§15.10Διὰ τί αἱ ἀπὸ τῆς σελήνης σκιαὶ μείζους τῶν ἀπὸ τοῦ ἡλίου, ὅταν ἀπὸ τῆς αὐτῆς ὦσι καθέτου;
Why are the shadows from the moon larger than those from the sun, when they are from the same perpendicular?
ἢ διότι ἀνώτερος ὁ ἥλιος τῆς σελήνης;
Is it because the sun is higher than the moon?
ἀνάγκη οὖν ἐντὸς πίπτειν τὴν ἀπὸ τοῦ ἀνωτέρω ἀκτῖνα.
It is therefore necessary that the ray from the higher source falls inside.
γνώμων ἐφ’ ᾧ Α Δ, σελήνη Β, ἥλιος Γ. ἡ μὲν οὖν ἀπὸ τῆς σελήνης ἀκτὶς Β Ζ, ὥστε ἔσται σκιὰ ἡ τὸ Δ Ζ·
Let the gnomon be on A D, the moon B, and the sun Γ.
ἡ δὲ ἀπὸ τοῦ ἡλίου ἡ τὸ Γ Ε, ὥστε ἔσται σκιὰ ἐξ ἀνάγκης ἥττων· ἔσται γὰρ τὸ Δ Ε.
The ray from the moon is B Z, so that the shadow will be D Z; and that from the sun is Γ E, so that the shadow will of necessity be smaller, for it will be D E.
§15.11Διὰ τί ἐν ταῖς τοῦ ἡλίου ἐκλείψεσιν, ἐάν τις θεωρῇ διὰ κοσκίνου ἢ φύλλων, οἷον πλατάνου ἢ ἄλλου πλατυφύλλου, ἢ τοὺς δακτύλους τῆς ἑτέρας χειρὸς ἐπὶ τὴν ἑτέραν ἐπιζεύξας, μηνίσκοι αἱ αὐγαὶ ἐπὶ τῆς γῆς γίνονται;
Why in eclipses of the sun, if one looks through a sieve or leaves, such as of a plane tree or any other broad-leaved tree, or by joining the fingers of one hand over those of the other, do the beams of light on the earth become crescent-shaped?
ἢ ὅτι ὥσπερ δι’ ὀπῆς ἐὰν λάμπῃ εὐγωνίου τὸ φῶς, στρογγύλον καὶ κῶνος γίνεται;
Is it because just as when the light shines through an angular aperture it becomes round and a cone?
αἴτιον δὲ ὅτι δύο γίνονται κῶνοι, ὅ τε ἀπὸ τοῦ ἡλίου πρὸς τὴν ὀπὴν καὶ ὁ ἐντεῦθεν πρὸς τὴν γῆν, καὶ συγκόρυφοι.
The cause is that two cones are formed, one from the sun to the aperture and the other from there to the earth, and they share a common vertex.
ὅταν οὖν ἐχόντων οὕτως ἄνωθεν κύκλῳ ἀποτέμνηται, ἔσται μηνίσκος ἐξ ἐναντίας ἐπὶ τῆς γῆς τοῦ φωτός.
Therefore, when they are in this state and [the sun] is cut off circularly from above, there will be a crescent of light on the earth in the opposite direction.
ἀπὸ τοῦ μηνίσκου γὰρ τῆς περιφερείας γίνονται αἱ ἀκτῖνες, αἱ δὲ ἐν τοῖς δακτύλοις καὶ κοσκίνοις οἷον ὀπαὶ γίνονται· διὸ ἐπιδηλότερον γίνεται ἢ διὰ μεγάλων ὀπῶν.
For the rays come from the circumference of the crescent, and the spaces between the fingers and in the sieves act as apertures; hence it becomes more distinct than through large apertures.
ἀπὸ δὲ τῆς σελήνης οὐ γίνονται, οὔτε ἐκλειπούσης οὔτε ἐν αὐξήσει οὔσης ἢ φθίσει, διὰ τὸ μὴ ἀκριβεῖς τὰς ἀπὸ τῶν ἄκρων αὐγὰς εἶναι, ἀλλὰ τῷ μέσῳ φαίνειν· ὁ δὲ μηνίσκος μικρὸν τὸ μέσον ἔχει.
But from the moon this does not happen, neither when it is eclipsed nor when it is waxing or waning, because the beams from its extremities are not precise, but it shines by its center; and the crescent has a narrow center.
§15.12Διὰ τί παρήλιος οὐ γίνεται οὔτε μεσουρανοῦντος τοῦ ἡλίου οὔθ’ ὑπὲρ τὸν ἥλιον οὔθ’ ὑπὸ τὸν ἥλιον, ἀλλ’ ἐκ πλαγίων μόνον;
Why does a parhelion not occur either when the sun is in mid-heaven or above the sun or below the sun, but only from the sides?
ἢ διότι παρήλιος γίνεται κλωμένης τῆς ὄψεως πρὸς τὸν ἥλιον, αὕτη δὲ τοῦ ἀέρος ἡ στάσις, ἐφ’ ἧς ἀνακλᾶται ἡ ὄψις, οὔτ’ ἐγγὺς ἂν γένοιτο τοῦ ἡλίου οὔτε πόρρω.
Is it because a parhelion occurs when the vision is refracted toward the sun, and this condition of the air, on which the vision is reflected, can occur neither near the sun nor far from it?
ἐγγὺς μὲν γὰρ οὖσαν ὁ ἥλιος διαλύσει, πόρρω δὲ οὔσης ἡ ὄψις οὐκ ἀνακλασθήσεται· ὑπὸ γὰρ μικροῦ ἐνόπτρου πόρρω ἀνατεινομένη ἀσθενὴς γίνεται.
For if it is near, the sun will dissolve it, but if it is far, the vision will not be reflected; for when stretched far by a small mirror, it becomes weak.
διὸ καὶ ἅλως οὐ γίνονται.
Therefore, halos also do not occur.
ἐξ ἐναντίας τοῦ ἡλίου μὲν οὖν ἐὰν γίνηται καὶ ἐγγύς, διαλύσει ὁ ἥλιος, ἐὰν δὲ πόρρω, ἐλάττων ἡ ὄψις προσπεσεῖται.
Now, if it occurs opposite to the sun and near, the sun will dissolve it, but if far, the vision will fall upon it more weakly.
ἐὰν δὲ ἐν τῷ πλαγίῳ, ἔστι τοσοῦτον ἀποστῆναι τὸ ἔνοπτρον, ὥστε μήτε τὸν ἥλιον διαλῦσαι, μήτε τὴν ὄψιν ἀθρόαν ἀνελθεῖν, διὰ τὸ ὑπὸ τὴν γῆν φέρεσθαι.
But if on the side, it is possible for the mirror to be at such a distance that the sun does not dissolve it, nor does the vision go up in a mass, because of its being directed under the earth.
ὑπὸ δὲ τὸν ἥλιον οὐ γίνεται διὰ τὸ πλησίον μὲν τῆς γῆς ὄντος διαλύεσθαι ἂν ὑπὸ p. τοῦ ἡλίου, ἄνω δὲ μεσουρανίου τὴν ὄψιν διασπᾶσθαι.
But it does not occur below the sun because when it is near the earth, it would be dissolved by the sun, and when it is high in mid-heaven, the vision is dissipated.
καὶ ὅλως οὐδὲ ἐκ πλαγίας μεσουρανίου γίνεται, ὅτι ἡ ὄψις ὑπὸ τὴν γῆν ἐὰν λίαν φέρηται, ὀλίγη ἥξει εἰς τὸ ἔσοπτρον, ὥστε ἀνακλωμένη πᾶν ἔσται ἀσθενής.
And generally, it does not occur on the side when the sun is in mid-heaven, because if the vision is directed too far under the earth, only a little will reach the mirror, so that when refracted it will be entirely weak.
§15.13Διὰ τί τῆς σκιᾶς τὸ ἄκρον τοῦ ἡλίου τρέμειν φαίνεται;
Why does the edge of the shadow from the sun appear to tremble?
οὐ γὰρ δὴ διὰ τὸ φέρεσθαι τὸν ἥλιον· ἀδύνατον γὰρ κινεῖσθαι εἰς τἀναντία, ὁ δὲ τρόμος τοιοῦτος.
For it is surely not because the sun is moving; for it is impossible for it to move in opposite directions, but trembling is of this sort.
ἔτι δὲ ἄδηλος ἡ μετάβασις, ὥσπερ καὶ τοῦ ἡλίου αὐτοῦ.
Furthermore, its movement is imperceptible, just as that of the sun itself.
ἢ διὰ τὸ κινεῖσθαι τὰ ἐν τῷ ἀέρι;
Is it because the things in the air are moving?
καλεῖται δὲ ξύσματα.
They are called motes.
φανερὰ δὲ ἔσται ἐν ταῖς ἀκτῖσι ταῖς διὰ τῶν θυρίδων· ταῦτα γὰρ κινεῖται κἀν νηνεμίᾳ.
They will be visible in the rays that come through the windows; for these move even in calm weather.
ἔκ τε οὖν τῆς σκιᾶς εἰς τὸ φῶς ἔκ τε τοῦ φωτὸς εἰς τὴν σκιὰν φερομένων ἀεί, καὶ ὁ ὅρος ὁ κοινὸς τοῦ φωτὸς καὶ τῆς σκιᾶς φαίνεται κινούμενος παρεγγύς.
Since, therefore, they are always being carried from the shadow into the light and from the light into the shadow, the common boundary of light and shadow also appears to move nearby.
ᾗ γὰρ οἷον σκιὰν ποιοῦσιν, ᾗ δὲ φῶς, ἑκατέρωθεν μεταβάλλονται ταῦτα.
For where they make a sort of shadow, and where they make light, these change from both sides.
ὥστε ἡ σκιὰ φαίνεται κινεῖσθαι, οὐ κινουμένη αὐτὴ οὕτως, ἀλλ’ ἐκεῖναι.
So the shadow appears to move, not that it is itself moving in this way, but those motes.