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Euclid: Elementa

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Click to Expand/Collapse OptionTitle
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Click to Expand/Collapse OptionBook I
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gre IΙ,1
Ἐὰν ὦσι δύο εὐθεῖαι, τμηθῇ δὲ ἡ ἑτέρα αὐτῶν εἰς ὁσαδηποτοῦν τμήματα, τὸ περιεχόμενον ὀρθογώνιον ὑπὸ τῶν δύο εὐθειῶν ἴσον ἐστὶ τοῖς ὑπό τε τῆς ἀτμήτου καὶ ἑκάστου τῶν τμημάτων περιεχομένοις ὀρθογωνίοις.1
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1. a(b+c+d+...)=ab+ac+ad+...
eng
If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments.
lat Sic
Si fuerint due recte, dividatur autem altera ipsarum in quotlibet portiones, quod sub eis duabus rectis orthogonium continetur equale est eis que et sub indivisa et unaquaque portionum continetur orthogoniis.
lat Gerard
Si fuerint due recte linee quarum una in partes sit divisa quotcumque fuerint, superficies rectorum angulorum que comprehenditur ab his duabus rectis lineis equalis est superficiebus rectorum angulorum que a linea non divisa et ab unaquaque parte linee divise comprehenduntur.
lat Adelard
Si fuerint due linee quarum una in quotlibet partes dividatur, erit illud quod ex ductu unius in aliam fiet sicut illud quod ex ductu linee indivise in omnes partes linee particulatim divise.
lat Hermann
Si de duabus lineis altera in quotlibet partes divisa fuerit, illud quod ex ductu alterius in alteram fiet, equum est eis, que ex ductu linee indivise in omnes partes eius, que divisa est, producuntur.
ara Uppsala
No Arabic
ara Tuṣi p. 38
سطح الخط فى خط آخر يساوى جميع سطوحه فى اقسام ذلك الخط *
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ara Nairizi p. 6
 كل خطين مستقيمين يقسم احدهما باقسام كم كانت فان السطح الذى يحيط به الخطان مساو لجماعة السطوح التى يحيط بها الخط الذى لم يقسم وكل واحد من اقسام الخط الاخر المقسوم
san 79,5-6
tatraikarekhādvitītarekhāghātaḥ prathamarekhāyā dvitīyarekhākhaṇḍānāṃ ca ghātena tulyaḥ syāt |
lat Clavius
SI fuerint duæ rectæ lineæ, seceturque ipsarum altera in quotcunque segmenta: Rectangulum comprehensum sub illis duabus rectis lineis, æquale est eis, quæ sub insecta, & quolibet segmentorum comprehenduntur, rectangulis.
kin 幾何原本 p. 85
兩直線。任以一線、任分為若干分。其兩元線矩內直角形。與不分線、偕諸分線、矩內諸直角形幷、等。
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