Ἆρα τὰ πόρρω φαίνεται ἐλάττω καὶ τὰ πολὺ ἀφεστηκότα ὀλίγον δοκεῖ ἔχειν τὸ μεταξύ, τὰ δὲ ἐγγύθεν ἡλίκα ἐστὶ φαίνεται, καὶ ὅσην ἔχει τὴν ἀπόστασιν; ἐλάττω μὲν δοκεῖ τοῖς ὁρῶσι τὰ πόρρω, ὅτι συναιρεῖσθαι πρὸς τὴν ὄψιν ἐθέλει καὶ πρὸς τὸ μέγεθος τῆς κόρης τὸ φῶς — καὶ ὅσῳ ἂν πόρρω ἡ ὕλη ᾖ τοῦ ὁρωμένου, τόσῳ τὸ εἶδος οἷον μεμονωμένον ἀφικνεῖται καὶ τοῦ πηλίκου εἴδους καὶ αὖ τοῦ ποιοῦ, ὡς τὸν λόγον αὐτοῦ ἀφικνεῖσθαι μόνον· ἢ καί, ὅτι τὸ μὲν μέγεθος ἐν διεξόδῳ καὶ ἐπελεύσει καθ’ ἕκαστον μέρος ὅσον ἐστὶν αἰσθανόμεθα — παρεῖναι οὖν δεῖ αὐτὸ καὶ πλησίον εἶναι, ἵνα γνωσθῇ ὅσον· ἢ καί, ὅτι κατὰ συμβεβηκὸς ὁρᾶται τὸ μέγεθος τοῦ χρώματος πρώτως θεωρουμένου.
Do distant things appear smaller, and things far apart seem to have little space between them, while things near at hand appear as large as they are and with as much distance between them as they actually have? Distant things seem smaller to those who see them because the light tends to be drawn together toward the sight and to the size of the pupil—and the farther away the matter of the thing seen is, the more its form arrives, as it were, isolated, stripped both of the form of size and of quality too, so that only its rational principle arrives. Or else it is because we perceive magnitude, how large it is, by going through it and passing over it part by part—so it must be present and near for its size to be known. Or else it is because magnitude is seen incidentally, color being what is seen primarily.
πλησίον μὲν οὖν ὅσον κέχρωσται γινώσκεται, πόρρω δὲ ὅτι κέχρωσται, τὰ δὲ μέρη κατὰ ποσὸν συνδιαιρούμενα οὐκ ἀκριβῆ δίδωσι τὴν τοῦ ποσοῦ διάγνωσιν· ἐπεὶ καὶ τὰ χρώματα αὐτὰ ἀμυδρὰ προσέρχεται. τί οὖν θαυμαστόν, εἰ καὶ τὰ μεγέθη, ὥσπερ καὶ αἱ φωναί, ἐλάττω, ὅσῳ ἂν τὸ εἶδος αὐτῶν ἀμυδρὸν ἴῃ; εἶδος γὰρ κἀκεῖ ἡ ἀκοὴ ζητεῖ, τὸ δὲ μέγεθος κατὰ συμβεβηκὸς αἰσθάνεται. ἀλλὰ περὶ τῆς ἀκοῆς, εἰ τὸ μέγεθος κατὰ συμβεβηκός· τίνι γὰρ πρώτως τὸ ἐν τῇ φωνῇ μέγεθος, ὥσπερ δοκεῖ τῇ ἁφῇ τὸ ὁρώμενον;
Near at hand, then, we recognize how much is colored; at a distance, only that it is colored. And the parts, distinguished in quantity along with the color, do not give an accurate discernment of the quantity, since the colors themselves too reach us faint. So what wonder is it if magnitudes, like sounds, also become smaller in proportion as their form comes through faint? For there too it is form that hearing seeks; magnitude it perceives incidentally. But as for hearing—is magnitude really perceived incidentally? For to which sense does magnitude in sound belong primarily, in the way visible magnitude seems to belong to touch?
ἢ τὸ δοκοῦν μέγεθος ἡ ἀκοὴ οὐ κατὰ τὸ ποσόν, ἀλλὰ κατὰ τὸ μᾶλλον καὶ ἧττον, οὐ κατὰ συμβεβηκός, οἷον τὸ σφόδρα, ὡς καὶ ἡ γεῦσις τὸ σφόδρα τοῦ γλυκέος κατὰ συμβεβηκός· τὸ δὲ κυρίως μέγεθος φωνῆς τὸ ἐφ’ ὅσον· τοῦτο δὲ κατὰ συμβεβηκὸς ἐκ τοῦ σφόδρα σημήνειεν ἄν, οὐκ ἀκριβῶς δέ. τὸ μὲν γὰρ σφόδρα ἑκάστῳ τὸ αὐτό, τὸ δὲ εἰς πλῆθος εἰς ἅπαντα τὸν τόπον, ὃν ἐπέσχεν.
Or rather: hearing perceives apparent magnitude not by quantity but by more and less, and not incidentally—I mean intensity—just as taste, too, perceives the intensity of sweetness. Magnitude of sound in the strict sense is its extent; and hearing might indicate this incidentally from the intensity, but not accurately. For intensity is the same in each part, whereas magnitude as amount reaches over the whole place the sound has occupied.
ἀλλ’ οὐ σμικρὰ τὰ χρώματα, ἀλλὰ ἀμυδρά, τὰ δὲ μεγέθη σμικρά. ἢ ἐν ἀμφοτέροις κοινὸν τὸ ἧττόν ἐστι. χρῶμα μὲν οὖν τὸ ἧττον ἀμυδρόν, μέγεθος δὲ τὸ ἧττον σμικρόν, καὶ ἑπόμενον τῷ χρώματι τὸ μέγεθος ἀνὰ λόγον ἠλάττωται. σαφέστερον δὲ ἐπὶ τῶν ποικίλων γίνεται τὸ πάθος· οἷον ὀρῶν ἐχόντων πολλὰς οἰκήσεις καὶ δένδρων πλῆθος καὶ ἄλλα πολλά, ὧν ἕκαστον, εἰ μὲν ὁρῷτο, δίδωσιν ἐκ τῶν ὁρωμένων ἑκάστων μετρεῖν τὸ ὅλον· τοῦ δὲ εἴδους καθ’ ἕκαστον οὐκ ἰόντος ἀπεστέρηται τοῦ καθ’ ἕκαστον ὄψις μετροῦσα τὸ ὑποκείμενον μέγεθος τὸ πᾶν ὅσον ἐστὶ γινώσκειν.
But colors are not small, they are faint; whereas magnitudes are small. Or rather, what is common to both is the “less.” In a color, the less is faint; in a magnitude, the less is small; and magnitude, following the color, is diminished proportionally. The effect becomes clearer with things that are varied: for instance, mountains with many dwellings, a multitude of trees and many other things. Each of these, if it were seen, would let us measure the whole from the individual things seen; but when the form does not come through for each one, sight is deprived of the individual items and so of measuring the underlying magnitude and knowing how large the whole is.
ἐπεὶ καὶ τὰ πλησίον, ὅταν ποικίλα ᾖ ἀθρόως τε γίνηται ἡ ἐπιβολὴ πρὸς αὐτὰ καὶ μὴ πάντα τὰ εἴδη ὁρῷτο, ἐλάττω ἂν φανείη κατὰ λόγον, ὅσον ἂν ἕκαστον κλαπῇ ἐν τῇ θέᾳ· ὅταν δὲ πάντα ὀφθῇ, ἀκριβῶς μετρηθέντα ὅσα ἐστὶ γινώσκεται. ὅσα δὲ τῶν μεγεθῶν ὁμοειδῆ ὁμοιόχροα ὄντα, ψεύδεται καὶ ταῦτα τὸ ποσὸς αὐτῆς οὐ κατὰ μέρος πάνυ τι μετρεῖν δυναμένης [τῆς] ὄψεως, ὅτι ἀπολισθάνει κατὰ μέρος μετροῦσα, ὅτι μὴ ἔχει ἵστασθαι καθ’ ἕκαστον μέρος τῇ διαφορᾷ. ἐγγύθεν δὲ τὸ πόρρω, ὅτι [τὸ] μεταξὺ συναιρεῖται ὅσον ἐστὶ κατὰ τὴν αὐτὴν αἰτίαν. τὸ μὲν γὰρ πλησίον ὅσον ἐστὶν οὐ λανθάνει διὰ τὰ αὐτά· οὐ διεξοδεύουσα δὲ τὸ πόρρω τοῦ διαστήματος οἷόν ἐστι κατ’ εἶδος οὐκ ἂν δύναιτο οὐδ’ ὅσον ἐστὶ κατὰ μέγεθος εἰπεῖν.
Things near at hand too, when they are varied and our glance takes them in all at once and not all their forms are seen, would appear smaller in proportion to how much of each was stolen from our view; but when they have all been seen, they are measured accurately and we know how large they are. And magnitudes that are uniform in kind and color also deceive us about their quantity, since sight cannot really measure them part by part: it slips as it measures part by part, because there is no difference at which it can stop at each part. And something far away looks near because the interval between is contracted in its size, for the same reason. For how great what is near is does not escape us, for the same reasons; but sight, not going through the distant part of the interval and what it is like in form, could not say how large it is in magnitude either.
τὸ δὲ κατὰ τὰς τῆς ὄψεως γωνίας ἐλάττους εἴρηται μὲν καὶ ἐν ἄλλοις ὡς οὐκ ἔστι, καὶ νῦν δὲ ἐκεῖνο λεκτέον, ὡς ὁ λέγων ἔλαττον φαίνεσθαι ἐλάττονι γωνίᾳ καταλείπει τὴν ὄψιν ἔξωθέν τι ὁρῶσαν ἢ ἄλλο τι ὂν ἔξωθεν ὅλως, οἷον ἀέρα. ὅταν οὖν μηδὲν καταλείπῃ τῷ πολὺ εἶναι τὸ ὄρος, ἀλλ’ ἢ ἰσάζῃ καὶ μηκέτι ἄλλο οἷόν τε ᾖ αὐτῇ ὁρᾶν, ἅτε τοῦ διαστήματος αὐτῆς συναρμόσαντος τῷ ὁρωμένῳ, ἢ καὶ ὑπερτείνῃ τὸ ὁρώμενον ἐφ’ ἑκάτερα τὴν τῆς ὄψεως προσβολήν, τί ἄν τις ἐνταῦθα λέγοι ἐλάττονος μὲν ἢ ἔστι πολλῷ φαινομένου τοῦ ὑποκειμένου, πάσῃ δὲ τῇ ὄψει ὁρωμένου; εἰ δὲ δὴ καὶ ἐπὶ τοῦ οὐρανοῦ θεωροῖ, ἀναμφισβητήτως μάθοι ἄν τις.
As for the explanation by the smaller angles of sight, it has been said elsewhere too that this is not so; and now we should add this point. Whoever says that a thing appears smaller by a smaller angle leaves the sight seeing something outside the object—something else, which is outside it altogether, like air. So when the mountain, because it is large, leaves nothing over, but either is equal to the sight, so that the sight can no longer see anything else since its span fits exactly to the thing seen, or the thing seen even exceeds the sight’s reach on both sides—what would one say here, when the object appears much smaller than it is and yet is seen with the whole of the sight? And if one looks at the heavens, one would learn this beyond dispute.
πᾶν μὲν γὰρ τὸ ἡμισφαίριον οὐκ ἄν τις ὁρᾶν μιᾷ προσβολῇ δύναιτο, οὐδὲ ἐπὶ τοσοῦτον χυθῆναι ἡ ὄψις μέχρις αὐτοῦ ἐκτεινομένη. ἀλλ’ εἴ τις βούλεται, δεδόσθω. εἰ οὖν πᾶσα μὲν περιέλαβε πᾶν, πολλαπλάσιον δὲ τὸ μέγεθος τοῦ φαινομένου ὑπάρχει ἐν τῷ οὐρανῷ, τοῦ ἔλαττον πολλῷ ἢ ἔστι φαίνεσθαι πῶς ἂν ἐλάττωσιν γωνίας αἰτιῷτο;
No one could see the whole hemisphere in a single glance, nor could sight spread out so far as to extend all the way to it. But if anyone wants, let it be granted. If, then, the whole of sight has taken in the whole, and the magnitude in the heavens is many times greater than the apparent one, how could one blame a narrowing of the angle for its appearing much smaller than it is?