File:NLC416-08jh013694-31682 投影幾何學.pdf

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投影幾何學   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
蘇熊瑞編著
image of artwork listed in title parameter on this page
Title
投影幾何學
Publisher
國立中山大學出版部[發行者]
Description

目錄
第一章 一一相對
1 一一相對
2 基本序列
3 一與無限相對
4 無限之各級
習題
第二章 實存常數
1 參數
2 方程式中之常數在幾何學上之意義
3 條件
習題一
4 常數之多寡
習題二
5 度之概念
習題三
第三章 對偶
1 以綜合法說明對偶之原理
習題一
2 plucker之線座標
習題二
3 以解析法說明對偶之原理
4 由點方程式求線方程式
習題三
5 由線方程式求點方稅式
習題四
第四章 在無限遠之點與直線
2 在無限遠之點
2 在無限遠之直線
習題一
3 直線上無限遠點之代數的解說
4 方程式之無限根
5 以無限遠原素解釋矛盾方程式
習題二
6 齊次座標
習題三
7 圓錐曲線之分類
8 漸近線及雙曲線之定義
9 圓點
10 迷向直線
11 圓之分類
習題四
第五章 透視與投影
1 定義
2 透視與投影之互相關係
習題一
3 投影幾何學
4 投影幾何學與其他幾何學
習題二
第六章 透射變換
1 透視圖形
習題一
2 透射變換
3 透射變換之畫法
4 透射變換之特殊情形
習題二
第七章 複比
1 點形與直線形
2 四點形之性質
3 調和原素
4 四調和點之量度關係
5 四調和點之作法
習題一
6 複比
7 複比群
8 調和比
習題二
第八章 投影座標
1 一度之投影座標
2 直線上座標之移換
3 平直移換之性質
習題一
4 二度之投影座標
5 投影座標之曲線方程式
6 投影座標之直線方程式
習題二
7 參數與複比之關係
8 以複比表角值
9 兩直線及兩點之複比
10 四點形四點之投影座標
習題三
11 平面上座標之移換
習題四
第九章 透視三角形
1 透視三角形
2 巧合形
3 多方透視三角形
習題
第十章 投影序列
1 疊置序列
2 自對原素
3 非疊置序列
4 二級曲線及曲面
5 圓錐曲線之分類
習題一
6 投影之特殊情形
習題二
第十一章 圓錐曲線
(a) 以綜合法研究
1 圓錐曲線
2 切線與切點
3 圓錐曲線之確定
4 圓錐曲線之複比性
5 pascal 及brianchon之定理
6 圓錐曲線之作法
7 切線及切點之作法
8 內接四點形及外切四線形
9 內接三點形及外切三線形
10 退縮圓錐曲線
習題一
(b) 以解析法研究
11 圓錐曲線
12 pascal 及 brianchon之定理
習題二
第十二章 二次列線曲面
1 二次列線
2 二次列線之性質
3 向線
4 經三定直線之直線
5 二次列線曲面之切面與割面
6 二次列線之投影
7 二次列線曲面之分類與性質
習題
第十三章 極點與極線
1 極點與極線
2 極點與極線之位置
3 極點與極線之作法
4 對極三角形
5 對於錐體之極線與極面
6 對於二次列線曲面之極點與極面
習題一
7 非共軛線上之共軛點及非共軛點上之共軛線
8 圓錐曲線內接及外切三角形之共軛點及共軛線
9 二次移換
習題二
第十四章 直徑與中心
1 直徑
2 中心
3 各種圓錐曲線之直徑及中心
4 圓錐曲線之直徑與內接及外切平行四邊形
5 圓錐曲線之軸及頂點
6 軸之作法
7 正雙曲線
8 圓錐曲線之法線
9 圓錐曲線法線之作法
10 雙曲線及漸近線
11 以漸近線為座標軸之雙曲線方程式
12 以共軛直徑為座標軸之有心圓錐曲線方程式
13 拋物線方程式
習題
第十五章 投影二次序列
1 二次序列之調和原素
2 二次序列之透視關係
3 二次序列之投影關係
4 一次序列與二次序列之投影關係
5 一次序列與三次序列之平面曲線
6 空間曲線與三次束面
7 相投性
8 steiner求耦點法
9 重對原素之相投性
10 相投性之循環序
習題
第十六章 直射變換與直射對換
1 直射變換之定義
2 直射變換之固定點
3 直射變換之分類
4 平直移換之不變性
5 直射變換最簡式之量度性
習題一
6 直射對換之定義
7 以行列式表一直射對換
8 直射對換之耦點及分類
9 直射對換最簡式之量度性
習題二
10 圓錐曲線上之直射對換
11 直射對換耦點之作法
12 desargues之定理
習題三
13 拋物線上之正交切線
14 三角形之正心
15 圓錐曲線上之切線
習題四
第十七章 經定點之圓錐曲線
1 經四定點之拋物線
2 經五定點之圓錐曲線
習題
第十八章 焦點
1 焦點之定義
2 焦點之確定
3 焦徑
4 同焦圓錐曲線
5 切線及法線與焦點之關係
6 準線
7 切線及準線與焦點之關係
8 心差率
9 垂焦弦
習題
第十九章 投影法與反極法
1 投影法
習題一
2 反極法
3 對於圓之反極
習題二
4 對於圓反極之別法
習題三
第二十章 圓錐曲線之解析的研究
1 圓錐曲線之參數方程式
2 參數方程式之最簡式
3 經兩點之直線
習題一
4 從有理曲線之點方程式求其線方程式
5 圓錐曲線上之直射對換
習題二
6 圓錐曲線之殊異點
7 極點與極線
8 圓錐曲線之線方程式
習題三
9 以不同三角形為標準三角形之圓錐曲線各種方程式
習題四
10 反照
11 極性與對偶
習題五
附錄
1 英中名辭對照索引
2 中英名辭對照索引

Language Chinese
Publication date [1931]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
主題
InfoField
射影幾何
中圖分類
InfoField
O185.1
載體形態
InfoField
297頁

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