimate Necessity in the atoms themselves, called in opposition to the of Anaxagoras. Infinite particles, floating, as chance directed, in infinite space, and forming infinite worlds was the cosmological conception of the atomists. In this infinity there was no creation, no destruction, but constant change—"Omnia mutantur, nihil interit." Man was a complex agglomeration of particles, having the finer inclosed and protected by the more dense—the soul within the body. His duty was to five so as to gratify the higher and inner nature. The ethics of Democritus inculcated moderation in all things, comparative abstinence from sensual pleasures, and a concentration of the mind on those more properly its own, the acquisition of knowledge, and the contemplation of nature. The crown of life was , tranquillity, freedom from passion and fear, the joy of a good conscience, and a clear understanding.—J. N.  DEMOCRITUS, the mystagogue, commonly styled , one of these Greeks of the later empire who tried to attract attention to their wretched sophistries by assuming the names of the great men of a former age. He was probably a contemporary of Zosimus or Olympiodorus. His treatise entitled is still extant.—R. M., A.  DE-MOIVRE,, a celebrated English mathematician, born in France in 1667; died in England in 1754. De-Moivre lived at the period of the revival of analysis, just after the discoveries of Newton; he may be said to have succeeded Cotes. His great work is the "Miscellanea analytica de seriebus et quadraturis." He generalized the famous theorems of Cotes, and in other labours greatly advanced the Doctrine of Chances. He takes rank among the most eminent of early British analysts. His methods are now superseded by far more comprehensive processes, and his widest theorems are only corollaries from truths that are greatly more extensive. His private life was a quiet one, presenting no point of special interest.—J. P. N.  DEMONAX, a Grecian philosopher of the second century, was born of a good family in Cyprus. Having removed to Athens, he become an imitator of Socrates, connecting himself with the school of the Cynics, but combining with its rigid discipline the more genial spirit of the Cyrenaic philosophy; and the reply which he is said to have given on one occasion, seems to indicate accurately the bent of his mind and character—"Socrates, I worship; Diogenes, I admire; Aristippus, I love." He acquired, according to Lucian's account, great popularity and influence among the Athenians, notwithstanding his stern denunciations of prevalent vices and the little respect paid by him to the worship of the heathen deities. His sagacity and ready wit, associated with the disinterested integrity and kindness of disposition which he displayed, were fitted to make him a favourite. His fellow-citizens vied with each other in bestowing gifts upon him; and when he died at the age of a hundred years, their sorrow and esteem were manifested by a public funeral, which the whole city attended.—W. B.  * DE MORGAN,, a mathematician and actuary, was born in south India in 1806. Having taken his degree at Cambridge, he entered at Lincoln's-inn, and studied for the bar. He afterwards abandoned his attention of prosecuting the legal profession, and in 1828 accepted the professorship of mathematics in the university of London, which in 1837 had its name changed to University college, when it became only one of the affiliated colleges, associated under the examining board, now enjoying the former designation. He has written largely on mathematical subjects. The work by which his name is more generally known is that on the theory of probabilities. From his profound knowledge of this subject, he occupies the first place among actuaries, though unconnected with any particular office. He has written a work on formal logic, and on this subject his name is associated with that of Sir William Hamilton, the subject having called forth a keen controversial discussion. He contributed largely to the publications of the Society for the Diffusion of Useful Knowledge. In 1831 Mr. De Morgan resigned his chair, but he resumed it in 1836, and still continues to discharge its duties.—W. L., M..  DEMOSTHENES: born in the deme of Pæania, according to the most probable account, in the year 382 ., the greatest orator of Athens, was junior by one year to Philip of Macedon, and two years younger than Aristotle. He died at the same date as that philosopher, after having lived through the period of the Theban supremacy, the subversion of Greek independence, and the conquests of Alexander. The main facts of his life arrange themselves naturally in three epochs.

