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Euclid: Elementa

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Euclid: Elementa
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gre VΙΙI,13
Ἐὰν ὦσιν ὁσοιδηποτοῦν ἀριθμοὶ ἑξῆς ἀνάλογον, καὶ πολλαπλασιάσας ἕκαστος ἑαυτὸν ποιῇ τινα, οἱ γενόμενοι ἐξ αὐτῶν ἀνάλογον ἔσονται: καὶ ἐὰν οἱ ἐξ ἀρχῆς τοὺς γενομένους πολλαπλασιάσαντες ποιῶσί τινας, καὶ αὐτοὶ ἀνάλογον ἔσονται [καὶ ἀεὶ περὶ τοὺς ἄκρους τοῦτο συμβαίνει].
Pic2682
eng
If there be as many numbers as we please in continued proportion, and each by multiplying itself make some number, the products will be proportional; and, if the original numbers by multiplying the products make certain numbers, the latter will also be proportional.
lat Sic
Si fuerint quotlibet numeri deinceps proportionales et multiplicans unusquisque se ipsum facit aliquem, facti ex ipsis proportionales erunt. Et si qui ex principio factos multiplicantes fecerint aliquos, et ipsi proportionales erunt. Et semper circa extremos hoc accidit.
lat Gerard
No Latin
lat Adelard
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lat Hermann
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ara Uppsala
No Arabic
ara Tuṣi
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ara Nairizi
No Arabic
per Shirazi
.
san
No Sanskrit
lat Clavius
No Latin
kin 幾何原本
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