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Euclid: Elementa

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Click to Expand/Collapse OptionTitle
Click to Expand/Collapse OptionPreface
Click to Expand/Collapse OptionBook I
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gre IΙ,8
Ἐὰν εὐθεῖα γραμμὴ τμηθῇ, ὡς ἔτυχεν, τὸ τετράκις ὑπὸ τῆς ὅλης καὶ ἑνὸς τῶν τμημάτων περιεχόμενον ὀρθογώνιον μετὰ τοῦ ἀπὸ τοῦ λοιποῦ τμήματος τετραγώνου ἴσον ἐστὶ τῷ ἀπό τε τῆς ὅλης καὶ τοῦ εἰρημένου τμήματος ὡς ἀπὸ μιᾶς ἀναγραφέντι τετραγώνῳ.1
Pic622
Pic661
1. 4(a + b)a + b2 = [(a + b) + a]2.
eng
If a straight line be cut at random, four times the rectangle contained by the whole and one of the segments together with the square on the remaining segment is equal to the square described on the whole and the aforesaid segment as on one straight line.
lat Sic
Si recta linea dividatur, ut accidit, quater sub tota er una portionum contentum orthogonium cum eo quod a reliqua portione tetragono equale est a tota et dicta portione ut ab una descripto tetragono.
lat Gerard
Si linea recta quolibet modo in duas separetur sectiones, quadruplum superficiei rectorum angulorum que a tota linea et una ex sectionibus eius cum quadrato facto ex reliqua sectione equale erit quadrato facto ex tota linea et sectione, quam nominavimus, cum una linea posite fuerint.
lat Adelard
No Latin
lat Hermann
No Latin
ara Uppsala
No Arabic
ara Tuṣi p. 41
اربعة امثال سطح الخط فى احد قسميه مع مربع القسم الاخر يساوى مربع يزيد على ذلك الخط بقدر القسم الاول *
ara Nairizi p. 38
كل خط مستقيم مفروض يقسم بقسمين اى قسمة كانت ويزاد فى طوله مثل احد القسمين فان مربع الخط المفروض مع الخط المزيد مساو لاربعة اضعاف السطح الذى يحيط به الخط المفروض والخط المزيد مع مربع القسم الاخر
san
No Sanskrit
lat Clavius
SI recta linea secetur vtcunque: Rectangulum qua- ter comprehensum sub tota, & vno segmentorum, cum eo, quod à reliquo segmento fit, quadrato, æquale est ei, quod a tota, & dicto segmento, tanquam ab vna linea describitur, quadrato.
kin 幾何原本 p. 98
一直線。任兩分之。其元線偕初分線、矩內直角形四、及分餘線上直角方形、幷。與元線偕初分線上直角方形、等。
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