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Excerpt from The University of New Mexico Bulletin: An Introduction to Mathematics; A Study of the Nature of Mathematical Knowledge By first principles in each genus I mean those the truth of which it is not possible to prove. What is denoted by the first (terms) and those derived from them is assumed; but, as regards their exist ence, this must be assumed for the principles but proved for the rest. Thus what a unit is; what the straight (line) is, or what a triangle is. (must be assumed) and the existence Of the unit Of magni tude must also be assumed, but the rest must be proved. N ow Of the premises used in demonstra tive sciences some are peculiar to each science and others common (to all), the latter being common by analogy, for Of course they are actually useful in so far as they are applied to the subject-matter in cluded under the particular science. Instances Of the first principles peculiar to a science are the assumptions that a line is Of such and such a char acter, and similarly for the straight (line) whereas it is a common principle, for instance, that, if equals be subtracted from equals, the remainders are equal. But it is enough that each of the com mon principles is true so far as regards the par ticular genus (subject-matter) for, (in geometry) the effect will be the same even if the common prin ciple be assumed to be true, not Of everything, but only Of magnitudes, and, in arithmetic, Of numbers. 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.

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