A KEY TO THE EXERCISES AND EXAMPLES CONTAINED IN A TEXT-BOOK OF EUCLID'S ELEMENTS BOOKS I.--VI. AND XI. In preparing this Key two objects have been kept in view. It is intended first to save the time and lighten the work of teachers, and secondly to remove the difficulties of private students, leaving however sufficient demands upon their thought and intelligence to make the solutions in themselves a useful geometrical exercise. The Examples therefore have not in the majority of cases been worked out in detail, and the drawing of figures has been left to the reader. The absence of figures may possibly give rise to some little difficulty in Examples which admit of a variety of cases, especially those in Book III. depending on angles in the same segment or on intersecting circles. It would of course be impossible within reasonable limits of space to deal separately with all the cases that may arise in every Example of this kind: we have therefore selected that case which we think would most naturally occur to a student in trying the problem for himself; and, when necessary, we have given some indication of the particular figure to which the proof refers. Other cases the student may easily, if he chooses, investigate for himself; the modifications which he will most frequently have to make will be the use of subtraction instead of addition of lines or angles, and the application of III. 22 instead of its kindred proposition III. 21. H. S. HALL. F. H. STEVENS. October, 1892. 857553 |