File:NLC416-08jh008771-8664 幾何原理.pdf

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幾何原理   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
〔法〕嚇爾勃特(D.Hilbert)原著
image of artwork listed in title parameter on this page
Title
幾何原理
Publisher
商務印書館[發行者] (上海)
Description

目錄
敘言
第一章 五類公理
1 幾何要素及五類公理
2 類ⅰ結合公理
3 類ⅱ順序公理
4 結合公理及順序公理之演論
5 類ⅲ平行公理（歐兒里特公理）
6 類ⅳ合同公理
7 合同公理之演論
8 類ⅴ連續公理（亞幾默德公理）
附 完備公理
第二章 公理之互相諧和及互相獨立
9 公理之互相諧和
10 平行公理之獨立（非歐幾里特幾何）
11 合同公理之獨立
12 連續公理之獨立（非亞幾默德幾何）
第三章 比例論
13 復素數組織
14 巴斯開定理之證明
15 根據巴斯開定理之線段計算法
16 比例及相似之定理
17 直線及平面之方程式
第四章 平面面積理論
18 多角形之算術的等積及代數的等積
19 等底且等高之平行四邊形及三角形
20 三角形及多角形之面積測度
21 代數的等積與面積測度
第五章 德沙格氏定理
22 德沙格氏定理及其在平面幾何用合同公理之證法
23 在平面幾何不用合同公理不能證明德沙格氏定理
24 根據德沙格氏定理而不用合同公理之線段計算新法續論
25 線段計算新法中加法之交換定律及結合定律
26 線段計算新法中乘法之結合定律及分配定律
27 以此線段計算新法為基礎之直線方程式
28 線段系，視如複數系
29 用德沙格氏數系創立空間幾何
30 德沙格氏定理之真諦
第六章 巴斯開定理
31 關於巴斯開定理之可否證明之二定理
32 乘法交換定律之於亞幾默德數系
33 乘法交換定律之於非亞幾默德數系
34 關於巴斯開定理之二定理之證明（非巴斯開幾何）
35 關於交點定理用巴斯開定理及德沙格氏定理之證明
第七章 根據五類公理之幾何作圖法
36 用直尺及線段遷移器之幾何作圖法
37 可用上述作圖法所得之點之坐標之解析的表徵
38 用平方之和表示代數的數及整的有理函數之方法
39 幾何作圖題可否用直尺及線段遷移器作成之準則
結論

Language Chinese
Publication date 民國21[1932]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
主題
InfoField
微分幾何
中圖分類
InfoField
O186
拼音題名
InfoField
ji he yuan li
載體形態
InfoField
144頁

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current08:28, 10 June 2023Thumbnail for version as of 08:28, 10 June 20231,239 × 1,754, 153 pages (3.35 MB)PencakeBot (talk | contribs)Upload 幾何原理 (1/1) by (法)嚇爾勃特(D.Hilbert)原著 (batch task; nlc:data_416,08jh008771,8664; 民國圖書.4; 幾何原理)

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