| George Roberts Perkins - Geometry - 1860 - 443 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 - 628 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 - 520 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 - 514 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 - 320 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 - 1868 - 338 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 - 566 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 - 382 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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