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Work: 證明論 Viewing: Source

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Reasoning

Digital keyboard

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Source page

數學需證明也，證明需有理也。因果關係，方方面面，皆步步細緻入微，毫無瑕疵矣。

題例

原命題
：三角中若兩腰等，則底線兩端之兩角等，而兩腰引出之其底之外兩角亦等。

解曰
：三角甲乙丙其甲丙與甲乙兩腰等。題言甲丙乙與甲乙丙兩角等又自甲丙線任引之戊甲乙線任引至丁。其乙丙戊與丙乙丁兩外角亦等。

論曰
：試如甲戊線稍長即從甲戊截取一段與甲丁等為甲己，次自丙至丁乙至己各作直線。
即甲己、乙甲、丁丙兩三角形必全等。何者？此兩三角形之甲角同甲己與甲丁兩腰又等，且甲乙與甲丙兩腰又等。則其底邊丙丁與乙己必等而底線兩端相當之各兩角亦等矣。
又，三角乙丙己與三角丙乙丁兩三角亦全等。何者？此兩形之角丙丁乙與角乙己丙既等。 （本論已證）而甲己甲丁兩腰各減相等之，甲丙、甲乙線即所存丙己乙丁兩腰又等（公論三：有多角之度等，若所減之角度等，則所存之度亦等）丙丁與乙己兩底又等（本論已證）。又，乙丙同腰即乙丙丁與丙乙己兩角亦相等也，

則丙之外、乙丙己與乙之外丙乙丁必等矣。

次觀角甲乙己與角甲丙丁兩角既等角甲乙己----角丙乙己、
角甲丙丁----角乙丙丁，則所存角甲丙乙等角甲乙丙（公論3：等量遞減）。故其底之外兩角等（等邊三角其三角俱等）。

引據

歐幾里得
《幾何原本》
徐光啟譯

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Metadata

Work ID: 93998
Document ID: 261293
Title: 證明論
Corpus root: 維基大典
Page title: 證明論
File: 證明論.txt
Path: 維基大典/clean/證明論/證明論.txt

Punctuation options

Preset Source Modern CJK (Traditional) Modern CJK (Simplified / PRC) Pure classical Strip Custom

Quotes

Family

Chinese quotation marks 「」『』 Latin speech marks “ ” ‘ ’ Chinese speech marks ＂＇ Off

Ordering

Traditional: 「甲『乙』丙」 Simplified: 『甲「乙」丙』 Vertical quote forms (﹁﹂﹃﹄)

Question / Exclamation Keep ？ Collapse ? → 。

Keep ！ Collapse ! → 。

Semicolon / Colon Keep ； Collapse ; → 。

Keep ： Collapse : → 。

Comma Use ， Use 、

Repetition mark No repetition mark (default) 々 (Horizontal) 〻 (Vertical) 二 (Western Zhou-style)

數學需證明也，證明需有理也。因果關係，方方面面，皆步步細緻入微，毫無瑕疵矣。題例原命題：三角中若兩腰等，則底線兩端之兩角等，而兩腰引出之其底之外兩角亦等。解曰：三角甲乙丙其甲丙與甲乙兩腰等。題言甲丙乙與甲乙丙兩角等又自甲丙線任引之戊甲乙線任引至丁。其乙丙戊與丙乙丁兩外角亦等。論曰：試如甲戊線稍長即從甲戊截取一段與甲丁等為甲己，次自丙至丁乙至己各作直線。即甲己、乙甲、丁丙兩三角形必全等。何者？此兩三角形之甲角同甲己與甲丁兩腰又等，且甲乙與甲丙兩腰又等。則其底邊丙丁與乙己必等而底線兩端相當之各兩角亦等矣。又，三角乙丙己與三角丙乙丁兩三角亦全等。何者？此兩形之角丙丁乙與角乙己丙既等。（本論已證）而甲己甲丁兩腰各減相等之，甲丙、甲乙線即所存丙己乙丁兩腰又等（公論三：有多角之度等，若所減之角度等，則所存之度亦等）丙丁與乙己兩底又等（本論已證）。又，乙丙同腰即乙丙丁與丙乙己兩角亦相等也，則丙之外、乙丙己與乙之外丙乙丁必等矣。次觀角甲乙己與角甲丙丁兩角既等角甲乙己----角丙乙己、角甲丙丁----角乙丙丁，則所存角甲丙乙等角甲乙丙（公論3：等量遞減）。故其底之外兩角等（等邊三角其三角俱等）。引據歐幾里得《幾何原本》徐光啟譯