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Euclid: Elementa

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Euclid: Elementa
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gre Χ,0
γ῾ Τούτων ὑποκειμένων δείκνυται, ὅτι τῇ προτεθείσῃ εὐθείᾳ ὑπάρχουσιν εὐθεῖαι πλήθει ἄπειροι σύμμετροί τε καὶ ἀσύμμετροι αἱ μὲν μήκει μόνον, αἱ δὲ καὶ δυνάμει. καλείσθω οὖν ἡ μὲν προτεθεῖσα εὐθεῖα ῥητή, καὶ αἱ ταύτῃ σύμμετροι εἴτε μήκει καὶ δυνάμει εἴτε δυνάμει μόνον ῥηταί, αἱ δὲ ταύτῃ ἀσύμμετροι ἄλογοι καλείσθωσαν.
eng
3. With these hypotheses, it is proved that there exist straight lines infinite in multitude which are commensurable and incommensurable respectively, some in length only, and others in square also, with an assigned straight line. Let then the assigned straight line be called rational, and those straight lines which are commensurable with it, whether in length and in square or in square only, rational, but those which are incommensurable with it irrational.
lat Sic
His subiacentibus demonstratur quoniam proposite recte sunt recte multitudine infinite commensurabiles et incommensurabiles, hee quidem longitudine et potentia, hee vero potentia solum. Vocetur ergo proposita quidem recta riti. Et que ipsi commensurabiles sive longitudine et potentia sive potentia solum rite. Que vero eidem incommensurabiles secundum coutrumque [hoc est longitudine et potentia] aloge vocentur.
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ara Uppsala
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ara Tuṣi
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ara Nairizi
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per Shirazi
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san
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lat Clavius
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kin 幾何原本
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