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Euclid: Elementa

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Euclid: Elementa
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gre V,19
Πόρισμα
Ἐκ δὴ τούτου φανερόν, ὅτι ἐὰν συγκείμενα μεγέθη ἀνάλογον ᾖ, καὶ ἀναστρέψαντι ἀνάλογον ἔσται:
ὅπερ ἔδει δεῖξαι.
Pic2588
eng
[PORISM.
From this it is manifest that, if magnitudes be proportional componendo, they will also be proportional convertendo.] Q. E. D.
lat Sic
(Porisma)
Ex hoc ergo manifestum quoniam si composite quantitates proportionales fuerint, et convertenti proportionales erunt. Quod oportebat ostendere.
Fiunt autem proportiones et in eque multiplicibus et in proportionalibus quoniam quidem si primum secundi eque fuerit multiplex et tertium quarti, erit et ut primum ad secundum ita tertium ad quartum. Nequaquam vero convertitur. Si fuerit ut primum ad secundum ita tertium ad quartum, non omnino erit et primum quidem secundi eque multiplex, tertium vero quarti quemadmodum in emioliis vel epitritis proportionibus vel talibus. Quod oportet ostendere.
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
No Chinese
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