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Euclid: Elementa

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Euclid: Elementa
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eng
For let AE be joined and drawn through to F.
lat Clavius
Includant enim primum duae AB, AC, duas DB, DC; et per centrum D, recta extendatur AE. Quoniam igitur rectae DA, DB, aequales sunt,1 erunt anguli DAB, DBA, aequales: Est autem externus angulus BDE,2 aequalis duobus angulis internis DAB, DBA. Quare BDE, plus erit alterius corum, ut anguli DAB. Eodem modo duplus ostendetur angulus CDE, anguli DAC. Quapropter totus BDC, duplus erit totius BAC. Quando enim duae magnitudines duarum sunt duplae, singulae singularum, est quoque aggregatum ex illis aggregati ex his duplum. Constat ergo propositum.
1. 5. primi. 2. 32. primi.
kin 幾何原本
先論分圜角、在乙甲、甲丙、之內者曰。如上圖。試從甲、過丁心、作甲戊線。其甲丁乙角形之丁甲、丁乙等。卽丁甲乙、丁乙甲、兩角等。一卷四而乙丁戊外角。與內相對兩角幷等。一卷卅二卽乙丁戊、倍大於乙甲丁矣。依顯丙丁戊、亦倍大於丙甲丁。則乙丁丙全角。亦倍大於乙甲丙全角。
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