PREFACE In the preparation of this text the author acknowledges joint authorship with Robert L. Short. Geometry is approached from the constructive side, all methods of construction needed for drawing any figure in Books I or II being given in the introduction. In cases where a geometric principle is used in any construction, a note at the end tells where the principle is proved. In all figures in the early portions of Book I, the construction lines and arcs are given; afterwards these are dispensed with. In Props. II and III, Book I, and in other places, colored diagrams are given in addition to the regular figures, in which the equal parts in the given triangles are represented by lines of the same color; this scheme will be found of great assistance to the pupil in the earlier portions of the work. Below each figure is a paragraph in smaller type, giving full directions for the construction of the diagram in accordance with the statement of the theorem. This gives the pupil a familiarity with the figure, and what in it is given, and what to be proved, that is of great value, and lessens the tendency to memorize. Many figures are omitted, but complete directions for their construction are given in each case. In all figures given in connection with theorems and problems, given and required lines are made heavy. Attention is invited to the order of theorems in Book I; in this case, the pupil begins with the easier proofs. From the start the student has practice in representing angles and lines by small letters. Only the outline of the proof is given after Book II, except in the more difficult demonstrations. In this outline work the pupil has explicit directions, but develops the demonstration himself. In all portions of the work proofs are omitted in |