« PreviousContinue »
Book III.—the circle; relieved of a great number of useless propositions. In addition to the topics usually treated, there are sections on the mensuration of the circle, a knowledge of which is generally assumed in works on solid geometry.
Book IV.—similarity. Here again much of Euclid VI. is omitted, as not really illustrating the subject of similar figures. Euclid's definition of proportion has gone, and is replaced by an easy algebraic treatment applicable (as is now permitted) to commensurable magnitudes only.
On the whole, the authors believe that with two-thirds of the number of theorems, more ground is covered than by Euclid I. IV. and VI.
References have generally been given in the proof of propositions; it is not supposed however that pupils will be required to quote references. Their presence in a book can be justified only on the ground that they may help a reader to follow the argument.
The authors desire to express their gratitude to many friends, whose criticisms have been both salutary and encouraging.
CAMBRIDGE, August 1903.