As for men upon whom nature has bestowed so much ingenuity, acuteness, and memory that they are able to have a thorough knowledge of geometry, astronomy, music, and the other arts, they go beyond the functions of architects and become pure mathematicians. Hence they can readily take up positions against those arts because many are the artistic weapons with which they are armed. Such men, however, are rarely found, but there have been such at times; for example, Aristarchus of Samos, Philolaus and Archytas of Tarentum, Apollonius of Perga, Eratosthenes of Cyrene, and among Syracusans Archimedes and Scopinas, who through mathematics and natural philosophy discovered, expounded, and left to posterity many things in connexion with mechanics and with sundials.
*6:That the moon subtends one fifteenth part of a sign of the zodiac.
*7:アリスタルコスは明示的には仮定としては掲げずに、皆既日食の際に太陽と月が完全に重なることの議論を行う命題8において、「しかし実際のところ、日食で全体が覆われるのであり、かつ日食で覆われたままであることはない、このことは観察から明らかである」(But it is in fact totally eclipsed and does not remain eclipsed: for this is manifest from observation.)と言って、太陽と月の視直径が同じであるとしている。
*15:該当部分のT.Lヒースの英訳は”that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.”