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Euclid: Elementa
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gre III,1
Πόρισμα
Ἐκ δὴ τούτου φανερόν, ὅτι ἐὰν ἐν κύκλῳ εὐθεῖά τις εὐθεῖάν τινα δίχα καὶ πρὸς ὀρθὰς τέμνῃ, ἐπὶ τῆς τεμνούσης ἐστὶ τὸ κέντρον τοῦ κύκλου:
Pic2512
eng
PORISM
From this it is manifest that, if in a circle a straight line cut a straight line into two equal parts and at right angles, the centre of the circle is on the cutting straight line.
lat Sic
(Porisma) Ex hoc ergo manifestum, quoniam si in circulo recta aliqua rectam aliquam in duo equalia et ad rectos secat, in secante est centrum circuli.
lat Gerard
Corollarium:
Et ex hoc manifestum est quod non est possibile ut sint due linee in circulo quarum una aliam in duo media secet super rectos angulos quin linea que aliam in duo media secat super rectos angulos per centrum transeat circuli.
lat Adelard 47r
Unde datur intelligi quia nulle due linee infra circulum supra angulos rectos sese per media secant nisi ille que per centrum transierint.
lat Hermann 18v
Unde collectum est, quod de duabus rectis lineis in circulo ad circumferentiam terminans neutra alteram per medium ortogonaliter secat nisi per centrum transeat.
ara Uppsala 28v9-10
وقد بين انه لا يكون وتران في دايرة يقطع احدهما ' الآخر بنصفين علي زاوية قايمة الا وهو يجوز علي المركز❊
ara Tuṣi p. 48
وقد تبيـن منه انه لا يتقاطـع وتران على قوائم وينصف احدهمــا الاخر الا ويجوز احدهما بالمركـز وبعبارة اخرى لا يخـرج عمود من منتصف وترا الا ويمر على المركــز
ara Nairizi p. 10
معما قد تبيّن مٍن وجودٍنا لمركز الدائرة قد تبيّن أيضا أن كل وترين يقسم احدهما الآخر بنصفين وعلى زوايا قائمة فإن عليه يكون مركزُ الدائرةٍ
per Shirazi
.
san p. 94
asmād idaṃ niścitaṃ yadi dve pūrṇajye tathā saṃpātaṃ kariṣyato yathā catvāri samakoṇakṣetrāṇi bhaviṣyanti | yady ekā pūrṇajyā dvitīyajyārddhe lagnā bhavati samakoṇakṣetradvayaṃ syāt tad ekā pūrṇajyā kendralagnā syāt | punar etan niścitam ekasyāḥ pūrṇajyāyā arddhān nisṛto lambaḥ kendre saṃpātaṃ karotīti |
lat Clavius p. 100
CORROLARIUM
HINC manifestum est, si in circulo recta aliqua linea aliquam rectam lineam bifariam, et ad angulos rectos secet, in secante esse centrum circuli.
kin 幾何原本 卷三，一
系。因此推顯、圜內有直線。分他線為兩平分、而作直角。卽圜心在其內。
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