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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. "
Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ... - Page 165
by George Roberts Perkins - 1856 - 235 pages
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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Elements of Geometry and Trigonometry: With Practical Applications

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....
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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....
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Elements of Geometry: With Practical Applications to Mensuration

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...
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Elements of Geometry: With Practical Applications to Mensuration

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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

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...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

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,...
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A Treatise on Special, Or Elementary Geometry

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,...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

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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