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Archimedes · Fragments §2.1

Atmospheric Refraction and Apparent Size of Stars

Passage 4 of 4 · Greek

Summary

Theon explains Ptolemy's view that the apparent enlargement of stars near the horizon is caused not by physical distance but by atmospheric refraction through humid air, citing Archimedes' Catoptrics to provide geometrical and physical evidence.

§2.1## Theon d᾿ Alexandrie, Comm. sur l᾿ Almageste, livre I, chap. 3, dans Comment. de Pappus et de Theon d᾿ Alexandrie sur I᾿ Almageste, ed. A. Rome, Studi e Τesti 72, p. 346, 347. ἵνα μὴ νομισθῇ ὅτι ὡς ἐξ ἐλάττονος δῆθεν διαστάσεως ὁρώμενα οὕτω φαίνεται (sc. μείζονα τὰ ἄστρα πρὸς αὐτοῖς τοῖς ὁρίζουσι), βούλεται (sc. ὁ Πτολεμαῖος) ἐνταῦθα τὸ τοιοῦτον ἐπιλύσασθαι καὶ δηλῶσαι ὅτι οὐ παρὰ τὸ ἀπόστημα τὸ ἀπὸ τῆς γῆς ἐπὶ τὸν οὐρανὸν τὸ τοιοῦτον συμβαίνει, ἀλλ᾿ ἐκ τῆς περὶ τὴν γῆν γινομένης ὑγροτάτης ἀναθυμιάσεως καὶ διὰ τοῦτο τῆς ὄψεως εἰς ἀχλυωδέστερον ἀέρα ἐμπιπτούσης καὶ τῶν ἀπ᾿ αὐτῆς ἐπὶ τὸν ἀέρα προσπιπτουσῶν ἀκτίνων κλάσιν ὑπομενουσῶν καὶ μείζονα ποιουσῶν τὴν πρὸς τῇ ὄψει γωνίαν, καθὰ καὶ Ἀρχιμήδης ἐν τοῖς Περὶ κατοπτρικῶν ἀπὲδειξεν.
In order that it may not be thought that (stars near the horizon itself appear larger) in this way, appearing as if seen from a shorter distance, Ptolemy wishes to resolve such a problem here and to show that such a thing does not happen because of the distance from the earth to the heaven, but from the very humid exhalation arising around the earth, and because of this, the sight falling into a mistier air and the rays falling from it onto the air undergoing refraction and making the angle at the eye larger, just as Archimedes also demonstrated in his Catoptrics.
φησὶν ὅτι 1 καὶ τὰ εἰς ὕδωρ ἐμβαλλόμενα μείζονα φαίνεται, καὶ ὅσῳ κάτω χωρεῖ, μείζονα καὶ κεκλάσθωσαν ἐπὶ τὰ Α, Β, ὡς αἱ ΕΘΑ, ΕΚΒ, καθὰ καὶ Ἀρχιμήδης ἐν τοῖς Περὶ κατοπτρικῶν, ὡς ἔφαμεν.
He says that things cast into water also appear larger, and the further down they go, the larger they appear. And let them be refracted towards A and B, like ETA and EKB, just as Archimedes did in his Catoptrics, as we said.

Notes

  1. §2.1παρὰ τὸ ἀπόστημα — The preposition παρά with the accusative here expresses cause or reason ('because of', 'on account of'), rather than its spatial sense ('along' or 'beyond'). It denies that the apparent enlargement of celestial bodies near the horizon is due to the physical distance from the earth to the heavens.
  2. §2.1τῆς ὄψεως ... ἐμπιπτούσης — These are genitive absolute constructions (τῆς ὄψεως... ἐμπιπτούσης and τῶν... ἀκτίνων... ὑπομενουσῶν καὶ... ποιουσῶν) explaining the physical and meteorological cause of the refraction. Linked by καὶ διὰ τοῦτο ('and because of this'), they function as causal adverbial clauses coordinated with the preceding prepositional phrase of cause ἐκ τῆς... ἀναθυμιάσεως.
  3. §2.1κεκλάσθωσαν — Third-person plural perfect imperative passive of the verb κλάω. It is used in mathematical and scientific prose to set up a geometrical assumption or construction ('let them be refracted').

Cite this passage

Archimedes, Fragments §2.1. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0552.tlg013.humanitext-grc1:2.1

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