Aristip´pus (c. 425-366 B.C.), a disciple of Socrates, and founder of a philosophical school among the Greeks, which was called the Cyrenaic, from his native city Cyrēnē, in Africa; flourished 380 B.C. His moral philosophy differed widely from that of Socrates, and was a science of refined voluptuousness. His fundamental principles were—that all human sensations may be reduced to two, pleasure and pain. Pleasure is a gentle, and pain a violent emotion. All living beings seek the former and avoid the latter. Happiness is nothing but a continued pleasure, composed of separate gratifications; and as it is the object of all human exertions, we should abstain from no kind of pleasure. Still we should always be governed by taste and reason in our enjoyments. His doctrines were taught only by his daughter Arĕtē, and by his grandson Aristippus the younger, by whom they were
systematized. Other Cyrenaics compounded them into a particular doctrine of pleasure, and are hence called Hedonici. His writings are lost.
Aristoc´racy (Gr. aristos, best, kratos, rule), a form of government by which the wealthy and noble, or any small privileged class, rules over the rest of the citizens. The term has now become almost entirely social in meaning, and is mostly applied to the nobility or chief persons in a State.
Aristogeiton (-gī´ton), a citizen of Athens, whose name is rendered famous by a conspiracy (514 B.C.) formed in conjunction with his friend Harmodius against the tyrants Hippias and Hipparchus, the sons of Pisistratus. Both Aristogeiton and Harmodius lost their lives through their attempts to free the country, and were reckoned martyrs of liberty.
Aristolochia (-lō´ki-a), a genus of plants, the type of the ord. Aristolochiaceæ, which consists of dicotyledonous monochlamydeous plants, with an inferior 3-6-celled fruit, found for the most part in the hotter parts of the world, and in many cases used medicinally on account of their tonic and stimulating properties. The genus has emmenagogic qualities, especially the European species A. rotunda, A. longa, and A. Clematītis. A. bracteāta is used in India as an anthelminthic; A. odoratissima, a West Indian species, is a valuable bitter and alexipharmic. A. serpentaria is the Virginian snake-root, popularly regarded as a remedy for snake bites.
Aristophanes (-tof´a-nēz), the greatest comic poet of ancient Greece, born at Athens probably about the year 455 B.C., died 375 B.C. Little is known of his life. He appeared as a poet in 427 B.C., and having indulged in some sarcasms on the powerful demagogue Cleon, was ineffectually accused by the latter of having unlawfully assumed the title of an Athenian citizen. He afterwards revenged himself on Cleon in his comedy of the Knights, in which he himself acted the part of Cleon, because no actor had the courage to do it. Of fifty-four (or forty-four) comedies attributed to him, eleven only remain; believed to be the flower of the ancient comedy, and distinguished by wit, humour, and poetry, as also by grossness. In them there is constant reference to the manners, actions, and public characters of the day, the freedom of the old Greek comedy allowing an unbounded degree of personal and political satire. The names of his extant plays are Acharnians, Knights, Clouds, Wasps, Peace, Birds, Lysistrata, Thesmophoriazusæ, Frogs, Ecclesiasuzæ, and Plutus.—Bibliography: B. B. Rogers, Complete Works of Aristophanes, with verse translation (by far the best translation); Hookham-Frere, Translation (five plays only); Couat, Aristophane et l'ancienne comédie attique.
Ar´istotle (Gr. Aristot´eles), a distinguished philosopher and naturalist of ancient Greece, the founder of the Peripatetic school of philosophy, was born in 384 B.C. at Stagira, in Macedonia; died at Chalcis, 322 B.C. His father, Nicomachus, was physician to Amyntas II, King of Macedonia, and claimed to be descended from Æsculapius. Aristotle had lost his parents before he came, at about the age of seventeen, to Athens to study in the school of Plato. With that philosopher he remained for twenty years, became pre-eminent among his pupils, and was known as the 'Intellect of the School'. Upon the death of Plato, 348 B.C., he took up his residence at Atarneus, in Mysia, on the invitation of his former pupil Hermeias, the ruler of that city, on whose assassination by the Persians, 343 B.C., he fled to Mitylene with his wife Pythias, a near relative of Hermeias. During his residence at Mitylene he received an invitation from Philip of Macedon to superintend the education of his son Alexander, then in his fourteenth year. This relationship between the great philosopher and the future conqueror continued for five or six years, during which the prince was instructed in grammar, rhetoric, poetry, logic, ethics, and politics, and in those branches of physics which had even then made some considerable progress. On Alexander succeeding to the throne Aristotle continued to live with him as his friend and councillor till he set out on his Asiatic campaign (334 B.C.). He returned to Athens and established his school in the Lyceum, a gymnasium attached to the temple of Apollo Lyceius, which was assigned to him by the State. He delivered his lectures in the wooded walks of the Lyceum while walking up and down with his pupils. From the action itself, or more probably from the name of the walks (peripatoi), his school was called Peripatetic. Pupils gathered to him from all parts of Greece, and his school became by far the most popular in Athens. The statement that he had two circles of pupils, the exoteric and the esoteric has given rise to much controversy. By some it has been held that Aristotle published during his lifetime popular discourses with a view to make way for his doctrines in Athenian society, then impregnated with Platonic theories, and that these are called exoteric in contradistinction to those in which are embodied his matured opinions. It was during the time of his teaching at Athens that Aristotle is believed to have composed the great bulk of his works. But it is not possible to speak with any certainty about the chronology of his writings, as the references may be additions of editors. On the death of Alexander a revolution occurred in Athens hostile to the Macedonian interests with which Aristotle was identified. He therefore retired to Chalcis, where he soon after died. Sir
Charles Walston, in 1891, opened a tomb near Eretria which he supposed to be that of Aristotle. According to Strabo he bequeathed all his works to Theophrastus, who, with other disciples of Aristotle, amended and continued them. They afterwards passed through various hands, till, about 50 B.C., Andronicus of Rhodes put the various fragments together and classified them according to a systematic arrangement. Many of the books bearing his name are spurious, others are of doubtful genuineness. The whole are generally divided into logical, theoretical, and practical. The logical works are comprehended under the title Organon (Instrument). The theoretical are divided into physics, mathematics, and metaphysics. The physical works (including those on natural history) are on the General Principles of Physical Science, The Heavens, Generation and Destruction, Meteorology, Natural History of Animals, On the Parts of Animals, On the Generation of Animals, On the Locomotion of Animals, On the Soul, On Memory, Sleep and Waking, Dreams, Divination. In mathematics there are two treatises, On Indivisible Lines and Mechanical Problems. The Metaphysics consist of fourteen books; the title (Ta meta ta Physika, 'the things following the Physics',) is the invention of an editor. The practical works embrace ethics, politics, economics, and treatises on art, and comprise the Nicomachæan Ethics (so called because dedicated to his son, Nicomachus), The Politics, Œconomics, Poetry, and Rhetoric. Among the lost works are the dialogues and others termed exoteric. A treatise On the Constitution of Athens was discovered in 1891. His style is devoid of grace and elegance. His works were first printed in a Latin translation, with the commentaries of Averroes, at Venice in 1489; the first Greek edition was that of Aldus Manutius (5 vols., 1495-8). See Peripatetic Philosophy.—Bibliography: Blakesley, Life of Aristotle; S. H. Butcher, Poetics (with translation and excursus); R. Shute, History of the Aristotelian Writings; J. C. Wilson, Aristotelian Studies; E. Zeller, Aristotle and the Earlier Peripatetics; E. Barker, Political Thought of Plato and Aristotle.
Aristox´enus, an ancient Greek musician and philosopher of Tarentum, born about 324 B.C. He studied music under his father Mnesias, and philosophy under Aristotle, whose successor he aspired to be. He endeavoured to apply his musical knowledge to philosophy, and especially to the science of mind, but it only appears to have furnished him with far-fetched analogies and led him into a kind of materialism. We have a work on the Elements of Harmony by him.
Arith´metic (Gr. arithmos, number) is primarily the science of numbers. As opposed to algebra it is the practical part of the science. Although the processes of arithmetical operations are often highly complicated, they all resolve themselves into the repetition of four primary operations—addition, subtraction, multiplication, and division. Of these the two latter are only complex forms of the two former, and subtraction again is merely a reversal of the process of addition. Little or nothing is known as to the origin and invention of arithmetic. Some elementary conception of it is in all probability coeval with the first dawn of human intelligence. In consequence of their rude methods of numeration, the science made but small advance among the ancient Egyptians, Greeks, and Romans, and it was not until the introduction of the decimal scale of notation and the Arabic, or rather Indian, numerals into Europe that any great progress can be traced. In this scale of notation every number is expressed by means of the ten digits, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, by giving each digit a local as well as its proper or natural value. The value of every digit increases in a tenfold proportion from the right towards the left; the distance of any figure from the right indicating the power of 10, and the digit itself the number of those powers intended to be expressed: thus 3464 = 3000 + 400 + 60 + 4 = 3 × 103 + 4 × 102 + 6 × 10 + 4. The earliest arithmetical signs appear to have been hieroglyphical, but the Egyptian hieroglyphics were too diffuse to be of any arithmetical value. The units were successive strokes to the number required, the ten an open circle, the hundred a curled palm-leaf, the thousand a lotus flower, ten thousand a bent finger. The letters of the alphabet afforded a convenient mode of representing figures, and were used accordingly by the Chaldeans, Hebrews, and Greeks. The first nine letters of the Hebrew alphabet represented the units, the second nine tens, the remaining four together with five repeated with additional marks, hundreds; the same succession of letters with added points was repeated for thousands, tens of thousands, and hundreds of thousands. The Greeks followed the same system up to tens of thousands. They wrote the different classes of numbers in succession as we do, and they transferred operations performed on units to numbers in higher places; but the use of different signs for the different ranks clearly shows a want of full perception of the value of place as such. They adopted the letter M as a sign for 10,000 and by combining this mark with their other numerals they could note numbers as high as 100,000,000. The Roman numerals, which are still used in marking dates or numbering chapters, were almost useless for purposes of computation. From one to four were represented by vertical strokes