PREFACE. IN preparing this edition of Chauvenet's Geometry I have endeavored to compel the student to think and to reason for himself, and I have tried to emphasize the fact that he should not merely learn to understand and demonstrate a few set propositions, but that he should acquire the power of grasping and proving any simple geometrical truth that may be set before him; and this power, it must be remembered, can never be gained by memorizing demonstrations. Systematic practice in devising proofs of new propositions is indispensable. On this account the demonstrations of the main propositions, which at first are full and complete, are gradually more and more condensed, until at last they are sometimes reduced to mere hints, by the aid of which the full proof is to be developed; and numerous additional theorems and problems are constantly given as exercises for practice in original work. A syllabus, containing the axioms, the postulates, and the captions of the main theorems and corollaries, has been added to aid student and teacher in reviews and examinations, and to make the preparation of new proofs more easy and definite. |