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Euclid: Elementa

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gre V,33
No Greek
eng
Proposition 33. If a:b>c:d then (a-c):(b-d)>a:b.
lat Sic
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lat Gerard
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lat Adelard
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lat Hermann
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ara Uppsala
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ara Tuṣi
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ara Nairizi
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san
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lat Clavius
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kin 幾何原本 p. 274
第三十三題
此全與彼全之比例。大於此全截分、與彼全截分之比例。則此全分餘、與彼全分餘之比例。大於此全與彼全之比例。
解曰。甲乙全與丙丁全之比例。大於兩截分、甲戊與丙己。題言兩分餘、戊乙與己丁之比例。大於甲乙與丙丁。
論曰。甲乙與丙丁之比例。旣大於甲戊與丙己。更之。卽甲乙與甲戊之比例。亦大於丙丁與丙己也。本篇 \\ 廿七又轉之。甲乙與戊乙之比例。小於丙丁與己丁也。本篇 \\ 三十又更之。甲乙與丙丁之比例。小於戊乙與己丁也。本篇 \\ 廿七戊乙與己丁。分餘也。則分餘之比例。大於甲乙全、與丙丁全矣。依顯兩全之比例。小於截分。則分餘之比例。小於兩全。
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