whereas its real value is less than a right angle by about half a minute only ; and hence he infers that the distance of the sun is between eighteen and twenty times greater than that of the moon, where- as the true ratio is about twenty times as great, the distances being to one another nearly as 400 to 1. The ratio of the true diameters of the sun and moon would follow immediately from that of their distances, if their apparent (angular) diameters were known. Aristai'chus assumes that their ap- parent diameters are equal, which is nearly true ; but estimates their common value at two degrees, which is nearly four times too great. The theory of parallax was as 3'et unknown, and hence, in order to compare the diameter of the earth with the magnitudes already mentioned, he compares the diameter of the moon with that of the earth's shadow in its neighbourhood, and assumes the latter to be twice as gre.it as the former. (Its mean value is about 84'.) Of course all the nume- rical results deduced from these assumptions are, like the one first mentioned, very erroneous. The geometrical processes employed shew that nothing like trigonoinetr' was known. No attempt is made to assign the absolute values of the magni- tudes whose ratios are investigated ; in fact, this could not be done without an actual measurement of the earth — an operation which seems to have been first attempted on scientific principles in the next generation. [Eratosthenes.] Aristarchus does not explain his method of determining the apparent diameters of the sun and of the earth's shadow ; but the latter must have been deduced from observations of lunar eclipses, and the former may probably have been observed by means of the skuphium by a method described by Macrobius. {Somn. Scip. i. 20.) This instrument is siiid to have been invented by Aristarchus (Vitruv. ix. .9): it consisted of an improved gnomon [Anaximan- dkr], the shadow being received not upon a hori- zontal plane, but upon a concave hemispherical surface having the extremity of the style at its centre, so that angles might be measured directly by oj'cs instead of bj' their tangents. The gross error in tlie vakie attributed to the sun's apparent diameter is remai'kable ; it appears, however, that Aristarchus must afterwards have adopted a mucli more correct estimate, since Archimedes in the i^a/x/uiTTjs (WaJlis, Op. vol. iii. p. 51.5) refers to a treatise in which he made it only half a degree. Pappus, whose commentary- on the book Trepi fj.eye- 6(ip, &c is extant, does not notice this emendation, whence it has been conjectured, that the other works of Aristarchus did not exist in his time, having perhaps perished with the Alexandrian library.
It has been the common opinion, at least in mo- dern times, that Anstarchus agreed with Philolaus and other astronomers of the Pythagorean school in considering the sun to be fixed, and attributing a motion to the eartL Plutarch {de/ac. in orb. lun. p. 922) siu's, that Cleanthes thought that Aristar- chus ought to be accused of impiety for supposing {yTToriQifxevos^ that the heavens were at rest, and that the earth moved in an oblique circle^ and also about its own axis (the true reading is evidently KkidvQ-ns (^€To diiv ^ApicTTapxov, k, t. X.) ; and Diogenes Laertius, in his list of the works of Cle- anthes mentions one wpos 'ApicxTapxov. (See also Sext. Empir. adv. Math. p. 410, c; Stobaeus, i. 26.) Archimedes, in the y^^a/jLjilr-qs (/. c), refers to the same theory. (viroTiQeTai yap, k. t. A.) But the treatise Tr^p yL^y^Qcov contains not a word upon the subject, nor does Ptolemy allude to it when he maintains the immobility of the earth. It seems therefore probable, that Aristarchus adopted it ra- ther as a hi/potlu'sis for particular purposes than as a statement of the actual system of the universe. In fact, Plutarch, in another place {Plat. Quaesi. p. 1006) expressly says, that Aristarchus tJiught it only hypotheticaliy. On this question, see Sciiau- bach. {Gesch. d. Griech. Astronomie, p. 468, <itc.) It appears from the passage in the ^afxixh-ns allud- ed to aboTe, that Aristarchus had much juster views than his predecessors concerning the extent of the universe. He maintained, namely, that the sphere of the fixed stars was so large, that it bore to the orbit of the earth the relation of a sphere to its centre. What he meant by the expression, is not clear : it may be interpreted as an anticipation of modern discoveries, but in this sense it could express only a conjecture which the observations of the age were not accurate enough either to con- firm or refute — a remark which is equally applica- ble to the theory of the earth's motion. Whatever may be the truth on these points, it is probable that even the opinion, that the sun was nearly twenty times as distant as the moon, indicates a great step in advance of the popular doctrines.
Censorinus {de Die Nata/i, c. 18) attributes to Aristarchus the invention of the magmas annus of 2484 years.
A Latin translation of the treatise irepl fieyeBtHv was published by Geor. Valla, Venet. 1498, and another by Commandine, Pisauri, 1572. The Greek text, with a Latin translation and the com- mentary of Pappus, was edited by Wallis, Oxon. 1688, and reprinted in vol. iii. of his works. There is also a French translation, and an edition of the text, Paris, 1810. (Delambre, Hid. de PAstronomie Ancienne^ liv. i. chap. 5 and 9 ; La- place, Syst. du Monde., p. 381; Schaubach in Ersch and Gruber's Encydop'ddic.) [W. F. D.]
ARISTARCHUS {'ApicrTapxos) of Tegea, a
tragic poet at Athens, was contemporary with
Euripides, and flourished about 454 B. c. He
lived to the age of a hundred. Out of seventy
tragedies which he exhibited, onh' two obtained
the prize. (Suidas, s. r. ; Eis,eh. Chron. Arincn.)
Nothing remains of his works, except a few lines
(Stobaeus, Tit. 63. § 9, tit. 120. § 2; Athen.
xiii. p. 612, f.), and the titles of three of his plays,
namely, the 'Ao-/cjirtos, which he is said to have
written and named after the god in gratitude for
his recovery from illness (Suidas), the 'AxtAAews,
which Ennius translated into Latin (Festus, s. v.
prolaio acre), and the TavTaXos. ^Stobaeus, ii.
L § 1.) ' [P. S.]
ARISTARETE, a painter, the daughter and
pupil of Nearchus, was celebrated for her picture
of Aesculapius. (Plin. xxxv. 40. § 43.) [P. S.]
ARI'STEAS ('Apjirreas), of Proconnesus, a son
of Caystrobius or Demochares, was an epic poet,
who flourished, according to Suidas, about the
time of Croesus and Cyrus. The accounts of his
life are as fabulous as those about Abaris the Hyper-
borean. According to a tradition, which Herodo-
tus (iv. 15) heard at Metapontum, in southern
Italy, he re-appeared there among the living 340
years after his death, and according to this tradi-
tion Aristeas would belong to the eighth or ninth
century before the Christian era ; and there are
