§8## η΄.
## 8.
Τὰ ὕψη καὶ τὰ βάθη ἀπὸ τῶν κυρτῶν ἐνόπτρων ἀνεστραμμένα φαίνεται.
Heights and depths appear inverted by convex mirrors.
ἔστω ὕψος τὸ ΑΕ, ἔνοπτρον δὲ κυρτὸν τὸ Α∠Γ, ὄψεις δὲ αἱ Β∠, Β ἀνακλώμεναι ἐπὶ τὰ Ε, Θ. δέδεικται, ὅτι οὐ συμπεσοῦνται.
Let the height be AE, the convex mirror ADG, and the reflected visual rays BD, B towards E, Th. It has been shown that they do not meet.
τὰ δὲ λοιπὰ ὁμοίως τοῖς ἐν τοῖς ἐπιπέδοις.
The rest is similar to the case of plane mirrors.
ἔστω πάλιν βάθος τὸ ΑΕ, ἔνοπτρον δὲ κυρτὸν τὸ ΑΓ, ὄμμα δὲ τὸ Β, ὄψεις δὲ ἀνακλώμεναι ἐπὶ τὰ Ε, Θ αἱ ΒΓΕ, Β∠Θ. τὰ δὲ λοιπὰ καθάπερ ἐν τοῖς ἐπιπέδοις.
Let again the depth be AE, the convex mirror AC, the eye B, and the reflected visual rays BGE, BDT towards E, Th. The rest is just as in the case of plane mirrors.
§9## θ΄.
## 9.
Τὰ πλάγια μήκη ἀπὸ τῶν ἐπιπέδων ἐνόπτρων, ὡς τῇ ἀληθείᾳ ἔχει, οὕτω καὶ φαίνεται.
Oblique widths appear by plane mirrors as they are in reality.
ἔστω ὄμμα τὸ Β, μῆκος δὲ πλάγιον τὸ ∠Ε, ἔνοπτρον δὲ τὸ ΑΓ. οὐκοῦν ἀνακλασθεισῶν τῶν ὄψεων φαίνεται τὸ μὲν ∠ ἐπὶ τὸ Α, τὸ δὲ Ε ἐπὶ τὸ Γ, καί ἐστιν οὕτω τῇ φαντασίᾳ, καθάπερ καὶ τῇ ἀληθείᾳ ἔχει, τὸ ἔγγιον ἔγγιον, τὸ ἀπώτερον ἀπώτερον.
Let the eye be B, the oblique width DE, and the mirror AC. Therefore, when the visual rays are reflected, D appears on A, and E on C, and it is in the appearance as it is in reality, the nearer appears nearer, and the further further.
§10## ι΄.
## 10.
Τὰ πλάγια μήκη ἀπὸ τῶν κυρτῶν ἐνόπτρων, καθάπερ ἐστὶν ἀληθῶς, καὶ φαίνεται.
Oblique widths appear by convex mirrors as they truly are.
ἔστω μῆκος τὸ Ε∠, ὄμμα δὲ τὸ Β, ἔνοπτρον δὲ κυρτὸν τὸ ΑΓ, ὄψεις δὲ ἀνακλώμεναι ἐπὶ τὰ Ε, ∠.
Let the length be ED, the eye B, the convex mirror AC, and the reflected visual rays towards E, D.
τὰ δὲ ἄλλα τὰ αὐτά.
The other things are the same.
§11## ια΄.
## 11.
Τὰ ὕψη καὶ τὰ βάθη ἀπὸ τῶν κοίλων ἐνόπτρων, ὅσα μέν ἐστιν ἐντὸς τῆς συμπτώσεως τῶν ὄψεων, ἀνεστραμμένα φαίνεται καθάπερ ἐν τοῖς ἐπιπέδοις καὶ κυρτοῖς ἐνόπτροις, ὅσα δέ ἐστιν ἐκτὸς τῆς συμπτώσεως, καθάπερ ἔστιν, καὶ φαίνεται.
Heights and depths by concave mirrors, such as are inside the meeting of the visual rays, appear inverted just as in plane and convex mirrors, but such as are outside the meeting, appear as they are.
ἔστω κοῖλον ἔνοπτρον τὸ ΑΓ, ὄμμα δὲ τὸ Β, ὄψεις δὲ ἀνακλώμεναι αἱ ΒΑ, ΒΓ, σύμπτωσις δὲ αὐτῶν ἐπὶ τὸ Ζ, ὕψη δὲ τό τε ∠Ε καὶ τὸ ΚΝ, καὶ τὸ μὲν ΚΝ ἐντὸς τῆς τοῦ Ζ συμπτώσεως, τὸ δὲ ∠Ε ἐκτὸς τῆς συμπτώσεως.
Let the concave mirror be AC, the eye B, and the reflected visual rays BA, BC, and their meeting be at Z, and the heights be DE and KN, and KN is inside the meeting of Z, and DE is outside the meeting.
οὐκοῦν ἐκβληθεισῶν τῶν ὄψεων καθάπερ ἐν τοῖς ἐπιπέδοις καὶ κυρτοῖς ἐνόπτροις φαίνεται τὸ μὲν Κ ἐπὶ τοῦ Μ, τὸ δὲ Ν ἐπὶ τοῦ Λ ὥστε ἀνεστραμμένα φαίνεται.
Therefore, when the visual rays are extended, just as in plane and convex mirrors, K appears on M, and N on L, so that they appear inverted.
πάλιν ἐπὶ τοῦ ἐκτὸς τῆς συμπτώσεως ὕψους φαίνεται τὸ μὲν ∠ ἐπὶ τοῦ Η, τὸ δὲ Ε ἐπὶ τοῦ Θ, ὡς ἔχει, οὕτως φαίνεται.
Again, in the case of the height outside the meeting, D appears on H, and E on Th; they appear as they are.
πάλιν βάθος μὲν τὸ ∠Ε καὶ ΚΘ, ἔνοπτρον δὲ κοῖλον τὸ ΑΓ, ὄμμα δὲ τὸ Β, ὄψεις δὲ ἀνακλώμεναι καὶ συμπίπτουσαι κατὰ τὸ Ζ. οὐκοῦν ἐκβληθεισῶν τῶν ὄψεων ὁμοίως τὰ μὲν Κ, Θ φαίνεται ἀνεστραμμένα, τὸ μὲν Κ κατὰ τὸ Γ, τὸ δὲ Θ κατὰ τὸ Α, καθάπερ ἐν τοῖς ἐπιπέδοις καὶ κυρτοῖς ἐνόπτροις, τὰ δὲ ∠, Ε, καθάπερ καὶ ἔστιν, τὸ μὲν Ε κάτω κατὰ τὸ Α, τὸ δὲ ∠ ἄνω κατὰ τὸ Γ.
Again, let the depth be DE and KTh, the concave mirror AC, the eye B, and the visual rays being reflected and meeting at Z. Therefore, when the visual rays are extended, similarly, K, Th appear inverted, K towards C, and Th towards A, just as in plane and convex mirrors; but D, E appear just as they are, E below towards A, and D above towards C.
§12## ιβ΄.
## 12.
Τὰ πλάγια μήκη ἀπὸ τῶν κοίλων ἐνόπτρων, ὅσα μὲν ἐντὸς τῆς συμπτώσεως κεῖται τῶν ὄψεων, καθάπερ ἔστιν, οὕτω καὶ φαίνεται, ὅσα δʼ ἐκτός, ἀντεστραμμένα.
Oblique widths by concave mirrors, as many as lie inside the meeting of the visual rays, appear as they are, but as many as are outside, inverted.
ἔστω γὰρ μήκη μὲν πλάγια τὰ Ε∠, ΘΚ, κοῖλον δὲ ἔνοπτρον τὸ ΑΓ, ὄμμα δὲ τὸ Β, ὄψεις δὲ ἀνακλώμεναι καὶ συμπίπτουσαι κατὰ Η τὸ αἱ ΒΑ∠, ΒΓΕ, καὶ τὸ μὲν ΘΚ πλάγιον μῆκος ἔστω ἐντὸς τῆς συμπτώσεως τῆς Η, τὸ δὲ ∠Ε ἐκτός.
For let the oblique widths be ED, ThK, the concave mirror AC, the eye B, and the visual rays being reflected and meeting at H be BAD, BGE, and let the oblique width ThK be inside the meeting of H, and DE outside.
οὐκοῦν τὰ μὲν Θ, Κ κατὰ φύσιν φαίνεται, καθάπερ ἐν τοῖς ἐπιπέδοις καὶ κυρτοῖς ἐνόπτροις, τὰ δὲ Ε, ∠ ἀντεστραμμένα· τὸ μὲν γὰρ ∠ ἐπὶ τοῦ Α φαίνεται, τὸ δὲ Ε ἐπὶ τοῦ Γ.
Therefore, Th, K appear according to nature, just as in plane and convex mirrors, but E, D inverted; for D appears on A, and E on C.