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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. "
Elements of Geometry and Trigonometry: With Notes - Page 161
by Adrien Marie Legendre - 1830 - 316 pages
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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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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 354 pages
...The volume of a right prism is equal to the product of its edge into its base. 594. COROLLARY 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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