Elements Of Solid Geometry: With Numerous Exercises (1894) - Softcover

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The whilom popular idea that each proposition must occupy an entire page or pages is discarded. A short demonstration is made short. The student is not deceived into thinking he has learned a page of geometrical truth, when in fact he has learned but a few lines. In the present work the diagrams are generally so simply lettered, that one glance is sufficient to fix it in the students mind, and he is under no necessity to turn to it again, this simplicity being secured by few letters, or where that is impossible, by suggestive or characteristic letters, as explained under the head of notation. Compare 24, 34, C4, 67, 135, 153, 174, etc. Special Characteristics. The problems in the construction of the regular polyhedrons (209) are solved upon tentative rather than upon dogmatic lines, with marked gain for the student. The student is not arbitrarily led per saU um, and the correctness of the step proved afterwards, but each solid is put together piece by piece, as one would do in the actual construction of a model. In the propositions relating to spherical surfaces, increased clearness has been gained by the use of the spherical degree as the unit of spherical surface, and it is defined much more precisely and comprehensively than is usual. Precision and comprehensiveness have been sought in all the definitions. See 298, 300, 301, 301|, 315. The very general solid, the prismatoid has been introduced, and made the basis of demonstration for its limiting cases, the wedge, pyramid, cone, etc. In the area of the spherical triangle, lune, etc., the expression of the angles in angular degrees or radians has been carefully distinguished.
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