Euclides 歐幾里得
,
Ji he yuan ben 幾何原本
,
1966
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21
(一)
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(二)
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(三)
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(四)
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(五)
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(六)
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(七)
30
(八)
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幾何原本 卷二
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<
s
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<
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<
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<
s
xml:id
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">題言甲乙線上直角方形。</
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<
s
xml:id
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xml:space
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">與甲丙、丙乙、線上
<
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/>
兩直角方形、及甲丙偕丙乙、丙乙偕甲丙、矩線內兩直角形幷、等。</
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</
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<
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s
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<
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<
s
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s
>
<
s
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xml:space
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">次作乙戊對角線。</
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>
<
s
xml:id
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">次從丙、作丙
<
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己線。</
s
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<
s
xml:id
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xml:space
="
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">與乙丁平行。</
s
>
<
s
xml:id
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">遇對角線於庚。</
s
>
<
s
xml:id
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xml:space
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">末從庚、作辛壬線。</
s
>
<
s
xml:id
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xml:space
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">與甲乙平行。</
s
>
<
s
xml:id
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xml:space
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">而分
<
lb
/>
本形為四直角形。</
s
>
<
s
xml:id
="
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xml:space
="
preserve
">卽甲乙戊角形之甲乙、甲戊、兩邊等。</
s
>
<
s
xml:id
="
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xml:space
="
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">而甲乙戊、與甲
<
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戊乙。</
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<
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xml:id
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xml:space
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">兩角亦等。</
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<
s
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">一卷五</
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">)</
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<
s
xml:id
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xml:space
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">夫甲乙戊形之三角幷。</
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>
<
s
xml:id
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xml:space
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">與兩直角等。</
s
>
<
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<
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">一卷卅二</
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<
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<
s
xml:id
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xml:space
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">而甲為
<
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/>
直角。</
s
>
<
s
xml:id
="
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xml:space
="
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">卽甲乙戊、甲戊乙、皆半直角。</
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>
<
s
xml:id
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xml:space
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">(</
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>
<
s
xml:id
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<
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">)</
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<
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xml:id
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xml:space
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">依顯丁乙戊角形之丁乙戊、丁戊乙、兩角。</
s
>
<
s
xml:id
="
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xml:space
="
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">亦皆半直角。</
s
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<
s
xml:id
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">則戊
<
lb
/>
己庚外角、與內角丁、等為直角。</
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<
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<
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<
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<
s
xml:id
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">而己戊庚、旣半直角。</
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>
<
s
xml:id
="
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xml:space
="
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">則己庚戊、等為半直角矣。</
s
>
<
s
xml:id
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xml:space
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">角旣等。</
s
>
<
s
xml:id
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xml:space
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">則己庚、己
<
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/>
戊、兩邊亦等。</
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<
s
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xml:space
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<
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<
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<
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<
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<
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<
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<
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xml:id
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">而辛己為直角方形也。</
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<
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xml:id
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">依顯丙壬亦直角方形也。</
s
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<
s
xml:id
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xml:space
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">又庚辛、與甲
<
lb
/>
丙、兩對邊等。</
s
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<
s
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<
s
xml:id
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<
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">)</
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<
s
xml:id
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xml:space
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">而乙丙、與庚丙、俱為直角方形邊。</
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<
s
xml:id
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">亦等。</
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<
s
xml:id
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">則辛己為甲丙線上直角方形。</
s
>
<
s
xml:id
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xml:space
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">丙壬為丙乙
<
lb
/>
線上直角方形也。</
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<
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xml:id
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<
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xml:id
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xml:space
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">各在甲丙、丙乙、矩線內也。</
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<
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xml:id
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">則甲丁直角方形。</
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<
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xml:id
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<
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/>
兩線上兩直角方形。</
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<
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xml:id
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xml:space
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">及兩線矩內兩直角形幷、等矣。</
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>
</
p
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<
p
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<
s
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">系。</
s
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<
s
xml:id
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s
>
<
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xml:id
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</
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<
p
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<
s
xml:id
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s
>
<
s
xml:id
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">甲乙線。</
s
>
<
s
xml:id
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xml:space
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">旣任分於丙。</
s
>
<
s
xml:id
="
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xml:space
="
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">則元線甲乙上直角方形。</
s
>
<
s
xml:id
="
N13E7A
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xml:space
="
preserve
">與元線偕各分線、矩內兩直角形幷、等。</
s
>
<
s
xml:id
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xml:space
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">(</
s
>
<
s
xml:id
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">本篇二</
s
>
<
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xml:id
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">)</
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<
s
xml:id
="
N13E85
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xml:space
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">又
<
lb
/>
甲乙偕甲丙、矩線內直角形。</
s
>
<
s
xml:id
="
N13E8A
"
xml:space
="
preserve
">與甲丙偕丙乙、矩線內直角形、及甲丙上直角方形幷、等。</
s
>
<
s
xml:id
="
N13E8D
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<
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<
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<
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