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Euclid: Elementa

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gre VI,31
ὅπερ ἔδει δεῖξαι.
Pic2627
eng
Q. E. D.
lat Sic
Quod oportebat ostendere.
Aliter. Quoniam similes figure in dupla proportione sunt omologorum laterum, figura ergo que a recta BG ad figuram que a recta BA duplam proportionem habet quam recta GB ad BA. Habet autem et quod a recta BG tetragonum ad illud quod a recta BA tetragonum duplam proportionem quam recta BG ad BA. Et sicut ergo figura que a recta GB ad figuram que a recta BA ita quod a recta GB tetragonum ad illud quod a recta BA tetragonum. Propter eadem ergo et sicut figura que a recta BG ad figuram que a recta GA ita quod a recta BG tetragonum ad illud quod a recta GA tetragonum. Quare et sicut figura que a recta BG ad figuras que a rectis BA, AG ita quod a recta BG tetragonum ad ea que a rectis BA, AG tetragona. Equale vero et quod a recta BG tetragonum eis que a rectis BA, AG tetragonis. Equalis ergo et figura que a recta BG figuris que a rectis BA, AG similibus et similiter scriptis.
lat Gerard
No Latin
lat Adelard
No Latin
lat Hermann
No Latin
ara Uppsala
No Arabic
ara Tuṣi
No Arabic
ara Nairizi
No Arabic
san
No Sanskrit
lat Clavius
No Latin
kin 幾何原本
No Chinese
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