Bibliotheca Polyglotta

Euclid: Elementa

Ἐὰν πρῶτον πρὸς δεύτερον τὸν αὐτὸν ἔχῃ λόγον καὶ τρίτον πρὸς τέταρτον, καὶ τὰ ἰσάκις πολλαπλάσια τοῦ τε πρώτου καὶ τρίτου πρὸς τὰ ἰσάκις πολλαπλάσια τοῦ δευτέρου καὶ τετάρτου καθ᾽ ὁποιονοῦν πολλαπλασιασμὸν τὸν αὐτὸν ἕξει λόγον ληφθέντα κατάλληλα.

eng

If a first magnitude have to a second the same ratio as a third to a fourth, any equimultiples whatever of the first and third will also have the same ratio to any equimultiples whatever of the second and fourth respectively, taken in corresponding order. If A:B=C:D, then mA:nB=mC:nD.

lat Sic

Si primum ad secundum eandem habeat proportionern et tertium ad quartum, et eque multiplicia primi et tertii ad eque multiplicia secundi et quarti secundum quamcumque multiplicationem eandem habebunt proportionem sumpta ad se invicem.

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