Plutarch, De Facie Quae in orbe Lunae Apparet, Harold Cherniss (Translator), William C. Helmbold (Translator), 17

Search the Perseus Catalog for:

← Previous Next →

[17] Sulla then broke in and said: No doubt this position has its plausible aspects; but what tells most strongly on the other side, did our comrade¹ explain that away or did he fail to notice it? What’s that? said Lucius, or do you mean the difficulty with respect to the half-moon? Exactly, said Sulla, for there is some reason in the contention that, since all reflection occurs at equal angles,² whenever the moon at the half is in mid-heaven the light cannot move earthwards from her but must glance off beyond the earth. The ray that then touches the moon comes from the sun on the horizon³ and therefore, being reflected at equal angles, would be produced to the point on the opposite horizon and would not shed its light upon us, or else there would be great distortion and aberration of the angle, which is impossible.⁴ Yes, by Heaven, said Lucius, there was talk of this too; and, looking at Menelaus the mathematician as he spoke, he said: In your presence, my dear Menelaus, I am ashamed to confute a mathematical proposition, the foundation, as it were, on which rests the subject of catoptrics. Yet it must be said that the proposition, all reflection occurs at equal angles,⁵ is neither self-evident nor an admitted fact.⁶ It is refuted in the case of convex⁷ mirrors when the point of incidence of the visual ray produces images that are magnified in one respect; and it is refuted by folding mirrors,⁸ either plane of which, when they have been inclined to each other and have formed an inner angle, exhibits a double image, so that four likenesses of a single object are produced, two reversed on the outer surfaces and two dim ones not reversed in the depth of the mirrors. The reason for the production of these images Plato explains,⁹ for he has said that when the mirror is elevated on both sides the visual rays interchange their reflection because they shift from one side to the other. So, if of the visual rays (some) revert straight to us (from the plane surfaces) while others glance off to the opposite sides of the mirrors and thence return to us again, it is not possible that all reflections occur at equal angles.¹⁰ Consequently (some people) take direct issue (with the mathematicians) and maintain that they confute the equality of the angles of incidence and reflection by the very streams of light that flow from the moon upon the earth, for they deem this fact to be much more credible than that theory. Nevertheless, suppose that this¹¹ must be conceded as a favour to geometry, the dearly beloveds3 In the first place, it is likely to occur only in mirrors that have been polished to exact smoothness; but the moon is very uneven and rugged, with the result that the rays from a large body striking against considerable heights which receive reflections and diffusions of light from one another are multifariously reflected and intertwined and the refulgence itself combines with itself, coming to us, as it were, from many mirrors. In the second place, even if we assume that the reflections on the surface of the moon occur at equal angles, it is not impossible that the rays as they travel through such a great interval get fractured and deflected¹² so as to be blurred and to bend their light. Some people even give a geometrical demonstration that the moon sheds many of her beams upon the earth along a line extended from the surface that is bent away from us¹³; but I could not construct a geometrical diagram while talking, and talking to many people too.

De Facie Quae in orbe Lunae Apparet. Plutarch. Harold Cherniss (Translator), William C. Helmbold (Translator). Cambridge, MA. 1957.

Sponsored by Perseus Project, Tufts University.

Funding provided by The National Endowment for the Humanities.

Current edition Perseus

Concerning the Face which Appears in the Orb Of the Moon (English) (Plutarch. Moralia, Vol. XII. Cherniss, Harold and William Clark Helmbold translators. Cambridge, MA: Harvard University Press; London: William Heinemann Ltd., 1957 (printing).)

Editions (1)

Περὶ τοῦ ἐμφαινομένου προσώπου τῷ κύκλῳ τῆς σελήνης Perseus (Plutarch. Plutarchi Chaeronensis Moralia, Vol. V. Vernardakēs, Grēgorios N., editor. Leipzig: Teubner, 1893.) — 17 focus

[17] ὑπολαβὼν δʼ ὁ Σύλλας ἀμέλει ταῦτʼ εἶπεν 929f ἔχει τινὰς πιθανότητας· ὃ, δʼ ἰσχυρότατόν ἐστι τῶν 10 ἀντιπιπτόντων, πότερον ἔτυχέ τινος παραμυθίας ἢ παρῆλθεν ἡμῶν τὸν ἑταῖρον; τί τοῦτο λέγεις ἔφη ὁ Λεύκιος ἢ τὸ πρὸς τὴν διχότομον ἀπορούμενον; πάνυ μὲν οὖν ὁ Σύλλας εἶπεν· ἔχει γάρ τινα λόγον τό, πάσης ἐν ἴσαις γωνίαις γιγνομένης ἀνακλάσεως, 15 ὅταν ἡ σελήνη διχότομος οὖσα μεσουρανῇ, μὴ φέρεσθαι τὸ φῶς ἐπὶ γῆς ἀπʼ αὐτῆς ἀλλʼ 930a ὀλισθάνειν ἐπέκεινα τῆς γῆς· ὁ γὰρ ἥλιος ἐπὶ τοῦ ὁρίζοντος ὢν ἅπτεται τῇ ἀκτῖνι τῆς σελήνης· διὸ καὶ κλασθεῖσα πρὸς ἴσας ἐπὶ θάτερον ἐκπεσεῖται 20 πέρας καὶ οὐκ ἀφήσει δεῦρο τὴν αὐγήν· ἢ διαστροφὴ μεγάλη καὶ παράλλαξις ἔσται τῆς γωνίας, ὅπερ ἀδύνατόν ἐστιν. ἀλλὰ νὴ Δίʼ εἶπεν ὁ Λεύκιος καὶ τοῦτʼ ἐρρήθη καὶ πρός γε Μενέλαον ἀποβλέψας ἐν τῷ διαλέγεσθαι τὸν μαθηματικὸν 25 αἰσχύνομαι μέν ἔφη σοῦ παρόντος, ὦ φίλε Μενέλαε, θέσιν ἀναιρεῖν μαθηματικήν, ὥσπερ θεμέλιον τοῖς κατοπτρικοῖς ὑποκειμένην πράγμασιν· ἀνάγκη δʼ εἰπεῖν ὅτι τὸ πρὸς τὰς ἴσας γίγνεσθαι γωνίας ἀνάκλασιν πᾶσαν, οὔτε φαινόμενον αὐτόθεν οὔθʼ 930b ὁμολογούμενόν ἐστιν· ἀλλὰ διαβάλλεται μὲν· ἐπὶ 5 τῶν κυρτῶν κατόπτρων, ὅταν ἐμφάσεις ποιῇ μείζονας ἑαυτῶν πρὸς ἓν τὸ τῆς ὄψεως σημεῖον, διαβάλλεται δὲ τοῖς διπτύχοις κατόπτροις, ὧν ἐπικλιθέντων πρὸς ἄλληλα καὶ γωνίας ἐντὸς γενομένης, ἑκάτερον τῶν ἐπιπέδων. διττὴν ἔμφασιν ἀποδίδωσι 10 καὶ ποιεῖ τέτταρας εἰκόνας ἀφʼ ἑνὸς προσώπου, δύο μὲν ἀντιστρόφους ἐν τοῖς ἔξωθεν, μέρεσι, δύο δὲ δεξιοφανεῖς ἀμαυρὰς ἐν βάθει τῶν κατόπτρων. ὧν 930c τῆς γενέσεως τὴν αἰτίαν Πλάτων ἀποδίδωσιν. εἴρηκε γὰρ ὅτι, τοῦ κατόπτρου ἔνθεν καὶ ἔνθεν ὕψος λαβόντος, 15 ὑπαλλάττουσιν αἱ ὄψεις τὴν ἀνάκλασιν ἀπὸ τῶν ἑτέρων ἐπὶ θάτερα μεταπίπτουσαν. εἴπερ οὖν τῶν ὄψεων αἱ μὲν εὐθὺς πρὸς ἡμᾶς ἀνατρέχουσιν, αἱ δʼ ἐπὶ θάτερα μέρη τῶν κατόπτρων ὀλισθάνουσαι πάλιν ἐκεῖθεν ἀναφέρονται πρὸς ἡμᾶς, οὐ δυνατὸν 20 ἐστιν ἐν ἴσαις γωνίαις γίγνεσθαι πάσας ἀνακλάσεις, ὅσας ὁμόσε χωρ οῦντες ἀξιοῦσιν αὑτοῖς τοῖς ἀπὸ τῆς σελήνης. ἐπὶ γῆν φερομένοις ῥεύμασι τὴν ἰσότητα 930d τῶν γωνιῶν ἀναιρεῖν, πολλῷ τοῦτʼ ἐκείνου πιθανώτερον εἶναι νομίζοντες. οὐ μὴν ἀλλʼ εἰ δεῖ τοῦτο χαρίζεσθαι τῇ πολλὰ δὴ. φίλῃ γεωμετρίᾳ καὶ 5 δοῦναι, πρῶτον μὲν ἀπὸ τῶν ἠκριβωμένων ταῖς λειότησι συμπίπτειν ἐσόπτρων εἰκός ἐστιν· ἡ δὲ σελήνη πολλὰς ἀνωμαλίας ἔχει καὶ τραχύτητας, ὥστε τὰς αὐγὰς ἀπὸ σώματος μεγάλου προσφερομένας ὕψεσιν ἀξιολόγοις, ἀντιλάμψεις καὶ διαδόσεις ἀπʼ 10 ἀλλήλων λαμβάνουσιν, ἀνακλᾶσθαί τε παντοδαπῶς καὶ περιπλέκεσθαι καὶ συνάπτειν αὐτὴν ἑαυτῇ τὴν, ἀνταύγειαν, οἷον ἀπὸ πολλῶν φερομένην πρὸς ἡμᾶς 930e κατόπτρων. ἔπειτα κἂν πρὸς αὐτῇ τῇ σελήνῃ τὰς ἀντανακλάσεις ἐν ἴσαις γωνίαις ποιῶμεν, οὐκ ἀδύνατον 15 φερομένας ἐν διαστήματι τοσούτῳ τὰς αὐγὰς κλάσεις ἴσχειν καὶ περιολισθήσεις, ὡς συγχεῖσθαι καὶ λάμπειν τὸ φῶς. ἔνιοι δὲ καὶ δεικνύουσι γράφοντες, ὅτι πολλὰ τῶν φώτων αὐγὴν ἀφίησι κατὰ γραμμὴν ὑπὸ τὴν κεκλιμένην ὑποταθεῖσαν· σκευωρεῖσθαι 20 δʼ ἅμα λέγοντι, διάγραμμα, καὶ ταῦτα πρὸς πολλούς, οὐκ ἐνῆν.

Translations (1)

Of the Face Appearing Within the Orb Of the Moon Perseus (Plutarch. Plutarch's Morals, Vol. V. Goodwin, William W., editor; G., A., translator. Boston: Little, Brown, and Company; Cambridge: Press of John Wilson and Son, 1874.) — 17 focus

[17] Sylla then, taking up the discourse, said: There is indeed a great deal of probability in all that you have spoken. But as to the strongest objection that is brought against it, has it, think you, been any way weakened by this discourse? Or has our friend quite passed it over in silence?

What opposition do you mean, said Lucius? Is it the difficulty about the moon, when one half of her appears enlightened?

The very same, answered Sylla. For there is some reason, seeing that all reflection is made by equal angles, that when the half-moon is in the midst of heaven, the light proceeding from her should not be carried upon the earth, but glance and fall beyond and on one side of it. For the sun, being placed in the horizon, touches the moon with its beams; which, being equally reflected, will therefore necessarily fall on the other bound of the horizon, and not send their light down hither; or else there will be a great distortion and difference of the angle, which is impossible.

And yet, by Jupiter, replied Lucius, this has not been forgotten or overpassed, but already spoken to. And casting his eye, as he was discoursing, upon the mathematician Menelaus; I am ashamed, said he, in your presence, dear Menelaus, to attempt the subverting and overthrowing of a mathematical position, which is supposed as a basis and foundation to the doctrine of the catoptrics concerning the causes and reasons of mirrors. And yet of necessity I must. For it neither appears of itself nor is confessed as true, that all reflections are at equal angles; but this position is first checked and contradicted in concave mirrors, when they represent the images of things, appearing at one point of sight, greater than the things themselves. And it is also disproved by double mirrors, which being inclined or turned one towards the other, so that an angle is made within, each of the glasses or plain superficies yields a double resemblance; so that there are four images from the same face, two answerable to the object without on the left side, and two others obscure and not so evident on the right side in the bottom of the mirror. Of which Plato renders the efficient cause; for he says, that a mirror being raised on the one and the other side, the sight varies the reflection, falling from one side to the other. And therefore, since of the views or visions some immediately have recourse to us, and others, sliding to opposite parts of the mirror, do again return upon us from thence, it is not possible that all reflections should be made at equal angles. Though those who closely impugn our opinion contend that, by these reflections of light from the moon upon the earth, the equality of angles is taken away, thinking this to be much more probable than the other.

Nevertheless, if we must of necessity yield and grant thus much to our dearly beloved geometry, first, this should in all likelihood befall those mirrors which are perfectly smooth and exquisitely polished; whereas the moon has many inequalities and roughnesses, so that the rays proceeding from a vast body, and carried to mighty altitudes, receive one from another and intercommunicate their lights, which, being sent to and fro and reciprocally distributed, are refracted and interlaced all manner of ways, and the counter-lights meet one another, as if they came to us from several mirrors. And then, though we should suppose these reflections on the superficies of the moon to be made at equal angles, yet it is not impossible that the rays, coming down unto us by so long an interval, may have their flexions, fractions, and delapsions, that the light being compounded may shine the more. Some also there are who prove by lineary demonstration, that many lights send a ray down by a line drawn below the line of reflection; but to make the description and delineation of it publicly, especially where there were many auditors, would not be very easy.

Notes on the current edition

Concerning the Face which Appears in the Orb Of the Moon

1. See 929 B and note a on p. 48 supra.

2. This expression is intended to have the same sense as πρὸς ἴσας γίγνεσθαι γωνίας ἀνάκλασιν πᾶσαν (930 A s.v.), and both of them mean ( pace Raingeard, p. 100, and Kepler in note 28 to his translation) the angle of reflection is always equal to the angle of incidence. cf. [Euclid], Catoptrica aà (= Euclid, Opera Omnia, vii, p. 286. 21-22 [Heiberg]) with Olympiodorus, In Meteor. p. 212. 7 = Hero Alexandrinus, Opera, ii. 1, p. 368. 5 (Nix-Schmidt) and [Ptolemy], Speculis, ii = Hero Alexandrinus, Opera, ii. 1, p. 320. 12-13 (Nix-Schmidt); and contrast the more precise formulation of Philoponus, In Meteor. p. 27. 34-35.

3. Kepler in note 19 to his translation points out that this is true only if μεσουρανῇ is in mid-heaven refers not to the meridian but to the great circle at right-angles to the ecliptic.

4. Cleomedes, ii. 4. 103 (p. 186. 7-14 [Ziegler]) introduces as σχεδὸν γνώριμον his summary of this argument against the theory that moonlight is merely reflected sunlight.

5. See note e on 929 F supra.

6. It has been suggested that οὔθ’ ὁμολογούμενον is a direct denial of ὡμολογηένον ἐστι παρὰ πᾶσιν at the beginning of Hero’s demonstration (Schmidt in Hero Alexandrinus, Opera [ed. Nix-Schmidt], ii. 1, p. 314. However that may be, the law is assumed in Proposition XIX of Euclid’s Optics, where it is said to have been stated in the Catoptrics (Euclid, Opera Omnia, vii, p. 30. 1-3 [Heiberg]); and a demonstration of it is ascribed to Archimedes ( Scholia in Catoptrica, 7 = Euclid, Opera Omnia, vii, p. 348. 17-22 [Heiberg]; cf. Lejeune, Isis, xxxviii [1947], pp. 51 ff.). It is assumed by Aristotle in Meteorology, iii. 3-5 and possibly also by Plato ( cf. Cornford, Platos Cosmology, pp. 154 f. on Timaeus, 46 B); cf. also Lucretius, iv. 322-323 and [Aristotle], Problemata, 901 B 21-22 and 915 B 30-35. Proposition XIX of Euclids Optics, referred to above, is supposed to be part of the Dioptrics of Euclid which Plutarch cites at Non Posse Suaviter Vivi, 1093 E ( cf. Schmidt, Op. cit. p. 304).

7. i.e. cylindrical, not spherical, convex mirrors; cf. Class. Phil. xlvi (1951), pp. 142-143 for the construction and meaning of this sentence.

8. For such mirrors cf. [Ptolemy], Speculis, xii = Hero Alexandrinus, Opera, ii. 1, p. 342. 7 ff.

9. Plutarch means Timaeus, 46 B - C, where Plato, however, describes a concave, cylindrical mirror, not a folding plane mirror. Plutarch apparently mistook the words ἔνθεν καὶ ἔνθεν ὕξη λαβoῦσα, by which Plato describes the horizontal curvature of the mirror, to mean that the two planes of a folding mirror were raised to form an angle at the hinge which joined them.

10. See note e on 929 F supra.

11. i.e. the theory that the angle of reflection is always equal to the angle of incidence.

12. With these words Plutarch means to refer to the effects of refraction; cf. Placitis, 894 C = Aëtius, iii. 5. 5 ( Dox. Graeci, p. 372. 21-26); Cleomedes, ii. 6. 124-125 (p. 224. 8-28 [Ziegler]); Alexander, In Meteor. p. 143. 7-10.

13. cf. the argument given by Cleomedes, ii. 4. 103 (pp. 186. 14-188.7 [Ziegler]) and especially: ὅτι δ᾽ ἀπὸ παντὸς τοῦ κύκλου αὐτῆς φωτίζεται ἡ γῆ, γνώριμον. εὐθέως γὰρ ἅμα τῷ τὴν πρώτην ἴτυν ἀνασχεῖν ἐκ τοῦ ὁρίζοντος φωτίζει τὴν γῆν, τούτων τῶν μερῶν αὐτῆς περικλινῶν ὄντων καὶ πρός τὸν οὐρανόν, ἀλλ᾽οὐχί, μὰ Δία, πρὸς τὴν γῆν ὁρώντων For ἡ ἐκκεκλιμένη cf. Hippocrates, Art. 38 (iv, p. 168. 18 [Littrè]).

Plutarch De Facie Quae in orbe Lunae Apparet 17

Harold Cherniss (Translator), William C. Helmbold (Translator)

Search the Perseus Catalog for:

Current edition Perseus

Notes on the current edition

Stable identifiers