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.

 

Word list:
μέγεθος, τό, greatness, magnitude (of stars)
ἀπόστημα, -ατος, τό, distance
ἥλιος, ὁ, sun
σελήνη, ἡ, moon
ὑπόθεσις, -εως, ἡ, hypothesis
αʹ.
φῶς, φωτός, τό,
light
λαμβάνω, take, receive (infinitive λαμβάνειν)
βʹ.
γῆ, γεῶν, ἡ,
earth
σημεῖον, τό, sign, mathematical point
κέντρον, τό, sharp point, center of a circle (as if drawn with a compass)
λόγος, ὁ, word, relation, computation, reckoning
ἔχω, have (infinitive ἔχειν)
σφαῖρα, -ας, ἡ, ball, sphere
γʹ.
ὅταν,
whenever
διχοτόμος, -ον, cut in half
ἡμῖν, to us (dative plural of ἐγώ)
φαῖνω, reveal, shine, appear (present middle subjunctive third person singular φαίνηται)
νεύω, incline, nod, bow (infinitive νεύειν)
ἡμέτερος, -α, -ον, our
ὄψις, ἡ, appearance, sight
διορίζω, separate, distinguish (present active participle διορίζων, -οντος)
σκιερός, -ά, -όν, shady, dark
λαμπρός, -ά, -όν, bright
μέγιστος, -η, -ον, largest, greatest (superlative of μέγας)
κύκλος, ὁ, circle, ring
δʹ.
ἀπέχω,
keep off, be away from, project, extend, differ (infinitive ἀπέχειν)
ἐλάσσων, -ονος, -ον, less
τεταρτημορίον, τό, fourth part, quarter, quadrant
τριακοστός, -η, -ον, thirtieth
εʹ.
σκιά, -ᾶς, ἡ,
shadow
πλάτος, -εος, τό, width
εἰμί, to be (infinitive εἶναι)
δύο, two
ϛʹ.
ὑποτείνω,
stretch under, subtend (infinitive ὑποτείνειν)
πεντεκαιδέκατος, -η, -ον, fifteenth
μέρος, -ους, τό, part
ζῴδιον, τό, sign of the zodiac, small figure

ἐπιλογίζομαι, reckon, conclude (third person singular ἐπιλογίζεται)
οὖν, therefore
μείζων, -ονος, -ον, greater (comparative of μέγας)
ὀκτωκαιδεκαπλάσιος, -α, -ον, eighteenfold
εἰκοσαπλάσιος, -α, -ον, twentyfold
διχοτομία, ἡ, a cutting in half
διάμετρος, ἡ, diameter, diagonal
εὑρίσκω, find (aorist passive participle εὑρεθείς, -έντος)

 

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.