| Charles Hutton - Science - 1815
...of a pyramid, is found by adding together the areas of all the triangles which form that surface. 5. **If a pyramid be cut by a plane parallel to the base,** the section will be a plane figure similar to the base; and these two figures will be in proportion... | |
| Timothy Walker - Geometry - 1829 - 129 pages
...the measure of the prism. We shall divide the reasoning into four distinct propositions. DEM. 1. — **If a pyramid be cut by a plane parallel to the base,** the section is a polygon similar to the base. Let GHIKL (fig. 93) be a section F 93 parallel to the... | |
| Thomas Holliday - 1838
...of a cone or pyramid may be found by dividing three times the solidity by the area of the bate. 6. **If a pyramid be cut by a plane parallel to the base,** the section will be similar to tbe base, and the section and the base will be to each other as the... | |
| Charles Davies - Geometry - 1840 - 252 pages
...planes NP and SV, parallel to the base, the polygons NP, and SV, will each be equal to the base. 17. **If a pyramid be cut by a plane parallel to the base,** the section will be similar to the base. Thus, if the pyramid $ — ABCDE, be cut by the plane abode... | |
| Samuel Hunter Christie - 1847
...ratio of the same sides; that is, in the triplicate ratio of the homologous sides. PROP. LXIII. THEOR. **If a pyramid be cut by a plane parallel to the base,** the section will be similar to the base; and this section and the base will be to one another in the... | |
| Charles Davies - Geometry - 1850 - 216 pages
...section of a cylinder, by a plane parallel to the base, is a circle equal to the base. THEOREM IV. **If a pyramid be cut by a plane parallel to the base,** I. The edges and altitude will be divided proportionally. II. The section will be a polygon similar... | |
| CHARLES DAVIS, L.L. D. - 1850
...section of a cylinder, by a plane parallel to the base, is a circle equal to the base. THEOREM IV. **If a pyramid be cut by a plane parallel to the base,** I. The edges and altitude will be divided proportionally. II. The section will be a polygon similar... | |
| Charles Davies - Geometry - 1886 - 324 pages
...section of a cylinder, by a plane parallel to the base, is a circle equal to the base. THEOREM 1T. **If a pyramid be cut by a plane parallel to the base,** I. The edges and altitude will be divided proportionally. II. The section will be a polygon similar... | |
| CHARLES DAVIES, LL.D. - 1863
...Every section of a prism, parallel to the bases, is equal to either base. PROPOSITION III. THEOREM. **If a pyramid be cut by a plane parallel to the base** : 1°. The edges and the altitude will be divided proportionally : 2°. The section will be a polygon... | |
| Edward Brooks - Geometry - 1868 - 275 pages
...into one-half of the slant height SH; that is, the convex surface of the pyramid equals THEOREM IX. **If a pyramid be cut by a plane parallel to the base;** 1. The edges and altitude will be divided proportionally. 2. The section will be a polygon similar... | |
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