所属 神奈川大学 情報学部 システム数理学科
神奈川大学大学院 工学研究科 工学専攻（情報システム創成領域）
|HOW TO PRESENT THE HEART OF NEWTON' S PRINCIPIA TO THE LAYPERSON:
A PRIMER ON THE CONIC SECTIONS WITHOUT APOLLONIUS OF PERGA
|Symmetry Festival 2009, Book of Abstract (CD-ROM)
|Newton's Philosophiae Naturalis Principia Mathematica is written in Latin and deeply depends on Conics by Apollonius of Perga. Both are the hurdles for modern readers to wish to read Principia. Language problems may be solved by good translations. The aim of this study is to prepare a primer on the conic sections dependent only on the knowledge of the first year students in the tertiary education without using calculus or higher analytic geometry. The purpose is fulfilled by use of symmetry, i.e., a circle and a rectangular hyperbola for elementary demonstrations, as well as coordinate straining to generalise the special results. In case of a parabola its symmetry is made most of, too. The result is structured by three definitions, two lemmas and six theorems to tackle at Newton's Lemmas XII, XIII, XIV and the Power of a Point Theorem.