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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
Click to Expand/Collapse OptionBook ΙI
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gre IΙ,7
Ἐὰν εὐθεῖα γραμμὴ τμηθῇ, ὡς ἔτυχεν, τὸ ἀπὸ τῆς ὅλης καὶ τὸ ἀφ᾽ ἑνὸς τῶν τμημάτων τὰ συναμφότερα τετράγωνα ἴσα ἐστὶ τῷ τε δὶς ὑπὸ τῆς ὅλης καὶ τοῦ εἰρημένου τμήματος περιεχομένῳ ὀρθογωνίῳ καὶ τῷ ἀπὸ τοῦ λοιποῦ τμήματος τετραγώνῳ.1
Pic621
Pic660
1. (a + b)2 + a2 = 2(a + b)a + b2 = (ΒΓ + ΑΓ)2 + ΒΓ2 = 2(ΒΓ + ΑΓ)ΒΓ + ΑΓ2.
eng
If a straight line be cut at random, the square on the whole and that on one of the segments both together are equal to twice the rectangle contained by the whole and the said segment and the square on the remaining segment.
lat Sic
Si recta linea dividatur, ut accidit, quod a tota et quod ab una portione coutraque tetragona equalia sunt et bis sub tota et dicta portione contento orthogonio et ei quod a reliqua portione tetragono.
lat Gerard
Si linea recta in duas sectiones quolibet modo dividatur, quadratum quod fit ex tota linea et quadratumquod fit ex una divisionum eius, quando con iungentur, duplo superficiei rectorum angulorum quecomprehenditur a tota linea et divisione, quam nominavimus, et quadrato facto ex reliqua divisione equaliaerunt.
lat Adelard
No Latin
lat Hermann
No Latin
ara Uppsala
No Arabic
ara Tuṣi p. 41
مربع الخط مع مربع احد قسميه يساوى مجموع ضعف سطح الخط فى ذلك القسم ومربع القسم الاخر ❊
ara Nairizi p. 32
كل خط مستقيم يقسم بقسمين اى قسمة كانت فان مربع الخط كله مع مربع احد القسمين اذا جمعا مساو لضعف السطح الذى يحيط به الخط كله وذلك القسم مع مربع القسم الاخر اذا جمعا
san
No Sanskrit
lat Clavius
SI recta linea secetur vtcunque; Quod a tota, quodque ab vno segmentorum, vtraque simul quadrata, æqualia sunt & illi, quod bis sub tota, & dicto segmento comprehenditur, rectangulo, & illi, quod a reliquo segmento sit, quadrato.
kin 幾何原本 p. 96
一直線。任兩分之。其元線上、及任用一分線上、兩直角方形、幷。與元線偕一分線、矩內直角形二、及分餘線上直角方形幷、等。
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