 | Euclid - 1835 - 540 pages
...part of the cylinder. Wherefore, " every cone" &c. QED PROP. XI. THEOR. See N. Cones and cylinders of the same altitude, are to one another as their bases. Let the cones and cylinders, of which the bases are the circles ABCD, EFGH, and the axes KL, MN, and AC,... | |
 | A. Bell - Conic sections - 1837 - 180 pages
...the solid AB to the solid CD. Con. 1. — From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the prisms BNM, DPG, the bases of which are the triangles AEM, CFG, have the same altitude ; complete... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...to the solid CD. Wherefore parallelepipeds, &c. Cor. From this it is manifest that triangular prisms of the same altitude, are to one another as their bases. Let the prisms, the bases of which are the triangles AEM, CFG, and NBO, PDQ the triangles opposite to them,... | |
 | Euclides - Geometry - 1841 - 378 pages
...the third part of the cylinder. Wherefore every cone, &c. QED PROP. XI. THEOR. Cones and cylinders of the same altitude, are to one another as their bases. Let the cones and cylinders, of which the bases are the circles ABCD, EFGH, and the diameters of their... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...solid AB to the solid CD. COR. 1. From this it is manifest, that prisms upon triangular bases, and of the same altitude, are to one another as their bases. Let the prisms BNM, DPG, the bases of which arc the triangles AEM, CFG, have the same altitude : complete... | |
 | Euclides - 1845 - 546 pages
...third part of the cylinder. Wherefore, every cone, &c. QKD PROPOSITION XI. THEOREM. Cones and cylinders of the same altitude, are to one another as their bases. Let the cones and cylinders, of which the bases are the circles ABCD, EFGH, and the axes KL, MN, and AC,... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...is the third part of the cylinder. A cone, therefore, &c. PROP. XI. THEOB. — Cones and cylinders of the same altitude, are to one another as their bases. Let the cones and cylinders, of which the bases are the circles ABCD, EFGH, and the axes KL, MN, and AC,... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...solid AB to the solid CD. COR. 1. From this it is manifest; that prisms upon triangular bases, and of the same altitude, are to one another as their bases. Let the prisms BNM, DPG, the bases of which are the triangles AEM, CFG, have the same altitude : complete... | |
 | Euclides - 1846 - 292 pages
...line drawn from its vertex perpendicular to the base. PROP. I. THEOR. Triangles and parallelograms of the same altitude are to one another as their bases. Let the triangles ABC, ACD, and the parallelograms EC, CF, have the same altitude, viz. the perpendicular... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...triangles СШя, ОАя, are similar, .-. OD : Oa :: Oa : OA ; that is, OD : OM : : OM : OA ; and since triangles of the same altitude are to one another as their bases, and that the altitude eD is the same for the triangles ODa, OMff, ОЛгг, it follows, from the proportion... | |
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From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the... 
