Excerpt from The Foundations of Mathematics: A Contribution to the Philosophy of Geometry

Finally, he adds what he calls Common Notions which embody some general principles of logic (of pure reason) specially needed in geometry, such as that things which are equal to the same thing are equal to one another; that if equals be added to equals, the wholes are equal, etc.

I need not mention here perhaps, since it is a fact of no consequence, that the readings of the several manuscripts vary, and that some propositions (e. g., that all right angles are equal to one another) are now missing, now counted among the postulates, and now adduced as common notions.

The commentators of Euclid who did not understand the difference between Postulates and Common Notions, spoke of both as axioms, and even to-day the term Common Notion is mostly so translated.

In our modern editions of Euclid we find a statement concerning parallel lines added to either the Postulates or Common Notions. Originally it appeared in Proposition 29 where it is needed to prop up the argument that would prove the equality of alternate angles in case a third straight line falls upon parallel straight lines.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. Это и многое другое вы найдете в книге The Foundations of Mathematics (Paul Carus)