A Text-Book of Euclid's Elements For: The Use of Schools, Books I-Vi and XI

Excerpt from A Text-Book of Euclid's Elements For: The Use of Schools, Books I-Vi and XI

This volume contains the first Six Books of Euclid's Elements, together with Appendices giving the most important elementary developments of Euclidean Geometry.

The text has been carefully revised, and special attention given to those points which experience has shewn to present difficulties to beginners.

In the course of this revision the Enunciations have been altered as little as possible; and, except in Book V., very few departures have been made from Euclid's proofs: in each case changes have been adopted only where the old text has been generally found a cause of difficulty; and such changes are for the most part in favour of well-recognised alternatives.

For example, the ambiguity has been removed from the Enunciations of Propositions 18 and 19 of Book I.: the fact that Propositions 8 and 26 establish the complete identical equality of the two triangles considered has been strongly urged; and thus the redundant step has been removed from Proposition 34. In Book II. Simson's arrangement of Proposition 13 has been abandoned for a well-known alternative proof.

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