Various Proofs of Newton's Theorem

Abstract

This article is taken from my lecture on Geometrical Methods which I have been accustomed to give to the stuLdents in Fukien Normal College for the past several years. But it appears here with some additions and improvements. We apply both the pure geometrical methods and analytic methods. It contains more than twenty proofs; some are new, and the others are taken from eminent books and periodicals as shown in the bibliography. It has been proved by experience that different proofs of a theorem can instruct the students to apply the various theorems ingeniously, and to be skillful in solving problems, and also can stimulate the interest of investigation, and to forget the difficulties in it. Moreover, it is of great value in training the coming geometry teachers to master the various methods of geometry, either the advanced methods or elementary. That is the goal of this paper. Now, we shall begin to discuss the proofs of the theorem.