SOLID G E O METRY BY CHARLES A. HOBBS, A. M. TEACHER OF MATHEMATICS AT LITTLE HALL CAMBRIDGE, MASS. CAMBRIDGE 1921 LIBRA JUN 9 1932 COPYRIGHT, 1921 BY CHARLES A. HOBBS THE NICHOLS PRESS, 113 MARKET ST., LYNN PREFACE SOLID GEOMETRY In passing from Plane Geometry to Solid Geometry many students find it hard to visualize in three dimensions a figure drawn on a plane surface. Hence it is necessary to give a beginner every possible assistance in forming space concepts. In this book the figures have been made as simple as possible in order that students not trained in drawing may be able readily to reproduce them. Students should be encouraged to construct models corresponding to the figures given in the book. Much can be accomplished in this direction by the use of cardboard to represent planes and stout wire to represent lines. For the study of figures on a sphere, every class room should be provided with a globe having a blackboard surface. The use of colored crayons is helpful, especially when each separate plane or curved surface has a separate color given it. The propositions corresponding to those of the National Syllabus are grouped as follows: Class I. "Those of fundamental importance and basal character." 204, 242, 243, 244 - Cor., 249, 253, 254, 256, 304, 327, 332, 333, 334, 335, 341, 343. Class II. “Those of considerable importance which are secondary only to the preceding ones. 232, 233, 236, 238, Ex. 1012, 247, 250, 252, 257, 258, 259, 260, 262- Cor., 264, 267, 268, 269, 287, 289, 297, 299, *303, 321, 324, 328, 329. Class III. “The student should be able to make a proof for anyone of them if allowed a reasonable interval for thought." *203, +206, +207, +208, 209, 210, 211, 212, Ex. 958, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, *228, *229, *230, 235-Cor. II, 239, 245, 248-Cor. II, 251, 261, *283, *292, 310, 312, 315, 316, 322, 342, 344. Class IV. "The theorems may be used by the examiner with the understanding that they are to be regarded in examinations as of the nature of exercises." 231, 234, *237, 240, 241, 246, 265, *272, 284-Cor. I, 293, 301, 317, 318, 319-Cor. I, 323, 325, 330, 336, 337, 346– Cor. II, 347. (Propositions marked with an asterisk (*) are designated as “theorems for informal proof.” For propositions marked with a dagger [+], only the latter part of the proof is required.) For the volume of the frustum of a pyramid, for that of the frustum of a cone, and for that of the spherical segment, separate formulas have been developed in order that any teacher who so desires may treat each volume by itself. In the judgment of the author, however, it is more economical of time to compute these volumes by means of the prismatoidal formula. |