File:NLC416-13jh009265-61882 幾何學.pdf

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幾何學   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Title
幾何學
image of artwork listed in title parameter on this page
Publisher
[出版者不詳]
Description

目錄
卷三
第一題 於三角形內作線與底平行此線分兩腰必有比例
系一 三角形各邊以公准個分後其兩腰所分之數段有比例
系二 凡比例有八式之其一式余可類推
系三 三角形內有諸線平行其底者則兩腰被分有比例
第二題 三角形內線分兩腰有比例者此線必與底平行
第三題 三角形平分其腰間角之線所分底線兩段之比例等於兩腰之比例
第四題 （上題反證）自三角形底邊內一點分底邊為二段若此二段底邊之比例等於兩腰之比例自此點至頂之線必為分角線
論相似多邊形
第五題 三角形內有一直線平行於其任邊所成之第二三角形必與原形相似
相似三角形之主要
二三角形為相似者
（一） 角相等者
（二） 相當之邊有比例者
（三） 若有一角等而等角旁之兩腰有比例者
（四） 相當之各邊平行或互為〓線者
第六題 （一）兩三角形若相當之三角等即為相似形
系一 兩三角形若有二角相等則為相似形
系二 兩勾股形有一銳角等者則為相似形
第七題 （二）兩三角形相當各邊有比例者即為相似形
第八題 （三）兩三角形若相當兩邊各有比例而其間所夾之角亦相等則兩形相似
第九題 （四）兩三角形各相當邊平等或互為垂線者即為相似形
第十題 兩相似多邊形必可分為等多三角形兩兩同方而相似
第十一題 （前題反證）兩多邊形若可為分等多之三角形兩兩同文而相似則多邊形必相似
第十二題 兩相似多邊形其周相比如兩多邊形任相當之二邊為相比
第十三題 自勾股形直角之〓至弦作垂線
（一） 所分之兩　三角形必各與原形相似亦彼此相似
（二） 垂線為弦兩段之中率
（三） 原形之兩腰各為弦及靠各腰一段之中率
系一 勾股形弦方　等於直角旁兩邊方之和數，直角旁一邊之方即弦方與他一邊方之較
系二 正方形之對角線不能分各邊
勾股形邊弦及高之計算法
射影
案 二幾何和及較之方由代數式得證
第十四題 凡三角形對銳角邊之方等於余兩邊方之和減去其底乘彼一邊射影之倍
案 鈍角三角形對鈍角邊之射影須遇於三角形外照上題作證
第十五題 凡三角形對銳角邊之方等於余兩邊方之和加其底乘彼一邊射影之倍
第十六題 圓內有兩弦相交則此弦兩段相乘必等於彼弦兩段相乘
第十七題 自圓外一點作圓之切線與割線則切線之方必等於割線乘其圓外之一段
有法多邊
釋明
第十八題 有法多邊形能作其外切圓及內切圓
（1） 有法多邊形能作其外切圓
（二） 有法多邊形能作其內切圓
系一 多邊形之外切圓及內切圓為同一圓之心
系二 內切多邊形各邊所對之圓心角等於多邊形邊數分四之直角
第十九題 兩等邊數之有法多邊形為相似形
第二十題 邊數等之有法多邊形其周相比如其內切圓之半徑或外切圓之半徑相比
無量幾何
釋明
第二十一題 圓周相比如其全徑相比
作法問題
第一題 平分已定直線為數等分
第二題 分已定直線與已知之他三直線有比例
第三題 有已知之三直線求其四率比例線
第四題 求一線為已知兩直線之中率對比
第五題 求分已知直線為二其大者自乘等於小者乘其全線
案 設以已知直線為a，求得之線為x則知x等於二分之a乘方根5減去7即〓
第六題 求作兩圓之公切線
（一） 兩圓之外公切線
（二） 兩圓之內公切線
第七題 求作兩圓之公切線
（一） 兩圓之外公切線
（二） 兩圓之內公切線
第八題 有一已知多邊形　一已知直線可自 已知直線上作 一多邊形相似已知多邊形
第九題 求作一內切正方形
系 內切正方形之邊等於其圓之半徑乘方根二
第十題 內切有法六邊形之邊等於其圓之半徑
系 內切等邊三角形之邊等於其圓之半徑乘方根三
第十一題 求於圓內作內切干邊形
案一 如以內切有法〓邊形之每二邊連一線即成內切有法五邊形
案二 同圓內切有法六邊形與內切有法十邊形之邊所乘弧之較其所余弧之弦即內切有法〓五邊形之邊
第十二題 於內切任有法多邊形內求作其邊數二倍之內切有法多邊形

Language Chinese
Publication date [19--?]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
館藏信息
InfoField
MG/O18/7
主題
InfoField
幾何
中圖分類
InfoField
O18
載體形態
InfoField
[27]頁

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