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Euclid: Elementa
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Q. E. D.
lat Clavius
Quod demonstrandum erat.

SCHOLION
QVOD si quis dicat, duas rectas A I, B I, parallelas esse rectæ C D, & tamen ipsas non esse parallelas; Occurrendum est, duas A I, B I, non esse duas lineas, sed partes tantum unius lineæ. Concipiendum enim est animo, quaslibet parallelas infinite esse productas; Constat autem A I, productam coincidere cum B I. Quamobrem quæ eidem rectæ lineæ parallelæ, & inter se sunt parallelæ: vel certe, quando inter se coeunt. Quod ita demonstrabitur. Sint duæ rectæ A B, A C, coeuntes in A, parallelæ ipsi D E. Dico illas in rectum esse constitutas. Ex puncto enim A, ducatur recta A F, secans D E, in F, utcunque. Quoniam igitur A B, D E, sunt parallelæ, erunt anguli alterni B A F, A F E, æquales. Addito ergo communi angulo C A F, erunt duo anguli ad A, æquales duobus angulis C A F, A F E. Sed hi duo æquales sunt duobus rectis, cum sint interni inter duas parallelas A C, D E. Igitur & duo anguli ad A, duobus eruntrectis æquales; ac propterea in rectum erunt constitutæ ipsæ AB, AC. Quod est propositum.
kin 幾何原本
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