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Euclid: Elementa

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eng
lat Clavius
SCHOLIUM. QVOD si ex AB, auferenda sit pars non aliquota, sed quae plures aliquotas non efficientes unam complectatur, nimirum quae contineat quatuor undecimas ipsius AB, sumendae erunt ex AC, undecim partes aquales usque ad D, punctum, ex quo ad B recta ducatur DB; et huic parallela EF, ex E, termino quatuor partium. Nam AF, erit pars imperata. Erit enim rursus ut DA, ad AE, ita BA, ad AF. Quare, et convertendo ut AE, ad AD, ita AF, ad AB: Est autem AE, pars continens quatuor undecimas ipsius AD, ex constructione. Igitur et AF, eadem pars erit rectae AB. Quod est propositum. Non aliter detrahetur ex AB, pars complectens quotcunque partes ipsius aliquotas non facientes unam.
Pic3439
kin 幾何原本
注曰。甲乙線。欲截取十一分之四。先作甲丙線、為丙甲乙角。從甲向丙。任平分十一分、至丁。次作丁乙線。末從甲取四分、得戊。作戊己線。與丁乙平行。卽甲己為十一分甲乙之四。何者。依上論、丁甲與戊甲之比例。若乙甲與己甲也。反之。甲戊與甲丁。若甲己與甲乙也。五卷四 甲戊為十一分甲丁之四。則甲己亦十一分甲乙之四矣。依此可推不盡分之數。蓋四不為十一之盡分故。
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