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" 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 are to each other as their bases ; prisms having equivalent bases and equal... "
Elements of Geometry and the First Principles of Modern Geometry - Page 170
by Wm. H. H. Phillips - 1878 - 209 pages
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1882 - 434 pages
...entire base by the altitude of the prism. -QED 544. COROLLARY. Prisms having equivalent bases are io each other as their altitudes ; prisms having equal...bases; and any two prisms are to each other as the product of their bases and altitudes. Any two prisms having equivalent bases and equal altitudes are...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...was to be proved. Cor. Any two prisms are to each other as the products of their bases and altitudes. Prisms having equal bases are to each other as their...equal altitudes are to each other as their bases. PROPOSITION XV. THEOREM. Two triangular pyramids having equul bases and equal altitudes are equal in...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...COROLLARY. Two pyramids having equivalent bases are to each other as their altitudes ; two pyramids having equal altitudes are to each other as their bases ; and any two pyramids are to each other as the products of their bases by their altitudes. Two pyramids having equal...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 166 pages
...altitude. 548. COROLLARY. Two prisms having equivalent bases are to each other as their altitudes ; two prisms having equal altitudes are to each other as their bases ; and ariy two prisms are to each other as the products of their bases by their altitudes. Two pris'ms having...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...sum of their bases, or the base of the given prism, multiplied by the common altitude. 613. COR. 2. Two prisms are to each other as the products of their bases and altitudes; two prisms having equivalent bases are to each other as their altitudes ; two prisms...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 398 pages
...other as their bases. 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. PYRAMIDS. DEFINITIONS. 510. A pyramid is a polyedron bounded by a polygon, and a series of triangles...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...any prism is measured by the product of its base and altitude. QED 536. COR. Prisms having equivalent bases are to each other as their altitudes; prisms...equal altitudes are to each other as their bases ; and prisms are to each other as the products of their bases and altitudes. EXERCISE 732. Two triangular...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 68 pages
...two prisms are to each other as the products of their bases and altitudes ; prisms having equivalent bases are to each other as their altitudes ; prisms...having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent. 596. The lateral area of a regular...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 564 pages
...D 677. COR. I. Two prisms having equivalent bases and equal altitudes are equivalent. 678. COR. II. Any two prisms are to each other as the products of their bases and altitudes. Hint. — Prove as in 387. 67.9. COR. III. Two prisms having equivalent bases are...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...ADE—F = ADE X AF. Adding these equalities, we have vol. ABCDE—F= ABCDE X AF. QED 46C. COR. 1.—Any two prisms are to each other as the products of their bases and altitudes. COR. 2.—Prisms having equal altitudes are to each other as their bases. COR. 3.—Prisms...
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