vol. II p.873-876
From Samos, a mathematician and astronomer, was a student of the Peripatetic Straton of Lampsakos (Aetios in Stob. Ekl. I 16, 1 p.313 b Diels). <page break 873/874> In the year 281/80, as Ptolemy (Synt. vol. I 162 Halma) reports with reference to Hipparchos, he managed to observe the summer solstice. His hypothesis that it wasn’t the earth, but the sun around which the planets revolved - including the earth - was heavily attacked by Kleanthes, probably at the time when he was already at the head of the Stoic school. <10> For this reason, we can assume that Aristarchos was still alive in 264. It remains to be determined whether he was working in Alexandria temporarily, or for an extended period of time (Susemihl Litt.-Gesch. I 718f.). His work περὶ μεγεθῶν καὶ ἀποστημάτων ἡλίου καὶ σελήνης was included in the collection of small astronomical writings (μικρὸς ἀστρονόμος or ἀστρονομούμενος, ie. τόπος), which was used in the schools of Alexandria alongside the great Syntaxis of Ptolemy (Fabricius Bibl. Gr. IV 16 Harl. Hultsch on Pappos vol. II 475. III 1143. Susemihl loc. cit. 760), <20> meaning that it has also been preserved to the present day. Editions: Aristarchi Samii lib. de magnit. et distant. solis et lunae ed. Wallis, Oxon 1688 and in Wallisii Op. mathem. III 565ff., Oxon. 1699. Histoire d’Aristarque de Samos par M. de F(ortia d’Urban), Paris 1810. Because it was compiled very carelessly, A….. with critical corrections edid. E. Nizze, Stralsund 1856 is unusable. <30> Latin editions: Aristarchi Samii de magnit. etc. in ‘Georgio Valla interprete. Hoc in volumine hec continentur Nicephori logica’ etc., Venetiis per Simonem Papiensem dictum Bevilaquam 1498. A. de magnit. etc. a F. Commandino in Lat. conversus ac comment. illustr., Pisauri 1572. German translation by A. Nokk, Freiburg 1854. The proof of the 7th proposition is handled by Hultsch Nachr. Gesellsch. d. Wiss. Göttingen 1893, 372ff. - <40> Excerpts from this work and extra explanations are given by Pappos (Synag. VI 554-568, cf. the scholia too vol. III 1183 Hultsch). The 9th proposition, which states that the diameter of the sun is between 18 and 20 times as large as that of the moon, is citied by Archim. aren. vol. II 248 Heiberg. Plut. de fac. lun. p.932 B is based on the 17th proposition. According to Tannery Mém. de la société des sciences de Bordeaux V 2 (1883), 237ff. (cf. dens. Hist. de l’astronomie ancienne 43. Heiberg Philol. XLIII 482), <50> Aristarchos had further developed the ancient method used by Eudoxos to get rough estimates of the diameters of the sun and the moon, and solidified it using geometric proofs. On Aristarchos’ method to determine the distance between the sun and the earth, cf. Grunert in Archiv für Math. und Phys. V (1844), 401ff. Marie Hist. des science mathém. I, Paris 1883, 69ff. Günther Quadrat. Irrationalitäten in Abhandl. zur Gesch. der Math. IV 12ff.; <60> Gesch. der Math. u. Naturwiss.2 282. - In the work mentioned above, Aristarchos had determined that the moon orbited around the earth (Hypoth. 2), and that the moon moved below (κατώτερον) the sun (Propos. 6). In Propos. 7, he also has the sun move around the earth; so, he had given in to the geocentric view which was universally popular at the time. <page break 874/875> We only have excerpts from another work of Aristarchos preserved in The Sand Reckoner by Archimedes, which was perhaps titled ὑποθέσεις, or even ὑποθέσεων γραφαί, ie. geometric constructions on hypotheses (on space) (Archim. II 244, 9 cites: Ἀρίσταρχος ὁ Σάμος ὑποθεσίων τινῶν ἐξέδωκεν γραφάς, cf. Hultsch Nachr. Gesellsch. d. Wiss. Göttingen 1893, 376, 1). Here, he dared to go beyond the narrow views of antiquity, <10> which still remained dominant even up to Galilei and Copernicus, and he didn’t only move over to the heliocentric system, but he even broadened the overall understanding of space. The sun is a fixed star like the rest of the fixed stars which we see in the sky (the apparent movement of the sun and the stars throughout the day is therefore because of the rotation of the earth). The earth moves around the sun (just like the other planets). <20> If we consider earth’s path as the largest circle on a sphere, then compared to all of space, this sphere would only be a mere dot (following the geocentric view, it was only allowed to consider the earth’s sphere as a point). If we choose to determine the distance between the earth and the sun, ie. the radius of the κόσμος as it is usually called (246, 5-7), in stadia, then this value should be squared, <30> to work out the distance between the earth and the fixed star sphere. Archim. aren. 244-248. 288. 290 Heib., cf. Heiberg ibid. 247 and Quaest. Archim. 202. Also from Plut. quaest. Plat. 8, 1; de fac. lun. 6. Aetios in Stob. I 25, 3 p.355 Diels. Sext. Empir. adv. math. X 174 p.512 Bekk. Simplic. on Aristot. de caelo p.200 Karsten, it can be concluded that in Aristarchos’ view, the earth is not stationary, but instead rotates around its own axis, and also moves around the sun in a plane at an angle to its rotational axis. <40> Though Plut. quaest. Plat. loc. cit. adds that Aristarchos only assumes this (ὑποθέμενος μόνον) and that Seleukos was the one to prove it, this doesn’t contradict our assumption above that Aristarchos had included geometric constructions with his hypotheses. cf. also Schaubach Gesch. der griech. Astronomie, Göttingen 1809. 450ff. and in Ersch and Gruber Encyclop. u. d. W. A., also R. Wolf Geschichte der Astronomie 35ff. <50> Tannery Hist. de l’astron. 97. 99. 100ff. Günther loc. cit. 277f. Diels S.-Ber. Akad. Berl. 1893, 118. Susemihl Litt.-Gesch. II S. VI. The Stoic Kleanthes wrote a work opposing these views which turned current beliefs on their heads, and in this work he accused Aristarchos of blasphemy (Plut. de fac. lun. 6. Diog. Laert. VII 174). - Aristarchos supposedly calculated the length of the solar year to be 365 + 18 + 11623days; <60> but perhaps a mistake got into the ms. tradition in Censorin (de die nat. 9, 2). The so-called great year, ie. the period after which all stars are in the same position they were at the beginning, was probably rounded by Aristarchos to 2484 by disregarding a small fractional part, Censorin 18, 1. Tannery Mém. de la société des sciences de Bordeaux, 3. série IV (1888), 79ff. (in Censorin, Tannery p.80 is inclined to read 2434 instead of the number 2484 which is handed down). <page break 875/876> - In order to record the solar elevation as precisely as possible, Aristarchos invented an improved gnomon, the so-called σκάφη, a hollow semisphere with a stick in the middle, which cast the sun’s shadow and made it possible to read off the height of the sun at any time of day using the dividing lines drawn onto the semisphere (Vitr. IX 9. Marie loc. cit. 76f.). - <10> Aristarchos also wrote about solar eclipses, light and colours, and the sense of sight (Aetios in Ps.-Plut. and Stob.: s. Doxographi Gr. ed. Diels 355. 313. 404 b, 1. 853. Diels S.-Ber. Akad. Berl. 1893, 119. Susemihl I 719f.).
[Hultsch.]
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