 | George Roberts Perkins - Geometry - 1860 - 472 pages
...elementary geometry, they are not, on that account, less rigorous or less satisfactory. THEOREM Xn. For, in the first place, any parallelopipedon (T....the same base are to each other as their altitudes. THROREM X1II. Similar prisms are to one another as the cubss of their homologous sides. Let P and p... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...altitude, the products of the bases by the altitudes will be as the bases (Prop. IX. Bk. II.) ; hence, prisms of the same altitude are to each other as their bases. For a like reason, prisms of the same base are to each other as their altitudes. PROPOSITION XIV. — THEOREM. 47G. Similar... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...altitude, the products of the bases by the altitudes will be as the bases (Prop. IX. Bk. II.) ; hence, prisms of the same altitude are to each other as their bases. For a liko reason, prisms of the same base are to each other as their altitudes. PROPOSITION XIV. — THEOREM.... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...products of the bases by the altitudes will be as the bases (Prop. IX. Bk. II.) ; hence, prisms of ike same altitude are to each other as their bases. For a like reason, prisms of the same base are to each other as their altitudes. PROPOSITION Х1Л7". — THEOREM. 476.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...altitude, the products of the bases by the altitudes will be as the bases (Prop. IX. Bk. II.) ; hence, prisms of the same altitude are to each other as their bases. For a like reason, prisms of the same base are to each other as their altitudes. PROPOSITION XIV. — THEOREM. 476. Similar... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...altitude, the products of the bases by the altitudes will be as the bases (Prop. IX. Bk. II.) ; hence, prisms of the same altitude are to each other as their bases. For a like reason, prisms of the same base are to each other as their altitudes. PROPOSITION XIV. — THEOREM. 476. Similar... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...altitude, the products of the bases by the altitudes, will be as the bases (Prop. VIII., B. II.) ; hence prisms of the same altitude are to each other as their bases. For the same reason, prisms of the same base are to each other as their altitudes ; and prisms generally... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...— The volume of a right prism is equal to the product of Us edge into its base. 400. COK. 2. — Prisms of the same altitude are to each other as their bases ; and prisms of the same or equivalent bases are to each other as their altitudes; and, in general,... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...COR. 1. — The volume of a right prism is equal to the product of its edge into its 400, COR. 2. — Prisms of the same altitude are to each other as their bases ; and prisms of the same or equivalent bases are to each other as their altitudes; and, in general,... | |
 | Charles Scott Venable - 1881 - 380 pages
...ABCD. COR. Parallelograms of the same base are to each other as their altitudes, and parallelograms of the same altitude are to each other as their bases : for, A, B, C being any three magnitudes, we have, generally, AxC :BxC :: A : B. PROPOSITION VI. THEOREM. The... | |
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... bases simply : hence two prisms of the same altitude are to each other as their bases. For a like reason, two prisms of the same base are to each other as their altitudes. 
