Page:The Elements of Euclid for the Use of Schools and Colleges - 1872.djvu/17

 Koenig and Blassiere. This edition has served as the model for that which is now offered to the student: some slight modifications have necessarily been made, owing to the difference in the size of the pages.

It will be perceived then, that in the present edition each distinct assertion in the argument begins a new line; and at the ends of the lines are placed the necessary references to the preceding principles on which the assertions depend. Moreover, the longer propositions are distributed into subordinate parts, which are distinguished by breaks at the beginning of the lines.

This edition contains all the propositions which are usually read in the Universities. After the text will be found a selection of notes; these are intended to indicate and explain the principal difficulties which have been noticed in the Elements of Euclid, and to supply the most important inferences which can be drawn from the propositions. The notes relate to Geometry exclusively; they do not introduce developments involving Arithmetic and Algebra, because these latter subjects are always studied in special works, and because Geometry alone presents sufficient matter to occupy the attention of early students. After some hesitation on the point, all remarks relating to Logic have also been excluded. Although the study of Logic appears to be reviving in this country, and may eventually obtain a more assured position than it now holds in a course of liberal education, yet at present few persons take up Logic before Geometry; and it seems therefore premature to devote space to a subject which will be altogether unsuitable to the majority of those who use a work like the present.

After the notes will be found an Appendix, consisting of propositions supplemental to those in the Elements of Euclid; it is hoped that a judicious choice has been made