Bibliotheca Polyglotta

Euclid: Elementa

Τὰ ἀπὸ τῶν μήκει συμμέτρων εὐθειῶν τετράγωνα πρὸς ἄλληλα λόγον ἔχει, ὃν τετράγωνος ἀριθμὸς πρὸς τετράγωνον ἀριθμόν: καὶ τὰ τετράγωνα τὰ πρὸς ἄλληλα λόγον ἔχοντα, ὃν τετράγωνος ἀριθμὸς πρὸς τετράγωνον ἀριθμόν, καὶ τὰς πλευρὰς ἕξει μήκει συμμέτρους. τὰ δὲ ἀπὸ τῶν μήκει ἀσυμμέτρων εὐθειῶν τετράγωνα πρὸς ἄλληλα λόγον οὐκ ἔχει, ὅνπερ τετράγωνος ἀριθμὸς πρὸς τετράγωνον ἀριθμόν: καὶ τὰ τετράγωνα τὰ πρὸς ἄλληλα λόγον μὴ ἔχοντα, ὃν τετράγωνος ἀριθμὸς πρὸς τετράγωνον ἀριθμόν, οὐδὲ τὰς πλευρὰς ἕξει μήκει συμμέτρους.

eng

The squares on straight lines commensurable in length have to one another the ratio which a square number has to a square number; and squares which have to one another the ratio which a square number has to a square number will also have their sides commensurable in length. But the squares on straight lines incommensurable in length have not to one another the ratio which a square number has to a square number; and squares which have not to one another the ratio which a square number has to a square number will not have their sides commensurable in length either.

lat Sic

Duo a longitudine commensurabilibus rectis tetragona ad se invicem proportionem habent quam tetragonus numerus ad tetragonurn numerum. Et tetragona proportionem habentia quam tetragonus numerus ad tetragonum numerum et latera habebunt longitudine commensurabilia. Que vero a longitudine incommensurabilibus rectis tetragona ad se invicem proportionem non habent Quam tetragonus numerus ad tetragonurn numerum. Et tetragona ad se invicem proportionem non habentia quam tetragonus numerus ad tetragonum numerum neque latera habebunt (longitudine) commensurabilia.

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