The Postulate of Parallels

Abstract

There are in the Mathematical Gazette for October 1924, three communications on the above subject.It will make my remarks on these clearer if I refer to the contents of my paper on the Postulate of Parallels in the Gazette for December 1923, and make an addition thereto. In that paper the demonstrations of Euc. I. 27 and 29 are deduced from Wallis’s Postulate of Similarity, viz.: “To every figure there exists a similar figure of arbitrary magnitude” taken as a substitute for Euclid’s Postulate of Parallels. The demonstration of Euc. I. 27 in this manner was first given (I believe) by Professor Nunn in the Gazette of May 1922. He has not, however, published in full his demonstration of Euc. I. 29. He was so kind as to communicate it to me, but I hope he will some day publish it in full. It is entirely different from the demonstration of Euc. I. 29 which I published in the Gazette of December 1923, which involves three successive applications of the Postulate of Similarity and makes use of Euc. I. 27 as proved by Professor Nunn, but does not include the proof of any other proposition.