ΑΡΙΣΤΑΡΧΟΥ ΠΕΡΙ ΜΕΓΕΘΩΝ ΚΑΙ
ΑΠΟΣΤΗΜΑΤΩΝ ΗΛΙΟΥ ΚΑΙ ΣΕΛΗΝΗΣ

(ΥΠΟΘΕΣΕΙΣ)

αʹ.  Τὴν σελήνην παρὰ τοῦ ἡλίου τὸ φῶς λαμβάνειν.
βʹ.  Τὴν γῆν σημείου τε καὶ κέντρου λόγον ἔχειν πρὸς τὴν τῆς σελήνης σφαῖραν.
γʹ.  Ὅταν ἡ σελήνη διχότομος ἡμῖν φαίνηται, νεύειν εἰς τὴν ἡμετέραν ὄψιν τὸν διορίζοντα τό τε σκιερὸν καὶ τὸ λαμπρὸν τῆς σελήνης μέγιστον κύκλον.
δʹ.  Ὅταν ἡ σελήνη διχότομος ἡμῖν φαίνηται, τότε αὐτὴν ἀπέχειν τοῦ ἡλίου ἔλασσον τεταρτεμορίου τῷ τοῦ τεταρτεμορίου τριακοστῷ.
εʹ.  Τὸ τῆς σκιᾶς πλάτος σεληνῶν εἶναι δύο.
ϛʹ.  Τὴν σελήνην ὑποτείνειν ὑπὸ πεντεκαιδέκατον μέρος ζῳδίου.

Ἐπιλογίζεται οὖν τὸ τοῦ ἡλίου ἀπόστημα ἀπὸ τῆς γῆς τοῦ τῆς σελήνης ἀποστήματος μεῖζον μὲν ἢ ὀκτωκαιδεκαπλάσιον, ἔλασσον δὲ ἢ εἰκοσαπλὰσιον, διὰ τῆς περὶ τὴν διχοτομίαν ὑποθέσεως· τὸν αὐτὸν δὲ λόγον ἔχειν τὴν τοῦ ἡλίου διάμετρον πρὸς τὴν τῆς σελήνης διάμετρον· τὴν δὲ τοῦ ἡλίου διάμετρον πρὸς τὴν τῆς γῆς διάμετρον μείζονα μὲν λόγον ἔχειν ἢ ὃν τὰ ιθʹ πρὸς γʹ, ἐλάσσονα δὲ ἢ ὃν μγʹ πρὸς ϛʹ, διὰ τοῦ εὑρεθέντος περὶ τὰ ἀποστήματα λόγου, τῆς (τε) περὶ τὴν σκιὰν ὑποθέσεως, καὶ τοῦ τὴν σελὴνην ὑπὸ πεντεκαιδέκατον μέρος ζῳδίου ὑποτείνειν.

 

ARISTARCHUS
ON THE SIZES AND DISTANCES OF THE SUN AND MOON

HYPOTHESES

1.  That the moon receives light from the sun.
2.  That the earth has a relation of both point and center to the sphere [of revolution] of the moon.
3.  That whenever the moon appears to us divided in half, the greatest circle separating the shadowed and bright [parts] of the moon inclines to our sight.
4.  That whenever the moon appears to us divided in half, then it is away from the sun less than a quadrant by one-thirtieth of a quadrant.
5.  That the width of the [earth’s] shadow is that of two moons.
6.  That the moon subtends a fifteenth part of a sign of the zodiac.

It is therefore concluded that the distance of the sun from the earth is greater than eighteen times, but less than twenty times, the distance of the moon, according to the hypothesis concerning the dividing in half; that the diameter of the sun has the same relationship to the diameter of the moon; and that the diameter of the sun has a relationship to the diameter of the earth greater than that of 19 to 3, but less than that of 43 to 6, according to the relationship which was found concerning the distances, the hypothesis concerning the shadow, and that of the moon subtending a fifteenth part of a sign of the zodiac.