256 



ARISTOTLE ARITHMETIC. 



school in opposition to the Platonic. It is certain 

 that there was some dispute between I In- two philo- 

 sophers, l)iit it never came to an open rupture. A. 

 constantly manifested the highest re\crence tor his 

 teacher, and everywhere, in his works, speaks with 

 great respect of him, even when he criticises him. 

 Tlie Athenians having declared war against Philip, 

 soon after Plato's death, A. left Athens for Atarnea, 

 where his friend llermias was sovereign, llennias 

 soon after was betrayed into the hands of Artaxerxes, 

 who dishonourably put him to death. A., deeply 

 moved by the fate of his friend, sought to perpetuate 

 his memory by an ode, which is rich in poetical 

 beauties : and espoused his niece. It appears that 

 A. lived some time after the death of his friend at 

 Mitylene; but, towards the year 343 B.C., he wns 

 invited by Philip to his court, to take ctiarge of the 

 education of Alexander, who was then thirteen years 

 old. The particulars of his method of instruction 

 are not known to us ; but when we see the greatness 

 of mind which Alexander displayed in the first years 

 of his reign, his command of his passions, till flattery 

 had corrupted him, and his regard for the arts and 

 sciences, we cannot but think that his education 

 W:IN judiciously conducted. It may be objected, that 

 Aristotle neglected to guard his pupil against ambi- 

 tion and the love of conquest ; but it must be recol- 

 lected that he was a Greek, and, of course, a natural 

 enemy to the Persian kings ; his hatred had been 

 deepened by the fate of his friend Hermias ; in short, 

 the conquest of Persia had, for a long time, been the 

 wish of all Greece. It was, therefore, natural that 

 Aristotle should exert all his talents to form his pupil 

 with the disposition and qualifications necessary for 

 the accomplishment of this object. Both father and 

 son sought to show their gratitude for the services of 

 such a teacher. Philip rebuilt Stagira, and established 

 a school there for Aristotle. The Stagirites, in gra- 

 titude for this sen-ice, appointed a yearly festival, 

 called AristoUlia. A. continued at Alexander's court 

 a year after his accession to the throne, and is said 

 to have then repaired to Athens. Ammonius the 

 Eclectic says that he followed his pupil in a part of 

 his campaigns ; and this seems very probable, be- 

 cause it is hardly possible that so many animals as 

 the philosopher describes could have been sent to 

 Athens, or that he could have given so accurate a 

 description of them without having personally dis- 

 sected and examined them. We may conjecture 

 that he accompanied Alexander as far as Egypt, and 

 returned to Athens about 331 B. C., provided with 

 the materials for his excellent History of Animals. 

 Here he opened a school of philosophy in the Ly- 

 ceum, a gymnasium not far from the city. Thither 

 he went twice a-day. The forenoon was devoted to 

 his most intimate pupils, when he explained to them 

 the difficult parts of science. In the evening, he 

 admitted all those who were desirous of hearing him, 

 while he discoursed, in a familiar and intelligible 

 way, on subjects more nearly connected with common 

 life. Accordingly, his works also are divided into 

 the esoteric or aLstruse, and the exoteric or familiar. 

 Alexander aided his extensive studies by sending him 

 presents from Asia, and, as a reward for his services, 

 gave him 800 talents. Notwithstanding this, he 

 afterwards conceived an enmity against his tutor. At 

 the death of that prince, 334 B. C. , A. was reported 

 to be concerned in his pretended assassination. The 

 Athenians, now hoping to recover the command of 

 Greece, endeavoured to prevail on the other states to 

 take arms against the Macedonians, and Aristotle 

 became an object of suspicion, on account of his con- 

 nexion with Philip, Alexander, and Antipater. The 

 demagogues, supported by his numerous enemies, 

 took this opportunity to accuse him. To escape pro- 



secution, on a chare of atheism, he left Athens wiifc 

 the observation (alluding to the condemnation of 

 Socrates), that he would spare them the guilt of a 

 second crime against philosophy. He retired, with 

 most of his scholars, to Chalcis, in Euboea, where he 

 shortly after took poison, 322 B. C., on being sum 

 immed, as it is said, U appear before the court of 

 areopagus at Athens, to answer to the accusation 

 against him. (For his doctrines and sect, see 

 I'/iitHsn]>/iy, rrrij>ntitic.)'l'\H' works of Aristotle, 

 which were not published during his lifetime, 

 first became known to the world when the Ro- 

 mans began totievote themselves to philosophy. The 

 original manuscripts of his works, and those oi'Thco- 

 phrastus, were brought by Sylla to Home, with the 

 library of Apellicon. Andronicus of Rhodesarrani il 

 them, and furnished them with indices. Many of his 

 important works are now lost. Those yet extant, 

 according to the edition of Sylburg, 5 vols., 4to., 

 Frankfort, 1587, which is esteemed the hot, are the 

 following: Organon; Rhetorica et Poetica; Ktliirn 

 ad Nicotnachum ; Ethica Magna ; Politico, et SEco- 

 nomica ; Animalium Historia ; De Aiihniilinin J'ur- 

 (if/us Physicce Attscultationis, lib. xiii., et alia Opera ; 

 De Ceelo ; De Generatione ct Conceptione ; De Miff 

 oris, lib. iv. ; De Mundo ; DC Anhna ; 1'arvu Xnt/t- 

 ralia ; Varia Opuscula ; Aristotelis, Alexandri et 

 Cascii Problemata ; Aristotelis et Theophrasti Mrtu- 

 physica. Besides the edition above-mentioned, those 

 of Casaubon and Duval are esteemed. The latest 

 edition is that of Buhle, not yet completed. See 

 Philosophy. 



ARITHMETIC (from the Greek ttfitpos, number); a 

 branch of mathematics, the object of which is, to 

 combine numbers according to certain rules, in order 

 to obtain results which satisfy given conditions. These 

 rules, methodically arranged, form a science, to 

 which the name of arithmetic is given. This science 

 is very ancient, and we find it (of course, in very 

 different degrees of perfection) among all nations. 

 The Greeks, it is well known, were ignorant of our 

 system of decimal notation, the simplest and most. 

 perfect of all inventions. They marked numbers 

 laboriously by help of the letters of their alphabet ; 

 and, though this method received successive improve- 

 ments, it was still unavoidably complicated, and al- 

 together irregular in the form of its constitution. The 

 idea of number is one of the latest and most difficult 

 to form. Before the mind can grasp such an abstract 

 conception, it must be familiar witli that process of 

 classification by which we successively remount from 

 individuals to species, from species to genera, and 

 from genera to orders. The savage is soon lost in 

 his attempts at numeration ; and significantly ex- 

 presses his inability to proceed, by holding up his 

 expanded fingers, or pointing to the hairs of his head. 

 The classification by pairs, which nature points out, 

 would suggest the simplest mode of reckoning. The 

 Dual accordingly, though retained by the Greeks, 

 occurs in the languages of all barbarous tribes. 

 Counting these pairs again by two's, and repeating 

 the same procedure, we arrive, by progressive steps, 

 at the radical terms 4, 8, 16, &c., to which the other 

 numbers are easily reducible. Thus, 13 being com- 

 posed of 8, 4, and 1, would, according to sucli a sys 

 tern of numeration, be called " quadruple pair, double 

 pair, and one," or denominated more concisely by 

 words of corresponding import. This plan of ar- 

 rangement, termed the binary scale, seems, at a 

 certain period of society, to have prevailed in most 

 countries. Vestiges of it are still found among tlio 

 Chinese ; and Leibnitz has extolled the system with 

 abundant extravagance. Jt would, no doubt, from 

 its naked simplicity, supersede the application ol 

 thought, and reduce all the operations which occur 



