- 學位論文
重訪牛頓《原理》第一卷第一章有關微積分的基礎知識及第二章面積律等價於向心力的證明
A revisit of Newton's Principia ─ the 11 lemmas founding the limit argument of calculus and the physical interpretation of Kepler's area law
摘要
本論文最主要的目的有二：一是分析牛頓著作《自然哲學之數學原理》中第一卷第一章有關微積分中極限知識的11個引理內容，除了以現代數學語言重新敘述並論證以外，更進一步探討牛頓在處理物體運動前，放入這些極限概念作為引理的目的與動機；二是對第二章有關刻卜勒面積律等價於向心力的命題1、2，以泰勒展開式的觀點，遵循牛頓原來的思路，給出嚴謹的證明。
關鍵字
無並列摘要
In this article , we have two main goals : The first goal is to analyze the 11 lemmas in the first chapter of the first volume in Newton's "Mathematical Principles of Natural Philosophy". These lemmas are related to elementary theory of limit in calculus. We will interpret these lemmas by modern language and discuss the motive of Newton. The second goal is to trace Newton's original idea and give a rigorous proof of the equivalence of the law of centripetal force and Kepler’s area law.
並列關鍵字
無參考文獻
1. 牛頓（Isaac Newston , 1642 - 1727）著，
2. Subrahmanyan Chandrasekhar.
《Newton’s Principia for the Common Reader》
4. Brackenridge B. 《The Key to Newton s Dynamics》
《自然哲學之數學原理》