ARISTARCHUS. De Magnitudinibus et Distantiis Solis et Lunae.
Pesaro: Franciscanus, 1572. First seperate edition.

This treatise is the sole extant work of Aristarchus - the first proponent of a heliocentric system - and marks “the first attempt to determine astronomical distances and dimensions by mathematical deductions based upon a set of assumptions.” (DSB).

Aristarchus “was the first to put forward the heliocentric hypothesis. In order to reconcile the apparent immobility of the fixed stars with the revolution of the earth around the sun, he assumed that the sphere of the fixed stars was incomparably greater than that containing the earth’s orbit. That is, the universe conceived by him was incomparably greater than that conceived by his predecessors. In his only extant treatise On the Sizes and Distances of the Sun and Moon he gave a scientific method to make these measurements. His results were grossly inaccurate, but the method was sound.” (Sarton, I:156).

“Some 1800 years before Copernicus, Aristarchus (c.310-c.230 B.C.) ventured the hypothesis - Archimedes is our source - ‘that the fixed stars and the sun are stationary, that the earth is borne in a circular orbit about the sun,’ and that the sphere of the fixed stars bears the same relationship to the sphere of the earth's orbit as the surface of a sphere to its center. In short, the earth is a planet and the sphere of the fixed stars motionless! Aristarchus also argued that the stars are so distant that the earth's motion produces no apparent shift, or parallax, in their position. This heliocentric or sun-centered universe attributed to Aristarchus seems to have received little attention among the ancients, but Copernicus was aware of the hypothesis, according to a deleted passage in a manuscript version of De Revolutionibus. The present translation of teh De Magnitudinibus was prepared at the request of the Duke of Urbino’s son by Frederico Commandino (1509-1575), who added extensive commentaries.” (The Barchas Collection, 1985, no. 5).

“After using sophisticated geometric calculations to estimate the size of the sun and moon, Aristarchus asserted that the former was much larger than the earth and that it was therefore more logical for the earth and the other planets to revolve around the earth. He wrote no treatise on the subject, but his claim was reported by Plutarch and earlier by Archimedes (who contested it) in his Arenarius, or Sandreckoner [see PMM 72 and Dibner 137]: ‘He supposes effectively that the sun and stars remain still and that the earth revolves around the sun in a circular path, the sun being at the centre of that circle.’ In his treatise On the Size and Distance of the Sun and the Moon Aristarchus calculated that the sun was some 18 to 20 times as far from the earth as the moon.” (Celestial Treasury, Oxford 2001, pp.31-32).

“This treatise is also of great mathematical interest because of it containing the calculation of ratios which are in fact trigonometrical ratios.” (Sarton, I p.156-57). “The propositions of Aristarchus are also of particular mathematical interest because the ratios of the sizes and distances which have to be calculated are really trigonometrical ratios, sines, cosines, &c., although at the time of Aristarchus trigonometry had not been invented, while no reasonably close approximation to the value of pi had been made (it was Archimedes who first obtained the value 22/7). Exact calculation of the trigonometrical ratios being therefore impossible for Aristarchus, he set himself to find upper and lower limits for them, and he succeeded in locating those which emerge in his propositions within tolerably narrow limits.” (Heath: Aristarchus of Samos, The Ancient Copernicus, p.328).

“The first printing of a Latin translation included [Aristarchus’] text tucked away in an eclectic volume by Georgio Valla of 24 works in philosophy, medicine, music theory, and mathematics (printed by Strata 1488, and reprinted by Bevilaquam 1498). The first significant Latin text is the translation and commentary made by Commandino (1572) near the end of this life [the offered edition, which is also the first to include Papus’ commentary]. The work appears as an independent treatise based around redrawn and mathematically coherent diagrams and accompanied by commentary fleshing out the mathematical argument. This publication has shaped the way the treatise has been read ever since. In fact, Wallis (1688) included Commandino’s translation, diagrams, and comments in his edition of the Greek text.” (Arch. Hist. Exact Sci. 61 (2007) 213–54).

Sparrow, Milestones of Science 10; Barchas Collection 82; Stanitz Sale 19; Sotheran’s 1360 in 770/1917; Houzeau & Lancaster 820.

4to: 181 x 127 mm. ff. [iv], 38. Provenance: The Macclesfield copy, fine 17th-century calf with crowned monogram of Gaston, Duke of Orléans (1608-1660), initials F.S.L.A. on title. Exceptionally fine and clean throughout.