§3.33 πρῶτον δὲ περὶ τῆς ἅλω τοῦ σχήματος εἴπωμεν, διότι τε κύκλος γίγνεται, καὶ διότι περὶ τὸν ἥλιον ἢ τὴν σελήνην, ὁμοίως δὲ καὶ περί τι τῶν ἄλλων ἄστρων· ὁ γὰρ αὐτὸς ἐπὶ πάντων ἀρμόδσει λόγος.
3 First, let us speak about the shape of the halo, both why it occurs as a circle, and why it occurs around the sun or the moon, and likewise also around any of the other stars; for the same explanation will apply to all.
γίγνεται μὲν οὖν ἡ ἀνάκλασις τῆς ὄψεως συνισταμένου τοῦ ἀέρος καὶ τῆς ἀτμίδος εἰς νέφος, ἐὰν ὁμαλὴς καὶ μικρομερὴς συνισταμένη τύχῃ.
Now, the reflection of vision occurs when the air and vapor condense into a cloud, if the condensing matter happens to be uniform and composed of small particles.
διὸ καὶ σημεῖον ἡ μὲν σύστασις ὕδατός ἐστιν, αἱ μέντοι διασπάσεις ἢ μαράνσεις, αὗται μὲν εὐδιῶν, αἱ δὲ διασπάσεις πνεύματος.
Wherefore, the condensation indeed is a sign of water, but the breakings-up or fadings: the latter indeed are signs of fair weather, while the breakings-up are signs of wind.
ἐὰν μὲν γὰρ μήτε καταμαρανθῇ μήτε διασπασθῇ, ἀλλʼ ἐαθῇ τὴν φύσιν ἀπολαμβάνειν τὴν αὑτῆς, ὕδατος εἰκότως σημεῖόν ἐστι· δηλοῖ γὰρ ἤδη γίγνεσθαι τοιαύτην τὴν σύστασιν, ἐξ ἧς τὸ συνεχὲς λαμβανούσης τῆς πυκνώσεως ἀναγκαῖον εἰς ὕδωρ ἐλθεῖν· διὸ καὶ μέλαιναι γίγνονται τὴν χρόαν αὗται μάλιστα τῶν ἄλλων.
For if it is neither faded nor broken up, but is allowed to attain its own nature, it is naturally a sign of water; for it shows that such a condensation is already taking place, from which, as the thickening takes on a continuous character, it must necessarily come to water; wherefore also these [clouds] become especially black in color, more than any others.
ὅταν δὲ διασπασθῇ, πνεύματος σημεῖον· ἡ γὰρ διαίρεσις ὑπὸ πνεύματος γέγονεν· ἤδη μὲν ὄντος, οὔπω δὲ παρόντος.
But when it is broken up, it is a sign of wind; for the division has been caused by wind, which is already in existence but not yet present.
σημεῖον δὲ τούτου διότι ἐντεῦθεν γίγνεται ὁ ἄνεμος, ὅθεν ἂν ἡ κυρία γίγνηται διάσπασις.
And a sign of this is that the wind arises from that direction where the main breaking-up occurs.
ἀπομαραινομένη δὲ εὐδίας· εἰ γὰρ μὴ ἔχει πως οὕτως ὁ ἀὴρ ὥστε κρατεῖν τοῦ ἐναπολαμβανομένου θερμοῦ μηδʼ ἔρχεσθαι εἰς πύκνωσιν ὑδατώδη, δῆλον ὡς οὔπω ἡ ἀτμὶς ἀποκέκριται τῆς ἀναθυμιάσεως [ἀπὸ] τῆς ξηρᾶς καὶ πυρώδους· τοῦτο δὲ εὐδίας αἴτιον.
But when it fades away, it is a sign of fair weather; for if the air is not in such a state as to master the enclosed heat and not to come to a watery thickening, it is clear that the vapor has not yet been separated from the dry and fiery exhalation; and this is the cause of fair weather.
πῶς μὲν οὖν ἔχοντος τοῦ ἀέρος γίγνεται ἡ ἀνάκλασις, εἴρηται.
How, then, the air is disposed when the reflection occurs, has been stated.
ἀνακλᾶται δʼ ἀπὸ τῆς συνισταμένης ἀχλύος περὶ τὸν ἥλιον ἢ τὴν σελήνην ἡ ὄψις· διὸ οὐκ ἐξ ἐναντίας ὥσπερ ἶρις φαίνεται.
But vision is reflected from the condensing mist around the sun or the moon; wherefore it does not appear opposite like a rainbow.
πάντοθεν δὲ ὁμοίως ἀνακλωμένης ἀναγκαῖον κύκλον εἶναι ἢ κύκλου μέρος· ἀπὸ γὰρ τοῦ αὐτοῦ σημείοιυ πρὸς τὸ αὐτὸ σημεῖον αἱ ἴσαι κλασθήσονται ἐπὶ κύκλου γραμμῆς ἀεί.
And since it is reflected from all sides in like manner, it is necessary that it be a circle or a part of a circle; for from the same point to the same point, equal lines will always be bent on the line of a circle.
ἔστω γὰρ ἀπὸ τοῦ σημείου ἐφʼ τὸ Α πρὸς τὸ Β κεκλασμένη κλασμένη ἥ τε τὸ ΑΓΒ καὶ ἡ τὸ ΑΖΒ καὶ ἡ τὸ AΔ Β· ἴσαι δὲ αὗταί τε αἱ ΑΓ ΑΖ ΑΔ ἀλλήλαις, καὶ αἱ πρὸς τὸ Β ἀλλήλαις, οἷον αἱ ΓΒ ΖΒ ΔΒ· καὶ ἐπεζεύχθω ἡ ΑΕΒ, ὥστε τὰ τρίγωνα ἴσα·
For let there be bent from the point A to B both the line AΓB, and AZB, and AΔB; and let these lines, AΓ, AZ, AΔ, be equal to each other, and those to B also equal to each other, namely, ΓB, ZB, ΔB; and let AEB be joined, so that the triangles are equal; for they are on the equal [common] line AEB.
καὶ γὰρ ἐπʼ ἴσης τῆς ΑΕΒ. ἢχθωσαν δὴ κἀθετοι ἐπὶ τὴν ΑΕΒ ἐκ τῶν γωνιῶν, ἀπὸ μὲν τῆς Γ ἡ τὸ ΓΕ, ἀπὸ δὲ τῆς Ζ ἡ τὸ ΖΕ, ἀπὸ δὲ τῆς Δ ἡ τὸ ΔΕ. ἴσαι δὴ αὗται·
Let perpendiculars then be drawn to AEB from the angles: from Γ the line ΓE, from Z the line ZE, and from Δ the line ΔE.
ἐν ἴσοις γὰρ τριγώνοις καὶ ἐν ἐνὶ ἐπιπέδῳ πᾶσαι· πρὸς ὀρθὰς γὰρ πᾶσαι τῇ ΑΕΒ, καὶ ἐφʼ ἓν σημεῖον τὸ Ε συνάπτουσι.
These then are equal; for they are all in equal triangles and in one plane; for they are all at right angles to AEB, and they meet at one point E.
κύκλος ἄρα ἔσται ἡ γραφομένη, κέντρον δὲ τὸ Ε. ἔστι δὴ τὸ μὲν Β ὁ ἥλιος, τὸ δὲ Α ἡ ὄφις, ἡ δὲ περὶ τὸ ΓΖΔ περιφέρεια τὸ νέφος ἀφʼ οὗ ἀνακλᾶται ἡ ὄψις πρὸς τὸν ἥλιον.
The line described, therefore, will be a circle, and its center will be E. Now, B is the sun, A is the vision, and the circumference around ΓZΔ is the cloud from which the vision is reflected to the sun.
δεῖ δὲ νοεῖν συνεχῇ τὰ ἔνοπτρα· ἀλλὰ διὰ μικρότητα ἕκαστον μὲν ἀόρατον, τὸ δʼ ἐξ ἁπάντων ἓν εἶναι δοκεῖ διὰ τὸ ἐφεξῆς.
But one must conceive the mirrors as continuous; but because of their smallness, each indeed is invisible, but that which is composed of all of them seems to be one because of their being in succession.
φαίνεται δὲ τὸ μὲν λευκόν, ὁ ἥλιος, κύκλῳ συνεχῶς ἐν ἑκάστῳ φαινόμενος τῶν ἐνόπτρων, καὶ μηδεμίαν ἔχων αἰσθητὴν διαίρεσιν, πρὸς δὲ τῇ γῇ μᾶλλον διὰ τὸ νηνεμώτερον εἶναι· πνεύματος γὰρ ὄντος οὐκ εἶναι στάσιν φανερόν.
And the white, namely the sun, appears, being seen continuously in a circle in each of the mirrors, and having no sensible division; and this is more so near the earth because it is calmer there; for when there is wind, it is clear that there is no stability.
παρὰ δὲ τοῦτο μέλαινα ἡ ἐχομένη περιφέρεια, διὰ τὴν ἐκείνης λευκότητα δοκοῦσα εἶναι μελαντέρα.
But beside this, the adjacent circumference is black, seeming to be blacker because of the whiteness of the other.
πλεονάκις δὲ γίγνονται αἱ ἅλῳ περὶ τὴν σελήνην διὰ τὸ τὸν ἥλιον θερμότερον ὄντα θᾶττον διαλύειν τὰς συστάσεις τοῦ ἀέρος.
And halos occur more often around the moon because the sun, being hotter, more quickly dissolves the condensations of the air.
περὶ δὲ τοὺς ἀστέρας γίγνονται μὲν διὰ τὰς αὐτὰς αἰτίας, οὐ σημειώδεις δʼ ὁμοίως, ὅτι μικρὰς πάμπαν ἐπιδηλοῦσι τὰς συστάσεις καὶ οὔπω γονίμους.
But around the stars they occur indeed for the same causes, but they are not signs in the same way, because they indicate very small condensations, and not yet productive [of rain].