Corpus Viewer

Work: clean Viewing: Source

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: 垂直
# DISPLAY_TITLE: 垂直
# AUTHOR:
# TIMES:
# PAGE_TITLE: 垂直
# CATEGORIES:
垂直者，成直角也。

觀乎坐標幾何，二線
之斜度相乘為負一也。

二曲線于相交點之切線垂直，曰二曲線垂直于相交點。

線垂直平面上直線者，曰線垂直于平面，而線曰平面之法線
。

二平面上直線咸垂直，同乎二平面之法線垂直，曰二平面垂直。

線交曲面于一點，而線垂直于交點之切面，曰線垂直曲面于相交點，而線曰曲面之法線
。

觀內積空間，垂直乃正交之別稱也。

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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References

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AI assistance disclosure

AI-assisted What was assisted?

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Evidence files

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Add companion material (creates a ticket)

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Material type

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Translation language (ISO 639-3)

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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

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AI assistance disclosure

AI-assisted What was assisted?

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Evidence files

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Propose a text edit (creates a ticket)

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Title

Summary

Reasoning

Edited text

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Evidence files

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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: 垂直 # DISPLAY_TITLE: 垂直 # AUTHOR: # TIMES: # PAGE_TITLE: 垂直 # CATEGORIES: 垂直者，成直角也。觀乎坐標幾何，二線之斜度相乘為負一也。二曲線于相交點之切線垂直，曰二曲線垂直于相交點。線垂直平面上直線者，曰線垂直于平面，而線曰平面之法線。二平面上直線咸垂直，同乎二平面之法線垂直，曰二平面垂直。線交曲面于一點，而線垂直于交點之切面，曰線垂直曲面于相交點，而線曰曲面之法線。觀內積空間，垂直乃正交之別稱也。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