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Create annotation system (creates a ticket)

Manual annotation is the default. Approved files are written as sibling pages under kanbun/, hanmun/, or hanvan/ with the same filename as this source page.

Annotation system

Summary

Reasoning

Digital keyboard

Kanbun-LM is not shown here because automatic generation is Japanese-only. This patch keeps the manual path as the default workflow.

Source page


# WORK_TITLE: 平行公理
# DISPLAY_TITLE: 平行公理
# AUTHOR:
# TIMES:
# PAGE_TITLE: 平行公理
# CATEGORIES:
α（角甲乙丙）合β（角乙甲丁）小於二直角，則引長二線交於此側

平行公理
者，
歐氏幾何
中第五公理也。

述

角甲乙丙合角乙甲丁小于二直角者，則乙丙從丙直行引長必相交甲丁從丁直行引長。

史

公理五不比前四者，甚為冗長，不易見其明也。有泰西疇人指其不足為公理也，然嘗以首四公理證平行公理，皆不可得，更有證其不可由四公理得者。

後有捨平行公理而造新幾何者，概稱
非歐幾何，
射影幾何、
雙曲幾何
等皆如是。

等價命題

有疇人稱其可證平行公理者，蓋皆引與公理五等價之命題而不成。舉些許示之：

過線外一點恰有一平行線

有一三角形，其內角和為二直角

凡三角形者，其內角和皆等

有二三角形，相似而不全等

凡三角形有外接圓

一四邊形，其三內角為直角，則其第四角亦為直角

有二線不相交而處處等距

二線皆與另一線平行，則前二線相平行

幾何
術語

點
｜

頂點
｜

相切
｜

線
｜

直線
｜

曲線
｜

測地線
｜

切線
｜

圓錐曲線
｜

拋物線
｜

雙曲線
｜

螺線
｜

螺旋
 ｜

面
｜

平面
｜

曲面
｜

切面
｜

三角形
｜

四邊形
｜

多邊形
｜

圓
｜

弦
｜

橢圓
｜

體
｜

長方體
｜

立方體
｜

棱錐
｜

正多面體
｜

錐體
｜

柱體
｜

球
｜

橢球
｜

角
｜

邊
｜

高
｜

長
｜

距
｜

周界
｜

面積
｜

體積
｜

圓周率
｜

黃金分割
｜

相似
｜

全等
｜

平行
｜

垂直
｜

平行公理
｜

勾股定理
｜

歐氏幾何
｜

尺規作圖
｜

非歐幾何
｜

球面幾何
｜

雙曲幾何
｜

流形
｜

坐標幾何
｜

射影幾何
｜

仿射幾何

Annotation-system text

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Add companion material (creates a ticket)

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Translator

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Translation text

Material files

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Related corpus path

Material links

Ticket summary

Reviewer reasoning

Material note *

Provenance *

Choose every label that applies. At least one is required.

User-made Public domain Historical source or manuscript Author-provided: the work's author supplied this translation

References

A formal citation style is welcome but not required.

AI assistance disclosure

AI-assisted What was assisted?

Evidence links

Links are preferred when the evidence already exists online.

Evidence files

Up to 10 files and 20 MB for this ticket. HTML, XHTML, and SVG are rejected.

Optional contact details

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Save this ticket key on this device

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Ticket ID:

Ticket key (save this):

Propose a text edit (creates a ticket)

This does not change the corpus directly. It creates a ticket with a unified diff attached.

Title

Summary

Reasoning

Edited text

Evidence links

Links are preferred when the evidence already exists online.

Evidence files

Up to 10 files and 20 MB for this ticket. HTML, XHTML, and SVG are rejected.

Optional contact details

Stored separately and encrypted. Deleted after 30 days or when the ticket closes.

Name Email Contact note

Save this ticket key on this device

Unchecked by default. The key is otherwise shown once and is not stored by the browser.

Ticket ID:

Ticket key (save this):

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)

# WORK_TITLE: 平行公理 # DISPLAY_TITLE: 平行公理 # AUTHOR: # TIMES: # PAGE_TITLE: 平行公理 # CATEGORIES: α（角甲乙丙）合β（角乙甲丁）小於二直角，則引長二線交於此側平行公理者，歐氏幾何中第五公理也。述角甲乙丙合角乙甲丁小于二直角者，則乙丙從丙直行引長必相交甲丁從丁直行引長。史公理五不比前四者，甚為冗長，不易見其明也。有泰西疇人指其不足為公理也，然嘗以首四公理證平行公理，皆不可得，更有證其不可由四公理得者。後有捨平行公理而造新幾何者，概稱非歐幾何，射影幾何、雙曲幾何等皆如是。等價命題有疇人稱其可證平行公理者，蓋皆引與公理五等價之命題而不成。舉些許示之：過線外一點恰有一平行線有一三角形，其內角和為二直角凡三角形者，其內角和皆等有二三角形，相似而不全等凡三角形有外接圓一四邊形，其三內角為直角，則其第四角亦為直角有二線不相交而處處等距二線皆與另一線平行，則前二線相平行幾何術語點｜頂點｜相切｜線｜直線｜曲線｜測地線｜切線｜圓錐曲線｜拋物線｜雙曲線｜螺線｜螺旋｜面｜平面｜曲面｜切面｜三角形｜四邊形｜多邊形｜圓｜弦｜橢圓｜體｜長方體｜立方體｜棱錐｜正多面體｜錐體｜柱體｜球｜橢球｜角｜邊｜高｜長｜距｜周界｜面積｜體積｜圓周率｜黃金分割｜相似｜全等｜平行｜垂直｜平行公理｜勾股定理｜歐氏幾何｜尺規作圖｜非歐幾何｜球面幾何｜雙曲幾何｜流形｜坐標幾何｜射影幾何｜仿射幾何