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" Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions. "
Elements of Geometry: With Practical Applications to Mensuration - Page 199
by Benjamin Greenleaf - 1863 - 320 pages
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 264 pages
...2. Two triangles having equal bases are to each other as their altitudes. 3. Any two triangles are to each other as the products of their bases by their altitudes. PROP. VI. THEOREM. 316. The area of a trapezoid is equal to one-half the sum of its bases multiplied...
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...parallelograms having equal bases are to each other as their altitudes; and any two parallelograms are to each other as the products of their bases by their altitudes. 260. 261. Cor. V. Can you show how to find the area of any triangle ? 262. Cor. VI. Can you show that...
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Plane Geometry

George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...Proof. Draw the altitudes CO and C'O'. A ACB ABxCO AB CO B' A A'C'B' A'B ' X C'O' A'B' C'O' (two A are to each other as the products of their bases by their altitudes). But 405 AB CO A'B ' C'O' 361 (the homologous altitudes of two similar A have the same ratio as...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...prism is equal to the product of its base by its altitude. That is, V=BXH. QED 629. COR. Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes...
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...parallelogram is equal to the product of its base by its altitude. 333. Cor. II. Parallelograms are to each other as the products of their bases by their altitudes; consequently, parallelograms which have equal altitudes are to each other as their bases, parallelograms...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...parallelograms having equal bases are to each other as their altitudes. 3. Any two parallelograms are to each other as the products of their bases by their altitudes. PROP. V. THEOREM. 312. The area of a triangle is equal to one-half the product of its base and altitude....
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 196 pages
...2. Two prisms having equivalent bases are to each other as their altitudes. 3. -Any two prisms are to each other as the products of their bases by their altitudes. 289 PYRAMIDS. DEFINITIONS. 502. A pyramid is a polyedron bounded by a polygon, called the base, and...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...the altitudes CO and C'O'. A ACB ABx CO AB CO Ihen ^^7^7 = A , B , x c , <) , = ^ * ^o, (two A are to each other as the products of their bases by their altitudes). But 7& = 7&' 361 (the homologous altitudes of two similar A have the same ratio as any two homologous...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...altitude a. But the sum of the bases of the triangular prism equals B. .-.V=Bxa. 570. COR. 1. Prisms are to each other as the products of their bases by their altitudes. i 572. COR. 3. Prisms that have equal altitudes are to each other as their bases. 573. COR. 4. Prisms...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 370 pages
...altitude a. But the sum of the bases of the triangular prism equals B. .:V=Bxa. 570. COR. 1. Prisms are to each other as the products of their bases by their altitudes. 572. COR. 3. Prisms that have equal altitudes are to each other as their bases. 573. COK. 4. Prisms...
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