Fobes (1919) · Webster (1923)
Webster (1923)
Book 3,Chapter 1 (370b3–371b17)
370b
Περὶ δὲ τῶν ὑπολοίπων εἴπωμεν ἔργων τῆς ἐκκρίσεως
ταύτης, τὸν ὑφηγημένον ἤδη τρόπον λέγοντες. τὸ γὰρ πνεῦμα
5 τοῦτο ἐκκρινόμενον κατὰ μικρὰ μὲν καὶ σποράδην διαχεόμενον
καὶ πολλάκις γιγνόμενον καὶ διαπνέον καὶ λεπτομερέστερον
ὂν βροντὰς ποιεῖ καὶ ἀστραπάς· ἂν δ' ἀθρόον
καὶ πυκνότερον, ἧττον δ' ἐκκριθῇ λεπτόν, ἐκνεφίας ἄνεμος
γίγνεται· διὸ καὶ βίαιος (τὸ γὰρ τάχος τῆς ἐκκρίσεως ποιεῖ
10 τὴν ἰσχύν). ὅταν μὲν οὖν συνακολουθήσῃ πολλὴ καὶ συνεχὴς
ἔκκρισις, τὸν αὐτὸν γίγνεται τρόπον ὥσπερ ὅταν πάλιν εἰς
τοὐναντίον ὁρμήσῃ· τότε γὰρ ὑετὸς καὶ ὕδατος γίγνεται πλῆθος.
ὑπάρχει μὲν οὖν ἄμφω δυνάμει ταῦτα κατὰ τὴν ὕλην·
ὅταν δὲ ἀρχὴ γένηται τῆς δυνάμεως ὁποτερασοῦν, ἀκολουθεῖ
15 συγκρινόμενον ἐκ τῆς ὕλης ὁποτέρου ἂν ᾖ πλῆθος ἐνυπάρχον
πλέον, καὶ γίγνεται τὸ μὲν ὄμβρος, τὸ δὲ τῆς ἑτέρας ἀναθυμιάσεως
ἐκνεφίας. ὅταν δὲ τὸ ἐκκρινόμενον πνεῦμα τὸ ἐν
τῷ νέφει ἑτέρῳ ἀντιτυπήσῃ οὕτως ὥσπερ ὅταν ἐξ εὐρέος εἰς
στενὸν βιάζηται ὁ ἄνεμος ἐν πύλαις ἢ ὁδοῖς (συμβαίνει γὰρ
20 πολλάκις ἐν τοῖς τοιούτοις ἀπωσθέντος τοῦ πρώτου μορίου τοῦ
ῥέοντος σώματος διὰ τὸ μὴ ὑπείκειν, ἢ διὰ στενότητα ἢ διὰ
τὸ ἀντιπνεῖν, κύκλον καὶ δίνην γίγνεσθαι τοῦ πνεύματος· τὸ
μὲν γὰρ εἰς τὸ πρόσθεν κωλύει προϊέναι, τὸ δ' ὄπισθεν ἐπωθεῖ,
ὥστε ἀναγκάζεται εἰς τὸ πλάγιον, ᾗ οὐ κωλύεται, φέρεσθαι,
25 καὶ οὕτως ἀεὶ τὸ ἐχόμενον, ἕως ἂν ἓν γένηται, τοῦτο
δ' ἐστὶ κύκλος· οὗ γὰρ μία φορὰ σχήματος, τοῦτο καὶ αὐτὸ
ἀνάγκη ἓν εἶναι)· ἐπί τε τῆς γῆς οὖν διὰ ταῦτα γίγνονται
οἱ δῖνοι, καὶ ἐν τοῖς νέφεσιν ὁμοίως κατὰ τὴν ἀρχήν, πλὴν
ὅτι, ὥσπερ, ὅταν ἐκνεφίας γίγνηται, ἀεὶ τὸ νέφος ἐκκρίνεται
30 καὶ γίγνεται συνεχὴς ἄνεμος, οὕτως ἐνταῦθα ἀεὶ τὸ συνεχὲς
ἀκολουθεῖ τοῦ νέφους· διὰ δὲ πυκνότητα οὐ δυνάμενον
ἐκκριθῆναι τὸ πνεῦμα ἐκ τοῦ νέφους στρέφεται μὲν κύκλῳ
τὸ πρῶτον διὰ τὴν εἰρημένην αἰτίαν, κάτω δὲ φέρεται διὰ
3Let us explain the remaining operations of this secretion in the same way as we have treated the rest. 5When this exhalation is secreted in small and scattered quantities and frequently, and is transitory, and its constitution rare, it gives rise to thunder and lightning. But if it is secreted in a body and is denser, that is, less rare, we get a hurricane. The fact that it issues in body explains its violence: it is due to the rapidity of the secretion. 10Now when this secretion issues in a great and continuous current the result corresponds to what we get when the opposite development takes place and rain and a quantity of water are produced. As far as the matter from which they are developed goes both sets of phenomena are the same. As soon as a stimulus to the development of either potentiality appears, 15that of which there is the greater quantity present in the cloud is at once secreted from it, and there results either rain, or, if the other exhalation prevails, a hurricane.
Sometimes the exhalation in the cloud, when it is being secreted, collides with another under circumstances like those found when a wind is forced from an open into a narrow space in a gateway or a road. 20It often happens in such cases that the first part of the moving body is deflected because of the resistance due either to the narrowness or to a contrary current, and so the wind forms a circle and eddy. It is prevented from advancing in a straight line: at the same time it is pushed on from behind; so it is compelled to move sideways in the direction of least resistance. 25The same thing happens to the next part, and the next, and so on, till the series becomes one, that is, till a circle is formed: for if a figure is described by a single motion that figure must itself be one. This is how eddies are generated on the earth, and the case is the same in the clouds as far as the beginning of them goes. Only here (as in the case of the hurricane which shakes off the cloud without cessation 30and becomes a continuous wind) the cloud follows the exhalation unbroken, and the exhalation, failing to break away from the cloud because of its density, first moves in a circle for the reason given and then descends, because clouds are always densest on the side where the heat escapes.
Sometimes the exhalation in the cloud, when it is being secreted, collides with another under circumstances like those found when a wind is forced from an open into a narrow space in a gateway or a road. 20It often happens in such cases that the first part of the moving body is deflected because of the resistance due either to the narrowness or to a contrary current, and so the wind forms a circle and eddy. It is prevented from advancing in a straight line: at the same time it is pushed on from behind; so it is compelled to move sideways in the direction of least resistance. 25The same thing happens to the next part, and the next, and so on, till the series becomes one, that is, till a circle is formed: for if a figure is described by a single motion that figure must itself be one. This is how eddies are generated on the earth, and the case is the same in the clouds as far as the beginning of them goes. Only here (as in the case of the hurricane which shakes off the cloud without cessation 30and becomes a continuous wind) the cloud follows the exhalation unbroken, and the exhalation, failing to break away from the cloud because of its density, first moves in a circle for the reason given and then descends, because clouds are always densest on the side where the heat escapes.
371a
1 τὸ ἀεὶ τὰ νέφη πυκνοῦσθαι, ᾗ ἐκπίπτει τὸ θερμόν. καλεῖται
δ', ἂν ἀχρωμάτιστον ᾖ, τοῦτο τὸ πάθος τυφῶν, ἄνεμος
ὤν, οἷον ἐκνεφίας ἄπεπτος. βορείοις δ' οὐ γίγνεται τυφῶν,
οὐδὲ νιπτικῶς ἐχόντων ἐκνεφίας, διὰ τὸ πάντα ταῦτ' εἶναι πνεῦμα,
5 τὸ δὲ πνεῦμα ξηρὰν εἶναι καὶ θερμὴν ἀναθυμίασιν.
ὁ οὖν πάγος καὶ τὸ ψῦχος διὰ τὸ κρατεῖν σβέννυσιν εὐθὺς
γιγνομένην ἔτι τὴν ἀρχήν. ὅτι δὲ κρατεῖ, δῆλον· οὐδὲ γὰρ ἂν
ἦν νιφετός, οὐδὲ βόρεια τὰ ὑγρά· ταῦτα γὰρ συμβαίνει
κρατούσης εἶναι τῆς ψυχρότητος. γίγνεται μὲν οὖν τυφῶν,
10 ὅταν ἐκνεφίας γιγνόμενος μὴ δύνηται ἐκκριθῆναι τοῦ νέφους·
ἔστι δὲ διὰ τὴν ἀντίκρουσιν τῆς δίνης, ὅταν ἐπὶ γῆν φέρηται
ἡ ἕλιξ συγκατάγουσα τὸ νέφος, οὐ δυναμένη ἀπολυθῆναι.
ᾗ δὲ κατ' εὐθυωρίαν ἐκπνεῖ, ταύτῃ τῷ πνεύματι κινεῖ, καὶ
τῇ κύκλῳ κινήσει στρέφει καὶ ἀναφέρει ᾧ ἂν προσπέσῃ
15 βιαζόμενον. ὅταν δὲ κατασπώμενον ἐκπυρωθῇ (τοῦτο δ'
ἐστὶν ἐὰν λεπτότερον τὸ πνεῦμα γένηται), καλεῖται πρηστήρ·
συνεκπίμπρησι γὰρ τὸν ἀέρα τῇ πυρώσει χρωματίζων. ἐὰν
δ' ἐν αὐτῷ τῷ νέφει πολὺ καὶ λεπτὸν ἐκθλιφθῇ πνεῦμα,
τοῦτο γίγνεται κεραυνός, ἐὰν μὲν πάνυ λεπτόν, οὐκ ἐπικάων
20 διὰ λεπτότητα, ὃν οἱ ποιηταὶ ἀργῆτα καλοῦσιν, ἐὰν δ' ἧττον,
ἐπικάων, ὃν ψολόεντα καλοῦσιν· ὁ μὲν γὰρ διὰ τὴν
λεπτότητα φέρεται, διὰ δὲ τὸ τάχος φθάνει διιὼν πρὶν ἢ
ἐκπυρῶσαι καὶ ἐπιδιατρίψας μελᾶναι· ὁ δὲ βραδύτερος
ἔχρωσε μέν, ἔκαυσε δ' οὔ, ἀλλ' ἔφθασε. διὸ καὶ τὰ
25 μὲν ἀντιτυπήσαντα πάσχει τι, τὰ δὲ μὴ οὐδέν, οἷον ἀσπίδος
ἤδη τὸ μὲν χάλκωμα ἐτάκη, τὸ δὲ ξύλον οὐδὲν ἔπαθεν·
διὰ γὰρ μανότητα ἔφθασε τὸ πνεῦμα διηθηθὲν καὶ διελθόν·
καὶ δι' ἱματίων ὁμοίως οὐ κατέκαυσεν, ἀλλ' οἷον τρῦχος
ἐποίησεν· ὥστε ὅτι γε πνεῦμα ταῦτα πάντα, δῆλον καὶ
30 ἐκ τῶν τοιούτων. ἔστι δ' ἐνίοτε καὶ τοῖς ὄμμασιν θεωρεῖν, οἷον
καὶ νῦν ἐθεωροῦμεν περὶ τὸν ἐν Ἐφέσῳ ναὸν καόμενον· πολλαχῇ
γὰρ ἡ φλὸξ ἐφέρετο συνεχής, ἀποσπωμένη χωρίς.
ὅτι μὲν γὰρ ὅ τε καπνὸς πνεῦμα καὶ κάεται ὁ καπνός, φανερόν,
1This phenomenon is called a whirlwind when it is colourless; and it is a sort of undigested hurricane. There is never a whirlwind when the weather is northerly, nor a hurricane when there is snow. The reason is that all these phenomena are 'wind', 5and wind is a dry and warm evaporation. Now frost and cold prevail over this principle and quench it at its birth: that they do prevail is clear or there could be no snow or northerly rain, since these occur when the cold does prevail.
10So the whirlwind originates in the failure of an incipient hurricane to escape from its cloud: it is due to the resistance which generates the eddy, and it consists in the spiral which descends to the earth and drags with it the cloud which it cannot shake off. It moves things by its wind in the direction in which it is blowing in a straight line, and whirls round by its circular motion and 15forcibly snatches up whatever it meets.
When the cloud burns as it is drawn downwards, that is, when the exhalation becomes rarer, it is called a fire-wind, for its fire colours the neighbouring air and inflames it.
When there is a great quantity of exhalation and it is rare and is squeezed out in the cloud itself we get a thunderbolt. If the exhalation is exceedingly rare 20this rareness prevents the thunderbolt from scorching and the poets call it 'bright': if the rareness is less it does scorch and they call it 'smoky'. The former moves rapidly because of its rareness, and because of its rapidity passes through an object before setting fire to it or dwelling on it so as to blacken it: the slower one does blacken the object, but passes through it before it can actually burn it. Further, 25resisting substances are affected, unresisting ones are not. For instance, it has happened that the bronze of a shield has been melted while the woodwork remained intact because its texture was so loose that the exhalation filtered through without affecting it. So it has passed through clothes, too, without burning them, and has merely reduced them to shreds.
Such evidence is enough by itself to show that the exhalation is at work in all these cases, 30but we sometimes get direct evidence as well, as in the case of the conflagration of the temple at Ephesus which we lately witnessed. There independent sheets of flame left the main fire and were carried bodily in many directions.
10So the whirlwind originates in the failure of an incipient hurricane to escape from its cloud: it is due to the resistance which generates the eddy, and it consists in the spiral which descends to the earth and drags with it the cloud which it cannot shake off. It moves things by its wind in the direction in which it is blowing in a straight line, and whirls round by its circular motion and 15forcibly snatches up whatever it meets.
When the cloud burns as it is drawn downwards, that is, when the exhalation becomes rarer, it is called a fire-wind, for its fire colours the neighbouring air and inflames it.
When there is a great quantity of exhalation and it is rare and is squeezed out in the cloud itself we get a thunderbolt. If the exhalation is exceedingly rare 20this rareness prevents the thunderbolt from scorching and the poets call it 'bright': if the rareness is less it does scorch and they call it 'smoky'. The former moves rapidly because of its rareness, and because of its rapidity passes through an object before setting fire to it or dwelling on it so as to blacken it: the slower one does blacken the object, but passes through it before it can actually burn it. Further, 25resisting substances are affected, unresisting ones are not. For instance, it has happened that the bronze of a shield has been melted while the woodwork remained intact because its texture was so loose that the exhalation filtered through without affecting it. So it has passed through clothes, too, without burning them, and has merely reduced them to shreds.
Such evidence is enough by itself to show that the exhalation is at work in all these cases, 30but we sometimes get direct evidence as well, as in the case of the conflagration of the temple at Ephesus which we lately witnessed. There independent sheets of flame left the main fire and were carried bodily in many directions.
371b
1 καὶ εἴρηται ἐν ἑτέροις πρότερον· ὅταν δ' ἀθρόον χωρῇ,
τότε φανερῶς δοκεῖ πνεῦμα εἶναι. ὅπερ οὖν ἐν ταῖς μικραῖς
πυρκαϊαῖς φαίνεται, τοῦτο καὶ τότε πολλῆς ὕλης καομένης
ἐγίγνετο πολλῷ ἰσχυρότερον. ῥηγνυμένων οὖν τῶν ξύλων, ὅθεν
5 ἡ ἀρχὴ τοῦ πνεύματος ἦν, πολὺ ἐχώρει ἀθρόον, ᾗ ἐξέπνει,
καὶ ἐφέρετο ἄνω πεπυρωμένον. ὥστ' ἐφαίνετο ἡ φλὸξ φέρεσθαι
καὶ εἰσπίπτειν εἰς τὰς οἰκίας. ἀεὶ γὰρ οἴεσθαι δεῖ ἐπακολουθεῖν
τοῖς κεραυνοῖς πνεῦμα καὶ προϊέναι· ἀλλ' οὐχ
ὁρᾶται, διὰ τὸ ἀχρωμάτιστον εἶναι. διὸ καὶ ᾗ μέλλει πατάξειν,
10 κινεῖται πρὶν πληγῆναι, ἅτε πρότερον προσπιπτούσης
τῆς ἀρχῆς τοῦ πνεύματος. καὶ αἱ βρονταὶ δὲ
διιστᾶσιν οὐ τῷ ψόφῳ, ἀλλ' ὅτι ἅμα συνεκκρίνεται τὸ τὴν
πληγὴν ποιῆσαν καὶ τὸν ψόφον πνεῦμα· ὃ ἐὰν πατάξῃ,
διέστησεν, ἐπέκαυσε δ' οὔ. περὶ μὲν οὖν βροντῆς καὶ ἀστραπῆς
15 καὶ ἐκνεφίου, ἔτι δὲ πρηστήρων τε καὶ τυφώνων καὶ κεραυνῶν,
εἴρηται, καὶ ὅτι ταὐτὸ πάντα, καὶ τίς ἡ διαφορὰ
πάντων αὐτῶν.
1Now that smoke is exhalation and that smoke burns is certain, and has been stated in another place before; but when the flame moves bodily, then we have ocular proof that smoke is exhalation. On this occasion what is seen in small fires appeared on a much larger scale because of the quantity of matter that was burning. The beams which 5were the source of the exhalation split, and a quantity of it rushed in a body from the place from which it issued forth and went up in a blaze: so that the flame was actually seen moving through the air away and falling on the houses. For we must recognize that exhalation accompanies and precedes thunderbolts though it is colourless and so invisible. Hence, where the thunderbolt is going to strike, 10the object moves before it is struck, showing that the exhalation leads the way and falls on the object first. Thunder, too, splits things not by its noise but because the exhalation that strikes the object and that which makes the noise are ejected simultaneously. This exhalation splits the thing it strikes but does not scorch it at all.
We have now explained thunder and lightning 15and hurricane, and further firewinds, whirlwinds, and thunderbolts, and shown that they are all of them forms of the same thing and wherein they all differ.
We have now explained thunder and lightning 15and hurricane, and further firewinds, whirlwinds, and thunderbolts, and shown that they are all of them forms of the same thing and wherein they all differ.
Book 3,Chapter 2 (371b18–372b11)
περὶ δὲ ἅλω καὶ ἴριδος, τί τε ἑκάτερον καὶ διὰ τίν'
αἰτίαν γίγνεται, λέγωμεν, καὶ περὶ παρηλίων καὶ ῥάβδων·
20 καὶ γὰρ ταῦτα γίγνεται πάντα διὰ τὰς αὐτὰς αἰτίας ἀλλήλοις.
πρῶτον δὲ δεῖ λαβεῖν τἂ πάθη καὶ τὰ συμβαίνοντα
περὶ ἕκαστον αὐτῶν. τῆς μὲν οὖν ἅλω φαίνεται πολλάκις
κύκλος ὅλος, καὶ γίγνεται περὶ ἥλιον καὶ σελήνην
καὶ περὶ τὰ λαμπρὰ τῶν ἄστρων, ἔτι δ' οὐδὲν ἧττον νυκτὸς
25 ἢ ἡμέρας καὶ περὶ μεσημβρίαν ἢ δείλην· ἕωθεν δ' ἐλαττονάκις
καὶ περὶ δύσιν. τῆς δ' ἴριδος οὐδέποτε γίγνεται κύκλος
οὐδὲ μεῖζον ἡμικυκλίου τμῆμα· καὶ δύνοντος μὲν καὶ ἀνατέλλοντος
ἐλαχίστου μὲν κύκλου, μεγίστη δ' ἡ ἁψίς, αἰρομένου
δὲ μᾶλλον κύκλου μὲν μείζονος, ἐλάττων δ' ἡ ἁψίς·
30 καὶ μετὰ μὲν τὴν μετοπωρινὴν ἰσημερίαν, ἐν ταῖς βραχυτέραις
ἡμέραις, πᾶσαν ὥραν γίγνεται τῆς ἡμέρας, ἐν δὲ ταῖς θεριναῖς
οὐ γίγνεται περὶ μεσημβρίαν. οὐδὲ δὴ δυοῖν πλείους ἴριδες
οὐ γίγνονται ἅμα. τούτων δὲ τρίχρως μὲν ἑκατέρα, καὶ τὰ
18Let us now explain the nature and cause of halo, rainbow, mock suns, and rods, 20since the same account applies to them all.
We must first describe the phenomena and the circumstances in which each of them occurs. The halo often appears as a complete circle: it is seen round the sun and the moon and bright stars, by night 25as well as by day, and at midday or in the afternoon, more rarely about sunrise or sunset.
The rainbow never forms a full circle, nor any segment greater than a semicircle. At sunset and sunrise the circle is smallest and the segment largest: as the sun rises higher the circle is larger and the segment smaller. 30After the autumn equinox in the shorter days it is seen at every hour of the day, in the summer not about midday. There are never more than two rainbows at one time. Each of them is three-coloured; the colours are the same in both and their number is the same, but in the outer rainbow they are fainter and their position is reversed.
We must first describe the phenomena and the circumstances in which each of them occurs. The halo often appears as a complete circle: it is seen round the sun and the moon and bright stars, by night 25as well as by day, and at midday or in the afternoon, more rarely about sunrise or sunset.
The rainbow never forms a full circle, nor any segment greater than a semicircle. At sunset and sunrise the circle is smallest and the segment largest: as the sun rises higher the circle is larger and the segment smaller. 30After the autumn equinox in the shorter days it is seen at every hour of the day, in the summer not about midday. There are never more than two rainbows at one time. Each of them is three-coloured; the colours are the same in both and their number is the same, but in the outer rainbow they are fainter and their position is reversed.
372a
1 χρώματα ταὐτὰ καὶ ἴσα τὸν ἀριθμὸν ἔχουσιν ἀλλήλαις,
ἀμυδρότερα δ' ἐν τῇ ἐκτὸς καὶ ἐξ ἐναντίας κείμενα κατὰ
τὴν θέσιν· ἡ μὲν γὰρ ἐντὸς τὴν πρώτην ἔχει περιφέρειαν
τὴν μεγίστην φοινικίαν, ἡ δ' ἔξωθεν τὴν ἐλαχίστην μὲν ἐγγύτατα
5 δὲ πρὸς ταύτην, καὶ τὰς ἄλλας ἀνάλογον. ἔστι δὲ
τὰ χρώματα ταῦτα ἅπερ μόνα σχεδὸν οὐ δύνανται ποιεῖν
οἱ γραφεῖς· ἔνια γὰρ αὐτοὶ κεραννύουσι, τὸ δὲ φοινικοῦν
καὶ πράσινον καὶ ἁλουργὸν οὐ γίγνεται κεραννύμενον· ἡ δὲ
ἶρις ταῦτ' ἔχει τὰ χρώματα. τὸ δὲ μεταξὺ τοῦ φοινικοῦ
10 καὶ πρασίνου φαίνεται πολλάκις ξανθόν. παρήλιοι δὲ καὶ
ῥάβδοι γίγνονται ἐκ πλαγίας αἰεὶ καὶ οὔτ' ἄνωθεν οὔτε πρὸς
τῆς γῆς οὔτ' ἐξ ἐναντίας, οὐδὲ δὴ νύκτωρ, ἀλλ' ἀεὶ περὶ τὸν
ἥλιον, ἔτι δὲ ἢ αἰρομένου ἢ καταφερομένου· τὰ πλεῖστα δὲ
πρὸς δυσμάς· μεσουρανοῦντος δὲ σπάνιον εἴ τι γέγονεν, οἷον ἐν
15 Βοσπόρῳ ποτὲ συνέπεσε· δι' ὅλης γὰρ τῆς ἡμέρας συνανασχόντες
δύο παρήλιοι διετέλεσαν μέχρι δυσμῶν. τὰ μὲν οὖν
περὶ ἕκαστον αὐτῶν συμβαίνοντα ταῦτ' ἐστίν· τὸ δ' αἴτιον τούτων
ἁπάντων ταὐτό· πάντα γὰρ ἀνάκλασις ταῦτ' ἐστί.
διαφέρουσι δὲ τοῖς τρόποις καὶ ἀφ' ὧν, καὶ ὡς συμβαίνει γίγνεσθαι
20 τὴν ἀνάκλασιν πρὸς τὸν ἥλιον ἢ πρὸς ἄλλο τι τῶν
λαμπρῶν. καὶ μεθ' ἡμέραν μὲν ἶρις γίγνεται, νύκτωρ δ'
ἀπὸ σελήνης, ὡς μὲν οἱ ἀρχαῖοι ᾤοντο, οὐκ ἐγίγνετο· τοῦτο
δ' ἔπαθον διὰ τὸ σπάνιον· ἐλάνθανε γὰρ αὐτούς· γίγνεται
μὲν γάρ, ὀλιγάκις δὲ γίγνεται. τὸ δ' αἴτιον ὅτι τ' ἐν τῷ
25 σκότει λανθάνει τὰ χρώματα, καὶ ἄλλα πολλὰ δεῖ συμπεσεῖν,
καὶ ταῦτα πάντα ἐν ἡμέρᾳ μιᾷ τοῦ μηνός· ἐν τῇ
πανσελήνῳ γὰρ γενέσθαι ἀνάγκη τὸ μέλλον ἔσεσθαι, καὶ
τότε ἀνατελλούσης ἢ δυνούσης· διόπερ ἐν ἔτεσιν ὑπὲρ τὰ
πεντήκοντα δὶς ἐνετύχομεν μόνον. ὅτι μὲν οὖν ἡ ὄψις
30 ἀνακλᾶται, ὥσπερ καὶ ἀφ' ὕδατος, οὕτω καὶ ἀπὸ ἀέρος
καὶ πάντων τῶν ἐχόντων τὴν ἐπιφάνειαν λείαν, ἐκ τῶν περὶ
τὴν ὄψιν δεικνυμένων δεῖ λαμβάνειν τὴν πίστιν, καὶ διότι
τῶν ἐνόπτρων ἐν ἐνίοις μὲν καὶ τὰ σχήματα ἐμφαίνεται,
ἐν ἐνίοις δὲ τὰ χρώματα μόνον· τοιαῦτα δ' ἐστὶν ὅσα μικρὰ
1In the inner rainbow the first and largest band is red; in the outer rainbow the band that is nearest 5to this one and smallest is of the same colour: the other bands correspond on the same principle. These are almost the only colours which painters cannot manufacture: for there are colours which they create by mixing, but no mixing will give red, green, or purple. These are the colours of the rainbow, though between the red 10and the green an orange colour is often seen.
Mock suns and rods are always seen by the side of the sun, not above or below it nor in the opposite quarter of the sky. They are not seen at night but always in the neighbourhood of the sun, either as it is rising or setting but more commonly towards sunset. They have scarcely ever appeared when the sun was on the meridian, though this once happened 15in Bosporus where two mock suns rose with the sun and followed it all through the day till sunset.
These are the facts about each of these phenomena: the cause of them all is the same, for they are all reflections. But they are different varieties, and are distinguished by the surface from which and the way in which 20the reflection to the sun or some other bright object takes place.
The rainbow is seen by day, and it was formerly thought that it never appeared by night as a moon rainbow. This opinion was due to the rarity of the occurrence: it was not observed, for though it does happen it does so rarely. The reason is that the colours are not so easy to see 25in the dark and that many other conditions must coincide, and all that in a single day in the month. For if there is to be one it must be at full moon, and then as the moon is either rising or setting. So we have only met with two instances of a moon rainbow in more than fifty years.
We must accept from the theory of optics the fact that sight 30is reflected from air and any object with a smooth surface just as it is from water; also that in some mirrors the forms of things are reflected, in others only their colours. Of the latter kind are those mirrors which are so small as to be indivisible for sense.
Mock suns and rods are always seen by the side of the sun, not above or below it nor in the opposite quarter of the sky. They are not seen at night but always in the neighbourhood of the sun, either as it is rising or setting but more commonly towards sunset. They have scarcely ever appeared when the sun was on the meridian, though this once happened 15in Bosporus where two mock suns rose with the sun and followed it all through the day till sunset.
These are the facts about each of these phenomena: the cause of them all is the same, for they are all reflections. But they are different varieties, and are distinguished by the surface from which and the way in which 20the reflection to the sun or some other bright object takes place.
The rainbow is seen by day, and it was formerly thought that it never appeared by night as a moon rainbow. This opinion was due to the rarity of the occurrence: it was not observed, for though it does happen it does so rarely. The reason is that the colours are not so easy to see 25in the dark and that many other conditions must coincide, and all that in a single day in the month. For if there is to be one it must be at full moon, and then as the moon is either rising or setting. So we have only met with two instances of a moon rainbow in more than fifty years.
We must accept from the theory of optics the fact that sight 30is reflected from air and any object with a smooth surface just as it is from water; also that in some mirrors the forms of things are reflected, in others only their colours. Of the latter kind are those mirrors which are so small as to be indivisible for sense.
372b
1 τῶν ἐνόπτρων, καὶ μηδεμίαν αἰσθητὴν ἔχει διαίρεσιν·
ἐν γὰρ τούτοις τὸ μὲν σχῆμα ἀδύνατον ἐμφαίνεσθαι (δόξει
γὰρ εἶναι διαιρετόν· πᾶν γὰρ σχῆμα ἅμα δοκεῖ σχῆμά
τ' εἶναι καὶ διαίρεσιν ἔχειν), ἐπεὶ δ' ἐμφαίνεσθαί τι ἀναγκαῖον,
5 τοῦτο δὲ ἀδύνατον, λείπεται τὸ χρῶμα μόνον ἐμφαίνεσθαι.
τὸ δὲ χρῶμα ὁτὲ μὲν λαμπρὸν φαίνεται τῶν
λαμπρῶν, ὁτὲ δέ, ἢ τῷ μείγνυσθαι τῷ τοῦ ἐνόπτρου ἢ διὰ
τὴν ἀσθένειαν τῆς ὄψεως, ἄλλου χρώματος ἐμποιεῖ φαντασίαν.
ἔστω δὲ περὶ τούτων ἡμῖν τεθεωρημένον ἐν τοῖς περὶ
10 τὰς αἰσθήσεις δεικνυμένοις· διὸ τὰ μὲν λέγωμεν, τοῖς δ'
ὡς ὑπάρχουσι χρησώμεθα αὐτῶν.
1It is impossible that the figure of a thing should be reflected in them, for if it is the mirror will be sensibly divisible since divisibility is involved in the notion of figure. But since something must be reflected in them 5and figure cannot be, it remains that colour alone should be reflected. The colour of a bright object sometimes appears bright in the reflection, but it sometimes, either owing to the admixture of the colour of the mirror or to weakness of sight, gives rise to the appearance of another colour.
However, we must accept the account we have given of these things in the theory of 10sensation, and take some things for granted while we explain others.
However, we must accept the account we have given of these things in the theory of 10sensation, and take some things for granted while we explain others.
Book 3,Chapter 3 (372b12–373a31)
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
15 αὐτὸς ἐπὶ πάντων ἀρμόσει λόγος. γίγνεται μὲν οὖν ἡ ἀνάκλασις
τῆς ὄψεως συνισταμένου τοῦ ἀέρος καὶ τῆς ἀτμίδος
εἰς νέφος, ἐὰν ὁμαλὴς καὶ μικρομερὴς συνισταμένη τύχῃ.
διὸ καὶ σημεῖον ἡ μὲν σύστασις ὕδατός ἐστιν, αἱ μέντοι
διασπάσεις ἢ μαράνσεις, αὗται μὲν εὐδιῶν, αἱ δὲ
20 διασπάσεις πνεύματος. ἐὰν μὲν γὰρ μήτε καταμαρανθῇ
μήτε διασπασθῇ, ἀλλ' 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
25 μέλαιναι γίγνονται τὴν χρόαν αὗται μάλιστα τῶν ἄλλων.
ὅταν δὲ διασπασθῇ, πνεύματος σημεῖον· ἡ γὰρ διαίρεσις
ὑπὸ πνεύματος γέγονεν ἤδη μὲν ὄντος, οὔπω δὲ παρόντος.
σημεῖον δὲ τούτου διότι ἐντεῦθεν γίγνεται ὁ ἄνεμος, ὅθεν
ἂν ἡ κυρία γίγνηται διάσπασις. ἀπομαραινομένη δὲ εὐδίας·
30 εἰ γὰρ μὴ ἔχει πως οὕτως ὁ ἀὴρ ὥστε κρατεῖν τοῦ ἐναπολαμβανομένου
θερμοῦ μηδ' ἔρχεσθαι εἰς πύκνωσιν ὑδατώδη,
δῆλον ὡς οὔπω ἡ ἀτμὶς ἀποκέκριται τῆς ἀναθυμιάσεως [ἀπὸ] τῆς
ξηρᾶς καὶ πυρώδους· τοῦτο δὲ εὐδίας αἴτιον. πῶς μὲν οὖν
ἔχοντος τοῦ ἀέρος γίγνεται ἡ ἀνάκλασις, εἴρηται. ἀνακλᾶται
12Let us begin by explaining the shape of the halo; why it is a circle and why it appears round the sun or the moon or one of the other stars: 15the explanation being in all these cases the same.
Sight is reflected in this way when air and vapour are condensed into a cloud and the condensed matter is uniform and consists of small parts. Hence in itself it is a sign of rain, but if it fades away, of fine weather, 20if it is broken up, of wind. For if it does not fade away and is not broken up but is allowed to attain its normal state, it is naturally a sign of rain since it shows that a process of condensation is proceeding which must, when it is carried to an end, result in rain. 25For the same reason these haloes are the darkest. It is a sign of wind when it is broken up because its breaking up is due to a wind which exists there but has not reached us. This view finds support in the fact that the wind blows from the quarter in which the main division appears in the halo. Its fading away is a sign of fine weather 30because if the air is not yet in a state to get the better of the heat it contains and proceed to condense into water, this shows that the moist vapour has not yet separated from the dry and firelike exhalation: and this is the cause of fine weather.
So much for the atmospheric conditions under which the reflection takes place.
Sight is reflected in this way when air and vapour are condensed into a cloud and the condensed matter is uniform and consists of small parts. Hence in itself it is a sign of rain, but if it fades away, of fine weather, 20if it is broken up, of wind. For if it does not fade away and is not broken up but is allowed to attain its normal state, it is naturally a sign of rain since it shows that a process of condensation is proceeding which must, when it is carried to an end, result in rain. 25For the same reason these haloes are the darkest. It is a sign of wind when it is broken up because its breaking up is due to a wind which exists there but has not reached us. This view finds support in the fact that the wind blows from the quarter in which the main division appears in the halo. Its fading away is a sign of fine weather 30because if the air is not yet in a state to get the better of the heat it contains and proceed to condense into water, this shows that the moist vapour has not yet separated from the dry and firelike exhalation: and this is the cause of fine weather.
So much for the atmospheric conditions under which the reflection takes place.
373a
1 δ' ἀπὸ τῆς συνισταμένης ἀχλύος περὶ τὸν ἥλιον ἢ τὴν
σελήνην ἡ ὄψις· διὸ οὐκ ἐξ ἐναντίας ὥσπερ ἶρις φαίνεται.
πάντοθεν δὲ ὁμοίως ἀνακλωμένης ἀναγκαῖον κύκλον εἶναι
ἢ κύκλου μέρος· ἀπὸ γὰρ τοῦ αὐτοῦ σημείου πρὸς τὸ αὐτὸ
5 σημεῖον αἱ ἴσαι κλασθήσονται ἐπὶ κύκλου γραμμῆς ἀεί.
ἔστω γὰρ ἀπὸ τοῦ σημείου ἐφ' ᾧ τὸ Α πρὸς τὸ Β κεκλασμένη
ἥ τε τὸ ΑΓΒ καὶ ἡ τὸ ΑΖΒ καὶ ἡ τὸ ΑΔ
Β· ἴσαι δὲ αὗταί τε αἱ ΑΓ ΑΖ ΑΔ ἀλλήλαις, καὶ
αἱ πρὸς τὸ Β ἀλλήλαις, οἷον αἱ ΓΒ ΖΒ ΔΒ· καὶ
10 ἐπεζεύχθω ἡ ΑΕΒ, ὥστε τὰ τρίγωνα ἴσα· καὶ γὰρ ἐπ'
ἴσης τῆς ΑΕΒ. ἤχθωσαν δὴ κάθετοι 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· ἐν ἴσοις
γὰρ τριγώνοις καὶ ἐν ἑνὶ ἐπιπέδῳ πᾶσαι· πρὸς ὀρθὰς γὰρ
15 πᾶσαι τῇ ΑΕΒ, καὶ ἐφ' ἓν σημεῖον τὸ Ε συνάπτουσι.
κύκλος ἄρα ἔσται ἡ γραφομένη, κέντρον δὲ τὸ Ε. ἔστι δὴ
τὸ μὲν Β ὁ ἥλιος, τὸ δὲ Α ἡ ὄψις, ἡ δὲ περὶ τὸ ΓΖΔ
περιφέρεια τὸ νέφος ἀφ' οὗ ἀνακλᾶται ἡ ὄψις πρὸς τὸν
ἥλιον. δεῖ δὲ νοεῖν συνεχῆ τὰ ἔνοπτρα· ἀλλὰ διὰ μικρότητα
20 ἕκαστον μὲν ἀόρατον, τὸ δ' ἐξ ἁπάντων ἓν εἶναι δοκεῖ
διὰ τὸ ἐφεξῆς. 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
25 στάσιν φανερόν. παρὰ δὲ τοῦτο μέλαινα ἡ ἐχομένη περιφέρεια,
διὰ τὴν ἐκείνης λευκότητα δοκοῦσα εἶναι μελαντέρα.
πλεονάκις δὲ γίγνονται αἱ ἅλῳ περὶ τὴν σελήνην διὰ
τὸ τὸν ἥλιον θερμότερον ὄντα θᾶττον διαλύειν τὰς συστάσεις
τοῦ ἀέρος. περὶ δὲ τοὺς ἀστέρας γίγνονται μὲν διὰ τὰς
30 αὐτὰς αἰτίας, οὐ σημειώδεις δ' ὁμοίως, ὅτι μικρὰς πάμπαν
ἐπιδηλοῦσι τὰς συστάσεις καὶ οὔπω γονίμους.
1The reflection is from the mist that forms round the sun or the moon, and that is why the halo is not seen opposite the sun like the rainbow.
Since the reflection takes place in the same way from every point the result is necessarily a circle or a segment of a circle: for if the lines start from the same point and end at the same 5point and are equal, the points where they form an angle will always lie on a circle.
Let AGB and AZB and ADB be lines each of which goes from the point A to the point B and forms an angle. Let the lines AG, AZ, AD be equal and those at B, GB, ZB, DB equal too. (See diagram.)
10Draw the line AEB. Then the triangles are equal; for their base Aeb is equal. Draw perpendiculars to AEB from the angles; GE from G, Ze from Z, DE from D. Then these perpendiculars are equal, being in equal triangles. And they are all in one plane, 15being all at right angles to AEB and meeting at a single point E. So if you draw the line it will be a circle and E its centre. Now B is the sun, A the eye, and the circumference passing through the points GZD the cloud from which the line of sight is reflected to the sun.
The mirrors must be thought of as contiguous: 20each of them is too small to be visible, but their contiguity makes the whole made up of them all to seem one. The bright band is the sun, which is seen as a circle, appearing successively in each of the mirrors as a point indivisible to sense. The band of cloud next to it is black, its colour being intensified by contrast with the brightness of the halo. The halo is formed rather near the earth because that is calmer: for where there is wind it is clear that 25no halo can maintain its position.
Haloes are commoner round the moon because the greater heat of the sun dissolves the condensations of the air more rapidly.
Haloes are formed round stars 30for the same reasons, but they are not prognostic in the same way because the condensation they imply is so insignificant as to be barren.
Since the reflection takes place in the same way from every point the result is necessarily a circle or a segment of a circle: for if the lines start from the same point and end at the same 5point and are equal, the points where they form an angle will always lie on a circle.
Let AGB and AZB and ADB be lines each of which goes from the point A to the point B and forms an angle. Let the lines AG, AZ, AD be equal and those at B, GB, ZB, DB equal too. (See diagram.)
10Draw the line AEB. Then the triangles are equal; for their base Aeb is equal. Draw perpendiculars to AEB from the angles; GE from G, Ze from Z, DE from D. Then these perpendiculars are equal, being in equal triangles. And they are all in one plane, 15being all at right angles to AEB and meeting at a single point E. So if you draw the line it will be a circle and E its centre. Now B is the sun, A the eye, and the circumference passing through the points GZD the cloud from which the line of sight is reflected to the sun.
The mirrors must be thought of as contiguous: 20each of them is too small to be visible, but their contiguity makes the whole made up of them all to seem one. The bright band is the sun, which is seen as a circle, appearing successively in each of the mirrors as a point indivisible to sense. The band of cloud next to it is black, its colour being intensified by contrast with the brightness of the halo. The halo is formed rather near the earth because that is calmer: for where there is wind it is clear that 25no halo can maintain its position.
Haloes are commoner round the moon because the greater heat of the sun dissolves the condensations of the air more rapidly.
Haloes are formed round stars 30for the same reasons, but they are not prognostic in the same way because the condensation they imply is so insignificant as to be barren.
Book 3,Chapter 4 (373a32–375b15)
ἡ δ' ἶρις ὅτι μέν ἐστιν ἀνάκλασις, εἴρηται πρότερον·
ποία δέ τις ἀνάκλασις, καὶ πῶς καὶ διὰ τίν' αἰτίαν ἕκαστα
γίγνεται τῶν συμβαινόντων περὶ ταύτην, λέγωμεν νῦν.
35 ἀνακλωμένη μὲν οὖν ἡ ὄψις ἀπὸ πάντων φαίνεται τῶν λείων,
32We have already stated that the rainbow is a reflection: we have now to explain what sort of reflection it is, to describe its various concomitants, and to assign their causes.
35Sight is reflected from all smooth surfaces, such as are air and water among others.
35Sight is reflected from all smooth surfaces, such as are air and water among others.
373b
1 τούτων δ' ἐστὶν καὶ ἀὴρ καὶ ὕδωρ. γίγνεται δὲ ἀπὸ μὲν
ἀέρος, ὅταν τύχῃ συνιστάμενος. διὰ δὲ τὴν τῆς ὄψεως
ἀσθένειαν πολλάκις καὶ ἄνευ συστάσεως ποιεῖ ἀνάκλασιν,
οἷόν ποτε συνέβαινέ τινι πάθος ἠρέμα καὶ οὐκ ὀξὺ βλέποντι·
5 ἀεὶ γὰρ εἴδωλον ἐδόκει προηγεῖσθαι βαδίζοντι αὐτῷ,
ἐξ ἐναντίας βλέπον πρὸς αὐτόν. τοῦτο δ' ἔπασχε διὰ
τὸ τὴν ὄψιν ἀνακλᾶσθαι πρὸς αὐτόν· οὕτω γὰρ ἀσθενὴς ἦν
καὶ λεπτὴ πάμπαν ὑπὸ τῆς ἀρρωστίας, ὥστ' ἔνοπτρον ἐγίγνετο
καὶ ὁ πλησίον ἀήρ, καὶ οὐκ ἐδύνατο ἀπωθεῖν—ὡς ὁ πόρρω
10 καὶ πυκνός· διόπερ αἵ τ' ἄκραι ἀνεσπασμέναι φαίνονται ἐν
τῇ θαλάττῃ, καὶ μείζω τὰ μεγέθη πάντων, ὅταν εὖροι
πνέωσι, καὶ τὰ ἐν ταῖς ἀχλύσιν, οἷον καὶ ἥλιος καὶ ἄστρα
ἀνίσχοντα καὶ δύνοντα μᾶλλον ἢ μεσουρανοῦντα. ἀπὸ δὲ
ὕδατος μάλιστα ἀνακλᾶται, καὶ ἀπὸ ἀρχομένου γίγνεσθαι
15 μᾶλλον ἔτι ἢ ἀπ' ἀέρος· ἕκαστον γὰρ τῶν μορίων ἐξ ὧν
γίγνεται συνισταμένων ἡ ψακὰς ἔνοπτρον ἀναγκαῖον εἶναι
μᾶλλον τῆς ἀχλύος. ἐπεὶ δὲ καὶ δῆλον καὶ εἴρηται πρότερον
ὅτι ἐν τοῖς τοιούτοις ἐνόπτροις τὸ χρῶμα μόνον ἐμφαίνεται,
τὸ δὲ σχῆμα ἄδηλον, ἀναγκαῖον, ὅταν ἄρχηται
20 ὕειν καὶ ἤδη μὲν συνιστῆται εἰς ψακάδας ὁ ἐν τοῖς νέφεσιν
ἀήρ, μήπω δὲ ὕῃ, ἐὰν ἐξ ἐναντίας ᾖ ὁ ἥλιος ἢ ἄλλο τι
οὕτω λαμπρὸν ὥστε γίγνεσθαι ἔνοπτρον τὸ νέφος, καὶ τὴν
ἀνάκλασιν γίγνεσθαι πρὸς τὸ λαμπρὸν ἐξ ἐναντίας, γίγνεσθαι
ἔμφασιν χρώματος, οὐ σχήματος. ἑκάστου δ' ὄντος
25 τῶν ἐνόπτρων μικροῦ καὶ ἀοράτου, τῆς δ' ἐξ ἁπάντων αὐτῶν
συνεχείας τοῦ μεγέθους ὁρωμένης, ἀνάγκη συνεχὲς μέγεθος
τοῦ αὐτοῦ φαίνεσθαι χρώματος· ἕκαστον γὰρ τῶν ἐνόπτρων
τὸ αὐτὸ ἀποδίδωσι χρῶμα τῷ συνεχεῖ. ὥστ' ἐπεὶ
ταῦτ' ἐνδέχεται συμβαίνειν, ὅταν τοῦτον ἔχῃ τὸν τρόπον ὅ
30 τε ἥλιος καὶ τὸ νέφος καὶ ἡμεῖς ὦμεν μεταξὺ αὐτῶν, ἔσται
διὰ τὴν ἀνάκλασιν ἔμφασίς τις. ἀλλὰ μὴν καὶ φαίνεται
τότε καὶ οὐκ ἄλλως ἐχόντων γιγνομένη ἡ ἶρις. ὅτι μὲν οὖν
ἀνάκλασις ἡ ἶρις τῆς ὄψεως πρὸς τὸν ἥλιόν ἐστι, φανερόν·
διὸ καὶ ἐξ ἐναντίας ἀεὶ γίγνεται, ἡ δ' ἅλως περὶ αὐτόν·
35 καίτοι ἄμφω ἀνάκλασις· ἀλλ' ἥ γε τῶν χρωμάτων ποικιλία
1Air must be condensed if it is to act as a mirror, though it often gives a reflection even uncondensed when the sight is weak. Such was the case of a man whose sight was faint and indistinct. 5He always saw an image in front of him and facing him as he walked. This was because his sight was reflected back to him. Its morbid condition made it so weak and delicate that the air close by acted as a mirror, just as distant 10and condensed air normally does, and his sight could not push it back. So promontories in the sea 'loom' when there is a south-east wind, and everything seems bigger, and in a mist, too, things seem bigger: so, too, the sun and the stars seem bigger when rising and setting than on the meridian. But things are best reflected from water, and even in process of formation 15it is a better mirror than air, for each of the particles, the union of which constitutes a raindrop, is necessarily a better mirror than mist. Now it is obvious and has already been stated that a mirror of this kind renders the colour of an object only, but not its shape. Hence it follows that when it is on the point of raining and 20the air in the clouds is in process of forming into raindrops but the rain is not yet actually there, if the sun is opposite, or any other object bright enough to make the cloud a mirror and cause the sight to be reflected to the object then the reflection must render the colour of the object without its shape. 25Since each of the mirrors is so small as to be invisible and what we see is the continuous magnitude made up of them all, the reflection necessarily gives us a continuous magnitude made up of one colour; each of the mirrors contributing the same colour to the whole. We may deduce that since these conditions are realizable there will be an appearance due to reflection whenever 30the sun and the cloud are related in the way described and we are between them. But these are just the conditions under which the rainbow appears. So it is clear that the rainbow is a reflection of sight to the sun.
35So the rainbow always appears opposite the sun whereas the halo is round it.
35So the rainbow always appears opposite the sun whereas the halo is round it.
374a
1 διαφέρει· ἡ μὲν γὰρ ἀφ' ὕδατος καὶ μέλανος γίγνεται
ἀνάκλασις καὶ πόρρωθεν, ἡ δ' ἐγγύθεν καὶ ἀπὸ ἀέρος
λευκοτέρου τὴν φύσιν. φαίνεται δὲ τὸ λαμπρὸν διὰ τοῦ μέλανος
ἢ ἐν τῷ μέλανι (διαφέρει γὰρ οὐδέν) φοινικοῦν (ὁρᾶν
5 δ' ἔξεστι τό γε τῶν χλωρῶν ξύλων πῦρ, ὡς ἐρυθρὰν ἔχει
τὴν φλόγα διὰ τὸ τῷ καπνῷ πολλῷ μεμεῖχθαι τὸ πῦρ
λαμπρὸν ὂν καὶ λευκόν)· καὶ δι' ἀχλύος καὶ καπνοῦ ὁ ἥλιος
φαίνεται φοινικοῦς. διὸ ἡ μὲν τῆς ἴριδος ἀνάκλασις ἡ μὲν
πρώτη τοιαύτην ἔχειν φαίνεται τὴν χρόαν (ἀπὸ ῥανίδων
10 γὰρ μικρῶν γίγνεται ἡ ἀνάκλασις), ἡ δὲ τῆς ἅλω οὔ. περὶ
δὲ τῶν ἄλλων χρωμάτων ὕστερον ἐροῦμεν. ἔτι δὲ περὶ αὐτὸν
μὲν τὸν ἥλιον οὐ γίγνεται διατριβὴ τοιαύτης συστάσεως, ἀλλ'
ἢ ὕει ἢ διαλύεται. ἐκ δὲ τῶν ἐναντίων ἐν τῷ μεταξὺ τῆς
τοῦ ὕδατος γενέσεως γίγνεταί τις χρόνος· τούτου γὰρ μὴ συμβαίνοντος
15 ἦσαν ἂν κεχρωματισμέναι αἱ ἅλως ὥσπερ ἡ ἶρις.
νῦν δ' ὅλα μὲν οὐ γίγνεται τοιαύτην ἔχοντα τὴν ἔμφασιν,
οὐδὲ κύκλῳ, μικρὰ δὲ καὶ κατὰ μόριον, αἳ καλοῦνται ῥάβδοι,
ἐπεὶ εἰ συνίστατο τοιαύτη ἀχλὺς οἵα γένοιτ' ἂν ὕδατος
ἤ τινος ἄλλου μέλανος, καθάπερ λέγομεν, ἐφαίνετο ἂν ἡ
20 ἶρις ὅλη, ὥσπερ ἡ περὶ τοὺς λύχνους. περὶ γὰρ τούτους τὰ
πλεῖστα νοτίων ὄντων ἶρις γίγνεται τοῦ χειμῶνος, μάλιστα δὲ
δήλη γίγνεται τοῖς ὑγροὺς ἔχουσι τοὺς ὀφθαλμούς· τούτων γὰρ
ἡ ὄψις ταχὺ δι' ἀσθένειαν ἀνακλᾶται. γίγνεται δ' ἀπό τε
τῆς τοῦ ἀέρος ὑγρότητος καὶ ἀπὸ λιγνύος τῆς ἀπὸ τῆς φλογὸς
25 ἀπορρεούσης καὶ μειγνυμένης· τότε γὰρ γίγνεται ἔνοπτρον,
καὶ διὰ τὴν μελανίαν· καπνώδης γὰρ ἡ λιγνύς· τὸ
δὲ τοῦ λύχνου φῶς οὐ λευκὸν ἀλλὰ πορφυροῦν φαίνεται κύκλῳ
καὶ ἰριῶδες, φοινικοῦν δ' οὔ· ἔστι γὰρ ἥ τε ὄψις ὀλίγη
ἡ ἀνακλωμένη, καὶ μέλαν τὸ ἔνοπτρον. ἡ δ' ἀπὸ τῶν κωπῶν
30 τῶν ἀναφερομένων ἐκ τῆς θαλάττης ἶρις τῇ μὲν θέσει
τὸν αὐτὸν γίγνεται τρόπον τῇ ἐν τῷ οὐρανῷ, τὸ δὲ χρῶμα
ὁμοιοτέρα τῇ περὶ τοὺς λύχνους· οὐ γὰρ φοινικῆν ἀλλὰ πορφυρᾶν
ἔχουσα φαίνεται τὴν χρόαν. ἡ δ' ἀνάκλασις ἀπὸ
τῶν μικροτάτων μὲν συνεχῶν δὲ γίγνεται ῥανίδων· αὗται
35 δ' ὕδωρ ἀποκεκριμένον εἰσὶν ἤδη παντελῶς. γίγνεται δὲ κἄν
1They are both reflections, but the rainbow is distinguished by the variety of its colours. The reflection in the one case is from water which is dark and from a distance; in the other from air which is nearer and lighter in colour. White light through a dark medium or on a dark surface (it makes no difference) looks red. 5We know how red the flame of green wood is: this is because so much smoke is mixed with the bright white firelight: so, too, the sun appears red through smoke and mist. That is why in the rainbow reflection the outer circumference is red (10the reflection being from small particles of water), but not in the case of the halo. The other colours shall be explained later. Again, a condensation of this kind cannot persist in the neighbourhood of the sun: it must either turn to rain or be dissolved, but opposite to the sun there is an interval during which the water is formed. If there were not this distinction 15haloes would be coloured like the rainbow. Actually no complete or circular halo presents this colour, only small and fragmentary appearances called 'rods'. But if a haze due to water or any other dark substance formed there we should have had, as we maintain, 20a complete rainbow like that which we do find lamps. A rainbow appears round these in winter, generally with southerly winds. Persons whose eyes are moist see it most clearly because their sight is weak and easily reflected. It is due to the moistness of the air and the soot 25which the flame gives off and which mixes with the air and makes it a mirror, and to the blackness which that mirror derives from the smoky nature of the soot. The light of the lamp appears as a circle which is not white but purple. It shows the colours of the rainbow; but because the sight that is reflected is too weak and the mirror too dark, red is absent. The rainbow that is seen when oars 30are raised out of the sea involves the same relative positions as that in the sky, but its colour is more like that round the lamps, being purple rather than red. The reflection is from very small particles continuous with one another, and 35in this case the particles are fully formed water.
374b
1 τις λεπταῖς ῥαίνῃ ῥανίσιν εἴς τι τοιοῦτον χωρίον ὃ τὴν θέσιν
πρὸς τὸν ἥλιον ἐστραμμένον ἐστὶ καὶ τῇ μὲν ὁ ἥλιος ἀνέχῃ
τῇ δὲ σκιάζῃ· ἐν τῷ τοιούτῳ γάρ, ἐὰν εἴσω τις ῥαίνῃ, τῷ
ἑστῶτι ἐκτός, ᾗ ἐπαλλάττουσιν αἱ ἀκτῖνες καὶ ποιοῦσι τὴν
5 σκιάν, φαίνεται ἶρις. ὁ δὲ τρόπος καὶ ἡ χρόα ὁμοία καὶ
τὸ αἴτιον τὸ αὐτὸ τῇ ἀπὸ τῶν κωπῶν· τῇ γὰρ χειρὶ κώπῃ
χρῆται ὁ ῥαίνων. ὅτι δὲ τὸ χρῶμα τοιοῦτον, ἅμα δῆλον
ἔσται καὶ περὶ τῶν ἄλλων χρωμάτων τῆς φαντασίας, ἐκ
τῶνδε. δεῖ γὰρ νοήσαντας, ὥσπερ εἴρηται, καὶ ὑποθεμένους
10 πρῶτον μὲν ὅτι τὸ λαμπρὸν ἐν τῷ μέλανι ἢ διὰ τοῦ μέλανος
χρῶμα ποιεῖ φοινικοῦν, δεύτερον δ' ὅτι ἡ ὄψις ἐκτεινομένη
ἀσθενεστέρα γίγνεται καὶ ἐλάττων, τρίτον δ' ὅτι τὸ μέλαν
οἷον ἀπόφασίς ἐστιν· τῷ γὰρ ἐκλείπειν τὴν ὄψιν φαίνεται
μέλαν· διὸ τὰ πόρρω πάντα μελάντερα φαίνεται, διὰ
15 τὸ μὴ διικνεῖσθαι τὴν ὄψιν. θεωρείσθω μὲν οὖν ταῦτ' ἐκ τῶν
περὶ τὰς αἰσθήσεις συμβαινόντων· ἐκείνων γὰρ ἴδιοι οἱ περὶ
τούτων λόγοι· νῦν δ' ὅσον ἀνάγκη, τοσοῦτον περὶ αὐτῶν λέγωμεν.
φαίνεται δ' οὖν διὰ ταύτην τὴν αἰτίαν τά τε πόρρω
μελάντερα καὶ ἐλάττω καὶ λειότερα, καὶ τὰ ἐν τοῖς ἐνόπτροις,
20 καὶ τὰ νέφη μελάντερα βλέπουσιν εἰς τὸ ὕδωρ ἢ
εἰς αὐτὰ τὰ νέφη. καὶ τοῦτο πάνυ ἐπιδήλως· διὰ γὰρ τὴν
ἀνάκλασιν ὀλίγῃ τῇ ὄψει θεωροῦνται. διαφέρει δ' οὐδὲν τὸ
ὁρώμενον μεταβάλλειν ἢ τὴν ὄψιν· ἀμφοτέρως γὰρ ἔσται
ταὐτόν. πρὸς δὲ τούτοις δεῖ μὴ λεληθέναι καὶ τόδε· συμβαίνει
25 γὰρ ὅταν ᾖ τοῦ ἡλίου νέφος πλησίον, εἰς μὲν αὐτὸ
βλέποντι μηδὲν φαίνεσθαι κεχρωματισμένον ἀλλ' εἶναι
λευκόν, ἐν δὲ τῷ ὕδατι αὐτὸ τοῦτο θεωροῦντι χρῶμά τι
ἔχειν τῆς ἴριδος. δῆλον τοίνυν ὅτι ἡ ὄψις ὥσπερ καὶ τὸ μέλαν
κλωμένη δι' ἀσθένειαν μελάντερον ποιεῖ φαίνεσθαι, καὶ
30 τὸ λευκὸν ἧττον λευκόν, καὶ προσάγει πρὸς τὸ μέλαν. ἡ
μὲν οὖν ἰσχυροτέρα ὄψις εἰς φοινικοῦν χρῶμα μετέβαλεν, ἡ
δ' ἐχομένη εἰς τὸ πράσινον, ἡ δὲ ἔτι ἀσθενεστέρα εἰς τὸ
ἁλουργόν. ἐπὶ δὲ τὸ πλέον οὐκέτι φαίνεται, ἀλλ' ἐν τοῖς
τρισίν, ὥσπερ καὶ τῶν ἄλλων τὰ πλεῖστα, καὶ τούτων ἔσχεν
35 τέλος· τῶν δ' ἄλλων ἀναίσθητος ἡ μεταβολή. διὸ καὶ ἡ
1We get a rainbow, too, if a man sprinkles fine drops in a room turned to the sun so that the sun is shining in part of the room and throwing a shadow in the rest. Then if one man sprinkles in the room, another, standing outside, sees a rainbow where the sun's rays cease and make the shadow. 5Its nature and colour is like that from the oars and its cause is the same, for the sprinkling hand corresponds to the oar.
That the colours of the rainbow are those we described and how the other colours come to appear in it will be clear from the following considerations. We must recognize, as we have said, and lay down: 10first, that white colour on a black surface or seen through a black medium gives red; second, that sight when strained to a distance becomes weaker and less; third, that black is in a sort the negation of sight: an object is black because sight fails; so everything at a distance looks blacker, 15because sight does not reach it. The theory of these matters belongs to the account of the senses, which are the proper subjects of such an inquiry; we need only state about them what is necessary for us. At all events, that is the reason why distant objects and objects seen in a mirror look darker and smaller and smoother, 20why the reflection of clouds in water is darker than the clouds themselves. This latter is clearly the case: the reflection diminishes the sight that reaches them. It makes no difference whether the change is in the object seen or. in the sight, the result being in either case the same. The following fact further is worth noticing. 25When there is a cloud near the sun and we look at it does not look coloured at all but white, but when we look at the same cloud in water it shows a trace of rainbow colouring. Clearly, then, when sight is reflected it is weakened and, as it makes dark look darker, 30so it makes white look less white, changing it and bringing it nearer to black. 35When the sight is relatively strong the change is to red; the next stage is green, and a further degree of weakness gives violet.
That the colours of the rainbow are those we described and how the other colours come to appear in it will be clear from the following considerations. We must recognize, as we have said, and lay down: 10first, that white colour on a black surface or seen through a black medium gives red; second, that sight when strained to a distance becomes weaker and less; third, that black is in a sort the negation of sight: an object is black because sight fails; so everything at a distance looks blacker, 15because sight does not reach it. The theory of these matters belongs to the account of the senses, which are the proper subjects of such an inquiry; we need only state about them what is necessary for us. At all events, that is the reason why distant objects and objects seen in a mirror look darker and smaller and smoother, 20why the reflection of clouds in water is darker than the clouds themselves. This latter is clearly the case: the reflection diminishes the sight that reaches them. It makes no difference whether the change is in the object seen or. in the sight, the result being in either case the same. The following fact further is worth noticing. 25When there is a cloud near the sun and we look at it does not look coloured at all but white, but when we look at the same cloud in water it shows a trace of rainbow colouring. Clearly, then, when sight is reflected it is weakened and, as it makes dark look darker, 30so it makes white look less white, changing it and bringing it nearer to black. 35When the sight is relatively strong the change is to red; the next stage is green, and a further degree of weakness gives violet.
375a
1 ἶρις τρίχρως φαίνεται, ἑκατέρα μέν, ἐναντίως δέ. ἡ μὲν οὖν
πρώτη τὴν ἔξω φοινικῆν ἔχει· ἀπὸ μεγίστης γὰρ περιφερείας
πλείστη προσπίπτει ὄψις πρὸς τὸν ἥλιον, μεγίστη δ'
ἡ ἔξω· ἡ δ' ἐχομένη καὶ ἡ τρίτη ἀνάλογον. ὥστ' εἰ τὰ περὶ
5 τῶν χρωμάτων τῆς φαντασίας εἴρηται καλῶς, ἀνάγκη τρίχρων
τε εἶναι αὐτὴν καὶ τούτοις τοῖς χρώμασι κεχρῶσθαι
μόνοις. τὸ δὲ ξανθὸν φαίνεται διὰ τὸ παρ' ἄλληλα φαίνεσθαι.
τὸ γὰρ φοινικοῦν παρὰ τὸ πράσινον λευκὸν φαίνεται.
σημεῖον δὲ τούτου· ἐν γὰρ τῷ μελαντάτῳ νέφει μάλιστα
10 ἄκρατος γίγνεται ἶρις· συμβαίνει δὲ τότε ξανθότερον εἶναι
δοκεῖν τὸ φοινικοῦν. ἔστι δὲ τὸ ξανθὸν ἐν τῇ ἴριδι χρῶμα μεταξὺ
τοῦ τε φοινικοῦ καὶ πρασίνου χρώματος. διὰ τὴν μελανίαν
οὖν τοῦ κύκλῳ νέφους ὅλον αὐτοῦ φαίνεται τὸ φοινικοῦν
λευκόν· ἔστι γὰρ πρὸς ἐκεῖνα λευκόν. καὶ πάλιν ἀπομαραινομένης
15 τῆς ἴριδος ἐγγύτατα, ὅταν λύηται τὸ φοινικοῦν· ἡ
γὰρ νεφέλη λευκὴ οὖσα, προσπίπτουσα παρὰ τὸ πράσινον,
μεταβάλλει εἰς τὸ ξανθόν. μέγιστον δὲ σημεῖον τούτων ἡ
ἀπὸ τῆς σελήνης ἶρις· φαίνεται γὰρ λευκὴ πάμπαν. γίγνεται
δὲ τοῦτο ὅτι ἔν τε τῷ νέφει ζοφερῷ φαίνεται καὶ
20 ἐν νυκτί. ὥσπερ οὖν πῦρ ἐπὶ πῦρ, μέλαν παρὰ μέλαν ποιεῖ
τὸ ἠρέμα λευκὸν παντελῶς φαίνεσθαι λευκόν· τοῦτο δ' ἐστὶν
τὸ φοινικοῦν. γίγνεται δὲ τοῦτο τὸ πάθος καταφανὲς καὶ ἐπὶ
τῶν ἀνθῶν· ἐν γὰρ τοῖς ὑφάσμασιν καὶ ποικίλμασιν ἀμύθητον
διαφέρει τῇ φαντασίᾳ ἄλλα παρ' ἄλλα τιθέμενα
25 τῶν χρωμάτων, οἷον καὶ τὰ πορφυρᾶ ἐν λευκοῖς ἢ
μέλασιν ἐρίοις, ἔτι δ' ἐν αὐγῇ τοιᾳδὶ ἢ τοιᾳδί· διὸ καὶ οἱ
ποικιλταί φασι διαμαρτάνειν ἐργαζόμενοι πρὸς τὸν λύχνον
πολλάκις τῶν ἀνθῶν, λαμβάνοντες ἕτερα ἀνθ' ἑτέρων. διότι
μὲν οὖν τρίχρως τε, καὶ ὅτι ἐκ τούτων φαίνεται τῶν χρωμάτων
30 μόνων ἡ ἶρις, εἴρηται. διπλῆ δὲ καὶ ἀμαυροτέρα τοῖς
χρώμασιν ἡ περιέχουσα, καὶ τῇ θέσει τὰς χρόας ἐξ ἐναντίας
ἔχει κειμένας διὰ τὴν αὐτὴν αἰτίαν· μακροτέρα γὰρ
ἀποτεινομένη ἡ ὄψις ὥσπερ τὸ πορρώτερον ὁρᾷ, καὶ τὸ ἐνταῦθα
τὸν αὐτὸν τρόπον. ἀσθενεστέρα οὖν ἀπὸ τῆς ἔξωθεν ἡ
1No further change is visible, but three completes the series of colours (as we find three does in most other things), and the change into the rest is imperceptible to sense. Hence also the rainbow appears with three colours; this is true of each of the two, but in a contrary way. The outer band of the primary rainbow is red: for the largest band reflects most sight to the sun, and the outer band is largest. The middle band and the third go on the same principle. So if the principles we laid down 5about the appearance of colours are true the rainbow necessarily has three colours, and these three and no others. The appearance of yellow is due to contrast, for the red is whitened by its juxtaposition with green. We can see this from the fact that 10the rainbow is purest when the cloud is blackest; and then the red shows most yellow. (Yellow in the rainbow comes between red and green.) So the whole of the red shows white by contrast with the blackness of the cloud around: for it is white compared to the cloud and the green. Again, 15when the rainbow is fading away and the red is dissolving, the white cloud is brought into contact with the green and becomes yellow. But the moon rainbow affords the best instance of this colour contrast. It looks quite white: this is because it appears on the dark cloud and 20at night. So, just as fire is intensified by added fire, black beside black makes that which is in some degree white look quite white. Bright dyes too show the effect of contrast. In woven and embroidered stuffs the appearance of colours is profoundly affected by their juxtaposition with one another (25purple, for instance, appears different on white and on black wool), and also by differences of illumination. Thus embroiderers say that they often make mistakes in their colours when they work by lamplight, and use the wrong ones.
We have now shown why the rainbow has three colours and that 30these are its only colours. The same cause explains the double rainbow and the faintness of the colours in the outer one and their inverted order. When sight is strained to a great distance the appearance of the distant object is affected in a certain way: and the same thing holds good here.
We have now shown why the rainbow has three colours and that 30these are its only colours. The same cause explains the double rainbow and the faintness of the colours in the outer one and their inverted order. When sight is strained to a great distance the appearance of the distant object is affected in a certain way: and the same thing holds good here.
375b
1 ἀνάκλασις γίγνεται διὰ τὸ πορρώτερον ποιεῖσθαι τὴν ἀνάκλασιν,
ὥστ' ἐλάττων προσπίπτουσα τὰ χρώματα ποιεῖ
ἀμαυρότερα φαίνεσθαι. καὶ ἀντεστραμμένως δὴ διὰ τὸ
πλείω ἀπὸ τῆς ἐλάττονος καὶ τῆς ἐντὸς περιφερείας προςπίπτειν
5 πρὸς τὸν ἥλιον· ἐγγυτέρω γὰρ τῆς ὄψεως οὖσα ἀνακλᾶται
ἀπὸ τῆς ἐγγυτάτω περιφερείας τῆς πρώτης ἴριδος.
ἐγγυτάτω δὲ ἐν τῇ ἔξωθεν ἴριδι ἡ ἐλαχίστη περιφέρεια, ὥστε
αὕτη ἕξει τὸ χρῶμα φοινικοῦν· ἡ δ' ἐχομένη καὶ ἡ τρίτη
κατὰ λόγον. ἡ ἔξω ἶρις ἐφ' ᾧ τὸ Β· ἡ ἔσω, ἡ πρώτη, ἐφ' ᾧ τὸ Α·
10 τὰ χρώματα δ', ἐφ' ᾧ τὸ Γ, φοινικοῦν, ἐφ' ᾧ τὸ Δ, πράσινον,
ἐφ' ᾧ Ε, ἁλουργόν· τὸ ξανθὸν δὲ φαίνεται ἐφ' οὗ τὸ
Ζ. τρεῖς δ' οὐκέτι γίγνονται, οὐδὲ πλείους ἴριδες, διὰ τὸ καὶ
τὴν δευτέραν γίγνεσθαι ἀμαυροτέραν, ὥστε καὶ τὴν τρίτην
ἀνάκλασιν πάμπαν ἀσθενῆ γίγνεσθαι καὶ ἀδυνατεῖν ἀφικνεῖσθαι
15 πρὸς τὸν ἥλιον.
1So the reflection from the outer rainbow is weaker because it takes place from a greater distance and less of it reaches the sun, and so the colours seen are fainter. Their order is reversed because more reflection reaches 5the sun from the smaller, inner band. For that reflection is nearer to our sight which is reflected from the band which is nearest to the primary rainbow. Now the smallest band in the outer rainbow is that which is nearest, and so it will be red; and the second and the third will follow the same principle. Let B be the outer rainbow, A the inner one; 10let R stand for the red colour, G for green, V for violet; yellow appears at the point Y. Three rainbows or more are not found because even the second is fainter, so that the third reflection can have no strength whatever and 15cannot reach the sun at all. (See diagram.)
Book 3,Chapter 5 (375b16–377a28)
ὅτι δ' οὔτε κύκλον οἷόν τε γενέσθαι τῆς ἴριδος οὔτε
μεῖζον ἡμικυκλίου τμῆμα, καὶ περὶ τῶν ἄλλων τῶν συμβαινόντων
περὶ αὐτήν, ἐκ τοῦ διαγράμματος ἔσται θεωροῦσι
δῆλον. ἡμισφαιρίου γὰρ ὄντος ἐπὶ τοῦ ὁρίζοντος κύκλου τοῦ
20 ἐφ' ᾧ τὸ Α, κέντρου δὲ τοῦ Κ, ἄλλου δέ τινος ἀνατέλλοντος
σημείου ἐφ' ᾧ τὸ Η, ἐὰν ἀπὸ τοῦ Κ γραμμαὶ κατὰ
κῶνον ἐκπίπτουσαι ποιῶσιν ὡσπερεὶ ἄξονα τὴν ἐφ' ᾗ ΗΚ,
καὶ ἀπὸ τοῦ Κ ἐπὶ τὸ Μ ἐπιζευχθεῖσαι ἀνακλασθῶσιν ἀπὸ
τοῦ ἡμισφαιρίου ἐπὶ τὸ Η ἐπὶ τὴν μείζω γωνίαν, πρὸς κύκλου
25 περιφέρειαν προσπεσοῦνται αἱ ἀπὸ τοῦ Κ· καὶ ἐὰν μὲν
ἐπ' ἀνατολῆς ἢ ἐπὶ δύσεως τοῦ ἄστρου ἡ ἀνάκλασις γένηται,
ἡμικύκλιον ἀποληφθήσεται τοῦ κύκλου ὑπὸ τοῦ ὁρίζοντος τὸ
ὑπὲρ γῆν γιγνόμενον, ἐὰν δ' ἐπάνω, ἀεὶ ἔλαττον ἡμικυκλίου·
ἐλάχιστον δέ, ὅταν ἐπὶ τοῦ μεσημβρινοῦ γένηται τὸ ἄστρον.
30 ἔστω γὰρ ἐπ' ἀνατολῆς πρῶτον, οὗ τὸ Η, καὶ ἀνακεκλάσθω
ἡ ΚΜ ἐπὶ τὸ Η, καὶ τὸ ἐπίπεδον ἐκβεβλήσθω ἐν ᾧ ἡ Α,
τὸ ἀπὸ τοῦ τριγώνου ἐν ᾧ τὸ ΗΚΜ. κύκλος οὖν ἡ τομὴ
ἔσται τῆς σφαίρας ὁ μέγιστος. ἔστω ὁ ἐφ' ᾧ Α· διοίσει γὰρ
οὐδὲν ἂν ὁποιονοῦν τῶν ἐπὶ τῆς ΗΚ κατὰ τὸ τρίγωνον τὸ
16The rainbow can never be a circle nor a segment of a circle greater than a semicircle. The consideration of the diagram will prove this and the other properties of the rainbow. (See diagram.)
20Let A be a hemisphere resting on the circle of the horizon, let its centre be K and let H be another point appearing on the horizon. Then, if the lines that fall in a cone from K have HK as their axis, and, K and M being joined, the lines KM are reflected from the hemisphere to H over the greater angle, 25the lines from K will fall on the circumference of a circle. If the reflection takes place when the luminous body is rising or setting the segment of the circle above the earth which is cut off by the horizon will be a semi-circle; if the luminous body is above the horizon it will always be less than a semicircle, and it will be smallest when the luminous body culminates. 30First let the luminous body be appearing on the horizon at the point H, and let KM be reflected to H, and let the plane in which A is, determined by the triangle HKM, be produced. Then the section of the sphere will be a great circle.
20Let A be a hemisphere resting on the circle of the horizon, let its centre be K and let H be another point appearing on the horizon. Then, if the lines that fall in a cone from K have HK as their axis, and, K and M being joined, the lines KM are reflected from the hemisphere to H over the greater angle, 25the lines from K will fall on the circumference of a circle. If the reflection takes place when the luminous body is rising or setting the segment of the circle above the earth which is cut off by the horizon will be a semi-circle; if the luminous body is above the horizon it will always be less than a semicircle, and it will be smallest when the luminous body culminates. 30First let the luminous body be appearing on the horizon at the point H, and let KM be reflected to H, and let the plane in which A is, determined by the triangle HKM, be produced. Then the section of the sphere will be a great circle.
376a
1 ΚΜΗ ἐκβληθῇ τὸ ἐπίπεδον. αἱ οὖν ἀπὸ τῶν Η Κ ἀναγόμεναι
γραμμαὶ ἐν τούτῳ τῷ λόγῳ οὐ συσταθήσονται τοῦ ἐφ'
ᾧ Α ἡμικυκλίου πρὸς ἄλλο καὶ ἄλλο σημεῖον· ἐπεὶ γὰρ
τά τε Κ Η σημεῖα δέδοται καὶ ἡ ΗΚ, δεδομένη ἂν εἴη
5 καὶ ἡ ΜΗ, ὥστε καὶ λόγος τῆς ΜΗ πρὸς ΜΚ. δεδομένης
οὖν περιφερείας ἐφάψεται τὸ Μ. ἔστω δὴ αὕτη ἐφ'
ἧς τὰ Ν Μ· ὥστε ἡ τομὴ τῶν περιφερειῶν δέδοται. πρὸς
ἄλλῃ δέ γε ἢ τῇ ΜΝ περιφερείᾳ ἀπὸ τῶν αὐτῶν σημείων
ὁ αὐτὸς λόγος ἐν τῷ αὐτῷ ἐπιπέδῳ οὐ συνίσταται.
10 ἐκκείσθω οὖν τις γραμμὴ ἡ ΔΒ, καὶ τετμήσθω ὡς ἡ ΜΗ
πρὸς ΜΚ ἡ Δ πρὸς Β. μείζων δὲ ἡ ΜΗ τῆς ΚΜ,
ἐπείπερ ἐπὶ τὴν μείζω γωνίαν ἡ ἀνάκλασις τοῦ κώνου· ὑπὸ
γὰρ τὴν μείζω γωνίαν ὑποτείνει τοῦ ΚΜΗ τριγώνου.
[μείζων ἄρα καὶ ἡ Δ τῆς Β.] προσπεπορίσθω οὖν πρὸς τὴν Β,
15 ἐφ' ἧς τὸ Ζ· ὥστ' εἶναι ὅπερ τὴν Δ πρὸς τὴν Β, τὴν ΒΖ
πρὸς τὴν Δ. εἶτα ὅπερ ἡ Ζ πρὸς τὴν ΚΗ, ἡ τὸ Β πρὸς
ἄλλην πεποιήσθω τὴν ΚΠ, καὶ ἀπὸ τοῦ Π ἐπὶ τὸ Μ ἐπεζεύχθω
ἡ τὸ ΜΠ. ἔσται οὖν τὸ Π πόλος τοῦ κύκλου, πρὸς
ὃν αἱ ἀπὸ τοῦ Κ γραμμαὶ προσπίπτουσιν· ἔσται γὰρ ὅπερ
20 ἡ Ζ πρὸς ΚΗ, καὶ ἡ Β πρὸς ΚΠ, καὶ ἡ Δ πρὸς
ΠΜ. μὴ γὰρ ἔστω, ἀλλ' ἢ πρὸς ἐλάττω ἢ πρὸς μείζω
τῆς ΠΜ· οὐδὲν γὰρ διοίσει. ἔστω πρὸς ΠΡ. τὸν αὐτὸν
ἄρα λόγον αἱ ΗΚ καὶ ΚΠ καὶ ἡ ΠΡ πρὸς ἀλλήλας
ἕξουσιν ὅνπερ αἱ Δ Β Ζ. αἱ δὲ Δ Β Ζ ἀνὰ λόγον
25 ἦσαν, ὅνπερ ἡ Δ πρὸς Β, ἡ ΖΒ πρὸς Δ· ὥστε ὅπερ ἡ ΠΗ
πρὸς τὴν ΠΡ, ἡ τὸ ΠΡ πρὸς τὴν ΠΚ. ἂν οὖν ἀπὸ τῶν
Κ Η αἱ ΗΡ καὶ ΚΡ ἐπὶ τὸ Ρ ἐπιζευχθῶσιν, αἱ ἐπιζευχθεῖσαι
αὗται τὸν αὐτὸν ἕξουσι λόγον ὅνπερ ἡ ΗΠ πρὸς
τὴν ΠΡ· περὶ γὰρ τὴν αὐτὴν γωνίαν τὴν Π ἀνάλογον αἵ
30 τε τοῦ ΗΠΡ τριγώνου καὶ τοῦ ΚΡΠ. ὥστε καὶ ἡ ΠΡ πρὸς
τὴν ΚΡ τὸν αὐτὸν ἕξει λόγον, καὶ ἡ τὸ ΗΠ πρὸς τὴν ΠΡ.
ἔχει δὲ καὶ ἡ ΜΗ πρὸς ΚΜ τοῦτον τὸν λόγον· ὅνπερ γὰρ
1Let it be A (for it makes no difference which of the planes passing through the line HK and determined by the triangle KMH is produced). Now the lines drawn from H and K to a point on the semicircle A are in a certain ratio to one another, and no lines drawn from the same points to another point on that semicircle can have the same ratio. For since both the points H and K and the line KH are given, 5the line MH will be given too; consequently the ratio of the line MH to the line MK will be given too. So M will touch a given circumference. Let this be NM. Then the intersection of the circumferences is given, and the same ratio cannot hold between lines in the same plane drawn from the same points to any other circumference but MN.
10Draw a line DB outside of the figure and divide it so that D:B=MH:MK. But MH is greater than MK since the reflection of the cone is over the greater angle (for it subtends the greater angle of the triangle KMH). Therefore D is greater than B. Then add to B 15a line Z such that B+Z:D=D:B. Then make another line having the same ratio to B as KH has to Z, and join MI.
Then I is the pole of the circle on which the lines from K fall. For the ratio of D to IM is the same as that of 20Z to KH and of B to KI. If not, let D be in the same ratio to a line indifferently lesser or greater than IM, and let this line be IP. Then HK and KI and IP will have the same ratios to one another as Z, B, and D. But the ratios between Z, B, and D 25were such that Z+B:D=D: B. Therefore Ih:IP=IP:IK. Now, if the points K, H be joined with the point P by the lines HP, KP, these lines will be to one another as IH is to IP, for the sides of 30the triangles HIP, KPI about the angle I are homologous. Therefore, HP too will be to KP as HI is to IP.
10Draw a line DB outside of the figure and divide it so that D:B=MH:MK. But MH is greater than MK since the reflection of the cone is over the greater angle (for it subtends the greater angle of the triangle KMH). Therefore D is greater than B. Then add to B 15a line Z such that B+Z:D=D:B. Then make another line having the same ratio to B as KH has to Z, and join MI.
Then I is the pole of the circle on which the lines from K fall. For the ratio of D to IM is the same as that of 20Z to KH and of B to KI. If not, let D be in the same ratio to a line indifferently lesser or greater than IM, and let this line be IP. Then HK and KI and IP will have the same ratios to one another as Z, B, and D. But the ratios between Z, B, and D 25were such that Z+B:D=D: B. Therefore Ih:IP=IP:IK. Now, if the points K, H be joined with the point P by the lines HP, KP, these lines will be to one another as IH is to IP, for the sides of 30the triangles HIP, KPI about the angle I are homologous. Therefore, HP too will be to KP as HI is to IP.
376b
1 ἡ τὸ Δ πρὸς τὴν Β ἀμφότεραι. ὥστε ἀπὸ τῶν Η Κ σημείων
οὐ μόνον πρὸς τὴν ΜΝ περιφέρειαν συσταθήσονται τὸν αὐτὸν
ἔχουσαι λόγον, ἀλλὰ καὶ ἄλλοθι· ὅπερ ἀδύνατον. ἐπεὶ οὖν
ἡ Δ οὔτε πρὸς ἔλαττον τοῦ ΜΠ οὔτε πρὸς μείζω (ὁμοίως
5 γὰρ δειχθήσεται), δῆλον ὅτι πρὸς αὐτὴν ἂν εἴη τὴν ἐφ' ᾗ Μ Π.
ὥστ' ἔσται ὅπερ ἡ ΜΠ πρὸς ΠΚ, ἡ ΠΗ πρὸς τὴν
ΜΠ [καὶ λοιπὴ ἡ τὸ ΜΗ πρὸς ΜΚ]. ἐὰν οὖν τῷ ἐφ' ᾧ τὸ
Π πόλῳ χρώμενος, διαστήματι δὲ τῷ ἐφ' ᾧ Μ Π, κύκλος
γραφῇ, ἁπασῶν ἐφάψεται τῶν γωνιῶν ἃς ἀνακλώμεναι
10 ποιοῦσιν αἱ ἀπὸ τοῦ ΜΑ κύκλου· εἰ δὲ μή, ὁμοίως δειχθήσονται
τὸν αὐτὸν ἔχουσαι λόγον αἱ ἄλλοθι καὶ ἄλλοθι τοῦ
ἡμικυκλίου συνιστάμεναι, ὅπερ ἦν ἀδύνατον. ἐὰν οὖν περιαγάγῃς
τὸ ἡμικύκλιον τὸ ἐφ' ᾧ τὸ Α περὶ τὴν ἐφ' ᾗ Η Κ Π
διάμετρον, αἱ ἀπὸ τοῦ ΗΚ ἀνακλώμεναι πρὸς τὸ ἐφ' ᾧ τὸ
15 Μ ἐν πᾶσι τοῖς ἐπιπέδοις ὁμοίως ἕξουσι, καὶ ἴσην ποιήσουσι
γωνίαν τὴν ΚΜΗ· καὶ ἣν ποιήσουσι δὲ γωνίαν αἱ ΗΠ
καὶ ΜΠ ἐπὶ τῆς ΗΠ, ἀεὶ ἴση ἔσται. τρίγωνα οὖν ἐπὶ τῆς
ΗΠ καὶ ΚΠ ἴσα τῷ ΗΜΠ ΚΜΠ συνεστήκασι. τούτων
δὲ αἱ κάθετοι ἐπὶ τὸ αὐτὸ σημεῖον πεσοῦνται τῆς ΗΠ
20 καὶ ἴσαι ἔσονται. πιπτέτωσαν ἐπὶ τὸ Ο. κέντρον ἄρα τοῦ
κύκλου τὸ Ο, ἡμικύκλιον δὲ τὸ περὶ τὴν ΜΝ ἀφῄρηται
ἀπὸ τοῦ ὁρίζοντος· τῶν μὲν γὰρ ἄνω τὸν ἥλιον οὐ κρατεῖν, τῶν
δὲ *προσπτεριζομένων* κρατεῖν, καὶ διαχεῖν τὸν ἀέρα·
καὶ διὰ τοῦτο τὴν ἶριν οὐ συμβάλλειν τὸν κύκλον· γίγνεσθαι
25 δὲ καὶ νύκτωρ ἀπὸ τῆς σελήνης ὀλιγάκις· οὔτε γὰρ ἀεὶ
πλήρης, ἀσθενεστέρα τε τὴν φύσιν ὥστε κρατεῖν τοῦ ἀέρος·
μάλιστα δ' ἵστασθαι τὴν ἶριν, ὅπου μάλιστα κρατεῖται ὁ
ἥλιος· πλείστη γὰρ ἐν αὐτῇ ἰκμὰς ἐνέμεινεν. πάλιν ἔστω
ὁρίζων μὲν ἐφ' οὗ τὸ ΑΚΓ, ἐπανατεταλκέτω δὲ τὸ Η, ὁ
30 δ' ἄξων ἔστω νῦν ἐφ' οὗ τὸ ΗΠ. τὰ μὲν οὖν ἄλλα πάντα
ὁμοίως δειχθήσεται ὡς καὶ πρότερον, ὁ δὲ πόλος τοῦ κύκλου
ὁ ἐφ' ᾧ Π κάτω ἔσται τοῦ ὁρίζοντος τοῦ ἐφ' ᾧ τὸ ΑΓ, ἀρθέντος
1But this is also the ratio of MH to MK, for the ratio both of HI to IP and of Mh to MK is the same as that of D to B. Therefore, from the points H, K there will have been drawn lines with the same ratio to one another, not only to the circumference MN but to another point as well, which is impossible. Since then D cannot bear that ratio to any line either lesser or greater than IM (5the proof being in either case the same), it follows that it must stand in that ratio to MI itself. Therefore as MI is to IK so IH will be to MI and finally MH to Mk.
If, then, a circle be described with I as pole at the distance MI it will touch all the angles which the lines from H and K 10make by their reflection. If not, it can be shown, as before, that lines drawn to different points in the semicircle will have the same ratio to one another, which was impossible. If, then, the semicircle A be revolved about the diameter HKI, the lines reflected from the points H, K at the point 15M will have the same ratio, and will make the angle KMH equal, in every plane. Further, the angle which HM and MI make with HI will always be the same. So there are a number of triangles on HI and KI equal to the triangles HMI and KMI. Their perpendiculars will fall on HI at the same point 20and will be equal. Let O be the point on which they fall. Then O is the centre of the circle, half of which, MN, is cut off by the horizon. (See diagram.)
25Next let the horizon be ABG but let H have risen above the horizon. 30Let the axis now be HI. The proof will be the same for the rest as before, but the pole I of the circle will be below the horizon Ag since the point H has risen above the horizon. But the pole, and the centre of the circle, and the centre of that circle (namely HI) which now determines the position of the sun are on the same line.
If, then, a circle be described with I as pole at the distance MI it will touch all the angles which the lines from H and K 10make by their reflection. If not, it can be shown, as before, that lines drawn to different points in the semicircle will have the same ratio to one another, which was impossible. If, then, the semicircle A be revolved about the diameter HKI, the lines reflected from the points H, K at the point 15M will have the same ratio, and will make the angle KMH equal, in every plane. Further, the angle which HM and MI make with HI will always be the same. So there are a number of triangles on HI and KI equal to the triangles HMI and KMI. Their perpendiculars will fall on HI at the same point 20and will be equal. Let O be the point on which they fall. Then O is the centre of the circle, half of which, MN, is cut off by the horizon. (See diagram.)
25Next let the horizon be ABG but let H have risen above the horizon. 30Let the axis now be HI. The proof will be the same for the rest as before, but the pole I of the circle will be below the horizon Ag since the point H has risen above the horizon. But the pole, and the centre of the circle, and the centre of that circle (namely HI) which now determines the position of the sun are on the same line.
377a
1 τοῦ ἐφ' ᾧ τὸ Η σημείου. ἐπὶ δὲ τῆς αὐτῆς ὅ τε πόλος
καὶ τὸ κέντρον τοῦ κύκλου καὶ τὸ τοῦ ὁρίζοντος νῦν τὴν
ἀνατολήν· ἔστι γὰρ οὗτος ἐφ' ᾧ τὸ ΗΠ. ἐπεὶ δὲ τῆς διαμέτρου
τῆς ΑΓ τὸ ΚΗ ἐπάνω, τὸ κέντρον εἴη ἂν ὑποκάτω
5 τοῦ ὁρίζοντος πρότερον τοῦ ἐφ' ᾧ τὸ ΑΓ, ἐπὶ τῆς ΚΠ γραμμῆς,
ἐφ' οὗ τὸ Β. ὥστ' ἔλαττον ἔσται τὸ ἐπάνω τμῆμα ἡμικυκλίου
τὸ ἐφ' ᾧ Ψ Υ· τὸ γὰρ ΨΥΟ ἡμικύκλιον ἦν,
νῦν δὲ ἀποτέτμηται ἀπὸ τοῦ ΑΓ ὁρίζοντος. τὸ δὴ ΟΥ ἀφανὲς
ἔσται αὐτοῦ, ἐπαρθέντος τοῦ ἡλίου· ἐλάχιστον δ', ὅταν ἐπὶ
10 μεσημβρίας· ὅσον γὰρ ἀνώτερον τὸ Η, κατώτερον ὅ τε πόλος
καὶ τὸ κέντρον τοῦ κύκλου ἔσται. ὅτι δ' ἐν μὲν ταῖς ἐλάττοσιν
ἡμέραις ταῖς μετ' ἰσημερίαν τὴν μετοπωρινὴν ἐνδέχεται
ἀεὶ γίγνεσθαι ἶριν, ἐν δὲ ταῖς μακροτέραις ἡμέραις ταῖς
ἀπὸ ἰσημερίας τῆς ἑτέρας ἐπὶ τὴν ἰσημερίαν τὴν ἑτέραν περὶ
15 μεσημβρίαν οὐ γίγνεται ἶρις, αἴτιον ὅτι τὰ μὲν πρὸς ἄρκτον
τμήματα πάντα μείζω ἡμικυκλίου καὶ ἀεὶ ἐπὶ μείζω ἡμικυκλίου,
τὸ δ' ἀφανὲς μικρόν, τὰ δὲ πρὸς μεσημβρίαν
τμήματα τοῦ ἰσημερινοῦ, τὸ μὲν ἄνω τμῆμα μικρόν, τὸ δ'
ὑπὸ γῆν μέγα, καὶ ἀεὶ δὴ μείζω τὰ πορρώτερα· ὥστ' ἐν
20 μὲν ταῖς πρὸς θερινὰς τροπὰς ἡμέραις διὰ τὸ μέγεθος τοῦ
τμήματος, πρὶν ἐπὶ τὸ μέσον ἐλθεῖν τοῦ τμήματος καὶ ἐπὶ
τὸν μεσημβρινὸν τὴν τὸ Η, κάτω ἤδη τελέως γίγνεται ἡ τὸ
Π, διὰ τὸ πόρρω ἀφεστάναι τῆς γῆς τὴν μεσημβρίαν διὰ
τὸ μέγεθος τοῦ τμήματος. ἐν δὲ ταῖς πρὸς τὰς χειμερινὰς
25 τροπὰς ἡμέραις, διὰ τὸ μὴ πολὺ ὑπὲρ γῆς εἶναι τὰ τμήματα
τῶν κύκλων, τοὐναντίον ἀναγκαῖον γίγνεσθαι· βραχὺ
γὰρ ἀρθείσης τῆς ἐφ' ᾧ τὸ Η, ἐπὶ τῆς μεσημβρίας γίγνεται
ὁ ἥλιος.
1But since KH lies above the diameter AG, the centre will be at O on the line KI 5below the plane of the circle AG determined the position of the sun before. So the segment YX which is above the horizon will be less than a semicircle. For YXM was a semicircle and it has now been cut off by the horizon AG. So part of it, YM, will be invisible when the sun has risen above the horizon, and the segment visible will be smallest when the sun is on 10the meridian; for the higher H is the lower the pole and the centre of the circle will be.
In the shorter days after the autumn equinox there may be a rainbow at any time of the day, but in the longer days from the spring to the autumn equinox there cannot be a rainbow about 15midday. The reason for this is that when the sun is north of the equator the visible arcs of its course are all greater than a semicircle, and go on increasing, while the invisible arc is small, but when the sun is south of the equator the visible arc is small and the invisible arc great, and the farther the sun moves south of the equator the greater is the invisible arc. Consequently, 20in the days near the summer solstice, the size of the visible arc is such that before the point H reaches the middle of that arc, that is its point of culmination, the point is well below the horizon; the reason for this being the great size of the visible arc, and the consequent distance of the point of culmination from the earth. But in the days near the winter 25solstice the visible arcs are small, and the contrary is necessarily the case: for the sun is on the meridian before the point H has risen far.
In the shorter days after the autumn equinox there may be a rainbow at any time of the day, but in the longer days from the spring to the autumn equinox there cannot be a rainbow about 15midday. The reason for this is that when the sun is north of the equator the visible arcs of its course are all greater than a semicircle, and go on increasing, while the invisible arc is small, but when the sun is south of the equator the visible arc is small and the invisible arc great, and the farther the sun moves south of the equator the greater is the invisible arc. Consequently, 20in the days near the summer solstice, the size of the visible arc is such that before the point H reaches the middle of that arc, that is its point of culmination, the point is well below the horizon; the reason for this being the great size of the visible arc, and the consequent distance of the point of culmination from the earth. But in the days near the winter 25solstice the visible arcs are small, and the contrary is necessarily the case: for the sun is on the meridian before the point H has risen far.
Book 3,Chapter 6 (377a29–378b6)
τὰς δ' αὐτὰς αἰτίας ὑποληπτέον καὶ περὶ παρηλίων
30 καὶ ῥάβδων ταῖς εἰρημέναις. γίγνεται γὰρ παρήλιος μὲν
ἀνακλωμένης τῆς ὄψεως πρὸς τὸν ἥλιον, ῥάβδοι δὲ διὰ τὸ
προσπίπτειν τοιαύτην οὖσαν τὴν ὄψιν, οἵαν εἴπομεν ἀεὶ γίγνεσθαι
ὅταν πλησίον ὄντων τοῦ ἡλίου νεφῶν ἀπό τινος ἀνακλασθῇ
τῶν ὑγρῶν πρὸς τὸ νέφος· φαίνεται γὰρ αὐτὰ μὲν
29Mock suns, 30and rods too, are due to the causes we have described. A mock sun is caused by the reflection of sight to the sun. Rods are seen when sight reaches the sun under circumstances like those which we described, when there are clouds near the sun and sight is reflected from some liquid surface to the cloud. Here the clouds themselves are colourless when you look at them directly, but in the water they are full of rods.
377b
1 ἀχρωμάτιστα τὰ νέφη κατ' εὐθυωρίαν εἰσβλέπουσιν, ἐν δὲ
τῷ ὕδατι ῥάβδων μεστὸν τὸ νέφος· πλὴν τότε μὲν ἐν τῷ
ὕδατι δοκεῖ τὸ χρῶμα τοῦ νέφους εἶναι, ἐν δὲ ταῖς ῥάβδοις
ἐπ' αὐτοῦ τοῦ νέφους. γίγνεται δὲ τοῦτο ὅταν ἀνώμαλος ἡ
5 τοῦ νέφους ᾖ σύστασις, καὶ τῇ μὲν πυκνότερον τῇ δὲ μανόν, καὶ
τῇ μὲν ὑδατωδέστερον τῇ δ' ἧττον· ἀνακλασθείσης γὰρ τῆς
ὄψεως πρὸς τὸν ἥλιον, τὸ σχῆμα μὲν [τοῦ ἡλίου] οὐχ ὁρᾶται
[διὰ μικρότητα τῶν ἐνόπτρων], τὸ δὲ χρῶμα· διὰ δὲ τὸ ἐν ἀνωμάλῳ
φαίνεσθαι λαμπρὸν καὶ λευκὸν τὸν ἥλιον, πρὸς ὃν
10 ἀνεκλάσθη ἡ ὄψις, τὸ μὲν φοινικοῦν φαίνεται, τὸ δὲ πράσινον
ἢ ξανθόν. διαφέρει γὰρ οὐδὲν διὰ τοιούτων ὁρᾶν ἢ ἀπὸ
τοιούτων ἀνακλωμένην· ἀμφοτέρως γὰρ φαίνεται τὴν χρόαν
ὅμοιον, ὥστ' εἰ κἀκείνως φοινικοῦν, καὶ οὕτως. αἱ μὲν οὖν
ῥάβδοι γίγνονται δι' ἀνωμαλίαν τοῦ ἐνόπτρου οὐ τῷ σχήματι
15 ἀλλὰ τῷ χρώματι· ὁ δὲ παρήλιος, ὅταν ὅτι μάλιστα
ὁμαλὸς ᾖ ὁ ἀὴρ καὶ πυκνὸς ὁμοίως· διὸ φαίνεται λευκός.
ἡ μὲν γὰρ ὁμαλότης τοῦ ἐνόπτρου ποιεῖ χρόαν μίαν τῆς ἐμφάσεως·
ἡ δ' ἀνάκλασις ἀθρόας τῆς ὄψεως, διὰ τὸ ἅμα
προσπίπτειν πρὸς τὸν ἥλιον ἀπὸ πυκνῆς οὔσης τῆς ἀχλύος,
20 καὶ οὔπω μὲν οὔσης ὕδωρ ἐγγὺς δ' ὕδατος, [διὰ] τὸ ὑπάρχον τῷ
ἡλίῳ ἐμφαίνεσθαι χρῶμα ποιεῖ, ὥσπερ ἀπὸ χαλκοῦ λείου
κλωμένην διὰ τὴν πυκνότητα. ὥστ' ἐπεὶ τὸ χρῶμα τοῦ ἡλίου
λευκόν, καὶ ὁ παρήλιος φαίνεται λευκός. διὰ δὲ τὸ αὐτὸ
τοῦτο μᾶλλον ὕδατος σημεῖον ὁ παρήλιος τῶν ῥάβδων·
25 μᾶλλον γὰρ συμβαίνει τὸν ἀέρα εὐεργῶς ἔχειν πρὸς γένεσιν
ὕδατος. ὁ δὲ νότιος τοῦ βορείου μᾶλλον, ὅτι μᾶλλον ὁ
νότιος ἀὴρ εἰς ὕδωρ μεταβάλλει τοῦ πρὸς ἄρκτον. γίγνονται
δ', ὥσπερ εἴπομεν, περί τε δυσμὰς καὶ περὶ τὰς ἀνατολάς,
καὶ οὔτε ἄνωθεν οὔτε κάτωθεν, ἀλλ' ἐκ τῶν πλαγίων
30 καὶ ῥάβδοι καὶ παρήλιοι· καὶ οὔτ' ἐγγὺς τοῦ ἡλίου λίαν
οὔτε πόρρω παντελῶς· ἐγγὺς μὲν γὰρ οὖσαν ὁ ἥλιος διαλύει
τὴν σύστασιν, πόρρω δ' οὔσης ἡ ὄψις οὐκ ἀνακλασθήσεται·
ἀπὸ γὰρ μικροῦ ἐνόπτρου πόρρω ἀποτεινομένη ἀσθενὴς γίγνεται·
διὸ καὶ αἱ ἅλως οὐ γίγνονται ἐξ ἐναντίας τοῦ ἡλίου. ἄνω
1The only difference is that in this latter case the colour of the cloud seems to reside in the water, but in the case of rods on the cloud itself. Rods appear when 5the composition of the cloud is uneven, dense in part and in part rare, and more and less watery in different parts. Then the sight is reflected to the sun: the mirrors are too small for the shape of the sun to appear, but, the bright white light of the sun, to which 10the sight is reflected, being seen on the uneven mirror, its colour appears partly red, partly green or yellow. It makes no difference whether sight passes through or is reflected from a medium of that kind; the colour is the same in both cases; if it is red in the first case it must be the same in the other.
Rods then are occasioned by the unevenness of the mirror-15as regards colour, not form. The mock sun, on the contrary, appears when the air is very uniform, and of the same density throughout. This is why it is white: the uniform character of the mirror gives the reflection in it a single colour, while the fact that the sight is reflected in a body and is thrown on the sun all together by the mist, which is dense and watery 20though not yet quite water, causes the sun's true colour to appear just as it does when the reflection is from the dense, smooth surface of copper. So the sun's colour being white, the mock sun is white too. This, too, is the reason why the mock sun is a surer sign of rain than the rods; 25it indicates, more than they do, that the air is ripe for the production of water. Further a mock sun to the south is a surer sign of rain than one to the north, for the air in the south is readier to turn into water than that in the north.
30Mock suns and rods are found, as we stated, about sunset and sunrise, not above the sun nor below it, but beside it. They are not found very close to the sun, nor very far from it, for the sun dissolves the cloud if it is near, but if it is far off the reflection cannot take place, since sight weakens when it is reflected from a small mirror to a very distant object. (This is why a halo is never found opposite to the sun.)
Rods then are occasioned by the unevenness of the mirror-15as regards colour, not form. The mock sun, on the contrary, appears when the air is very uniform, and of the same density throughout. This is why it is white: the uniform character of the mirror gives the reflection in it a single colour, while the fact that the sight is reflected in a body and is thrown on the sun all together by the mist, which is dense and watery 20though not yet quite water, causes the sun's true colour to appear just as it does when the reflection is from the dense, smooth surface of copper. So the sun's colour being white, the mock sun is white too. This, too, is the reason why the mock sun is a surer sign of rain than the rods; 25it indicates, more than they do, that the air is ripe for the production of water. Further a mock sun to the south is a surer sign of rain than one to the north, for the air in the south is readier to turn into water than that in the north.
30Mock suns and rods are found, as we stated, about sunset and sunrise, not above the sun nor below it, but beside it. They are not found very close to the sun, nor very far from it, for the sun dissolves the cloud if it is near, but if it is far off the reflection cannot take place, since sight weakens when it is reflected from a small mirror to a very distant object. (This is why a halo is never found opposite to the sun.)
378a
1 μὲν οὖν ἐὰν γίγνηται καὶ ἐγγύς, διαλύσει ὁ ἥλιος· ἐὰν δὲ
πόρρω, ἐλάττων ἡ ὄψις οὖσα ἢ ὥστε ποιεῖν ἀνάκλασιν οὐ
προσπεσεῖται. ἐν δὲ τῷ πλαγίῳ [ὑπὸ τὸν ἥλιον] ἐστὶ τοσοῦτον
ἀποστῆναι τὸ ἔνοπτρον, ὥστε μήτε τὸν ἥλιον διαλῦσαι, τήν
5 τε ὄψιν ἀθρόαν ἐλθεῖν, διὰ τὸ πρὸς τὴν γῆν φερομένην μὴ
διασπᾶσθαι ὥσπερ δι' ἀχανοῦς φερομένην. ὑπὸ δὲ τὸν ἥλιον
οὐ γίγνεται διὰ τὸ πλησίον μὲν τῆς γῆς διαλύεσθαι ἂν ὑπὸ τοῦ
ἡλίου, ἄνω δὲ μεσουρανίου <γιγνομένης συστάσεως> τὴν ὄψιν διασπᾶσθαι.
καὶ ὅλως οὐδ' ἐκ πλαγίου μεσουρανίου γίγνεται· ἡ γὰρ
10 ὄψις οὐχ ὑπὸ τὴν γῆν φέρεται, ὥστε ὀλίγη ἀφικνεῖται πρὸς
τὸ ἔνοπτρον, καὶ ἡ ἀνακλωμένη γίγνεται πάμπαν ἀσθενής.
ὅσα μὲν οὖν ἔργα συμβαίνει παρέχεσθαι τὴν ἔκκρισιν ἐν
τοῖς τόποις τοῖς ὑπὲρ τῆς γῆς, σχεδόν ἐστι τοσαῦτα καὶ
τοιαῦτα.
15 ὅσα δ' ἐν αὐτῇ τῇ γῇ, ἐγκατακλειομένη τοῖς τῆς
γῆς μέρεσιν, ἀπεργάζεται, λεκτέον. ποιεῖ γὰρ δύο διαφορὰς
σωμάτων διὰ τὸ διπλῆ πεφυκέναι καὶ αὐτή, καθάπερ
καὶ ἐν τῷ μετεώρῳ· δύο μὲν γὰρ αἱ ἀναθυμιάσεις, ἡ
μὲν ἀτμιδώδης ἡ δὲ καπνώδης, ὥς φαμεν, εἰσίν· δύο δὲ
20 καὶ τὰ εἴδη τῶν ἐν τῇ γῇ γιγνομένων, τὰ μὲν ὀρυκτὰ τὰ
δὲ μεταλλευτά. ἡ μὲν οὖν ξηρὰ ἀναθυμίασίς ἐστιν ἥ τις ἐκπυροῦσα
ποιεῖ τὰ ὀρυκτὰ πάντα, οἷον λίθων τε γένη τὰ
ἄτηκτα καὶ σανδαράκην καὶ ὤχραν καὶ μίλτον καὶ θεῖον
καὶ τἆλλα τὰ τοιαῦτα. τὰ δὲ πλεῖστα τῶν ὀρυκτῶν ἐστιν τὰ
25 μὲν κονία κεχρωματισμένη, τὰ δὲ λίθος ἐκ τοιαύτης γεγονὼς
συστάσεως, οἷον τὸ κιννάβαρι. τῆς δ' ἀναθυμιάσεως τῆς
ἀτμιδώδους, ὅσα μεταλλεύεται, καὶ ἔστιν ἢ χυτὰ ἢ ἐλατά,
οἷον σίδηρος, χρυσός, χαλκός. ποιεῖ δὲ ταῦτα πάντα ἡ
ἀναθυμίασις ἡ ἀτμιδώδης ἐγκατακλειομένη, καὶ μάλιστα
30 ἐν τοῖς λίθοις, διὰ ξηρότητα εἰς ἓν συνθλιβομένη καὶ πηγνυμένη,
οἷον ἢ δρόσος ἢ πάχνη, ὅταν ἀποκριθῇ. ἐνταῦθα δὲ
πρὶν ἀποκριθῆναι γεννᾶται ταῦτα. διὸ ἔστι μὲν ὡς ὕδωρ
ταῦτα, ἔστιν δ' ὡς οὔ· δυνάμει μὲν γὰρ ἡ ὕλη ὕδατος ἦν,
ἔστι δ' οὐκέτι, οὐδ' ἐξ ὕδατος γενομένου διά τι πάθος, ὥσπερ
1If the cloud is above the sun and close to it the sun will dissolve it; if it is above the sun but at a distance the sight is too weak for the reflection to take place, and so it will not reach the sun. But at the side of the sun, it is possible for the mirror to be at such an interval that the sun does not dissolve the cloud, 5and yet sight reaches it undiminished because it moves close to the earth and is not dissipated in the immensity of space. It cannot subsist below the sun because close to the earth the sun's rays would dissolve it, but if it were high up and the sun in the middle of the heavens, sight would be dissipated. Indeed, even by the side of the sun, it is not found when the sun is in the middle of the sky, for then 10the line of vision is not close to the earth, and so but little sight reaches the mirror and the reflection from it is altogether feeble.
Some account has now been given of the effects of the secretion above the surface of the earth; 15we must go on to describe its operations below, when it is shut up in the parts of the earth.
Just as its twofold nature gives rise to various effects in the upper region, so here it causes two varieties of bodies. We maintain that there are two exhalations, one vaporous the other smoky, 20and there correspond two kinds of bodies that originate in the earth, 'fossiles' and metals. The heat of the dry exhalation is the cause of all 'fossiles'. Such are the kinds of stones that cannot be melted, and realgar, and ochre, and ruddle, and sulphur, and the other things of that kind, most 'fossiles' being 25either coloured lye or, like cinnabar, a stone compounded of it. The vaporous exhalation is the cause of all metals, those bodies which are either fusible or malleable such as iron, copper, gold. All these originate from the imprisonment of the vaporous exhalation in the earth, and especially 30in stones. Their dryness compresses it, and it congeals just as dew or hoar-frost does when it has been separated off, though in the present case the metals are generated before that segregation occurs. Hence, they are water in a sense, and in a sense not. Their matter was that which might have become water, but it can no longer do so: nor are they, like savours, due to a qualitative change in actual water.
Some account has now been given of the effects of the secretion above the surface of the earth; 15we must go on to describe its operations below, when it is shut up in the parts of the earth.
Just as its twofold nature gives rise to various effects in the upper region, so here it causes two varieties of bodies. We maintain that there are two exhalations, one vaporous the other smoky, 20and there correspond two kinds of bodies that originate in the earth, 'fossiles' and metals. The heat of the dry exhalation is the cause of all 'fossiles'. Such are the kinds of stones that cannot be melted, and realgar, and ochre, and ruddle, and sulphur, and the other things of that kind, most 'fossiles' being 25either coloured lye or, like cinnabar, a stone compounded of it. The vaporous exhalation is the cause of all metals, those bodies which are either fusible or malleable such as iron, copper, gold. All these originate from the imprisonment of the vaporous exhalation in the earth, and especially 30in stones. Their dryness compresses it, and it congeals just as dew or hoar-frost does when it has been separated off, though in the present case the metals are generated before that segregation occurs. Hence, they are water in a sense, and in a sense not. Their matter was that which might have become water, but it can no longer do so: nor are they, like savours, due to a qualitative change in actual water.
378b
1 οἱ χυμοί· οὐδὲ γὰρ οὕτω γίγνεται τὸ μὲν χαλκὸς τὸ δὲ χρυσός,
ἀλλὰ πρὶν γενέσθαι παγείσης τῆς ἀναθυμιάσεως ἕκαστα
τούτων ἐστίν. διὸ καὶ πυροῦται πάντα καὶ γῆν ἔχει· ξηρὰν
γὰρ ἔχει ἀναθυμίασιν· ὁ δὲ χρυσὸς μόνος οὐ πυροῦται.
5 κοινῇ μὲν οὖν εἴρηται περὶ αὐτῶν ἁπάντων, ἰδίᾳ δὲ σκεπτέον
προχειριζομένοις περὶ ἕκαστον γένος.
1Copper and gold are not formed like that, but in every case the evaporation congealed before water was formed. Hence, they all (except gold) are affected by fire, and they possess an admixture of earth; for they still contain the dry exhalation.
5This is the general theory of all these bodies, but we must take up each kind of them and discuss it separately.
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5This is the general theory of all these bodies, but we must take up each kind of them and discuss it separately.
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