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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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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...606. THEOREM. Two prisms having equivalent bases are to each other as their altitudes. ( 607. THEOREM. Any two prisms are to each other as the products of their bases by their altitudes. ORIGINAL EXERCISES 1. How many faces has a parallelepiped? Edges? Vertices? How many faces has a hexagonal...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 338 pages
...other as their bases. 3. Two prisms having equivalent bases are to each other as their altitudes. 4. Any two prisms are to each other as the products of their bases by their altitudes. ' Ex. 18. The volume of a right prism whose base is a regular hexagon is 600. One side of the base...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...SUGGESTION. The cylinder may be regarded as the limit of an inscribed prism. 597. Exercise 1. Show that two prisms are to each other as the products of their bases and altitudes. (Why ?) (Why ?) 2. Show that two prisms with equal bases are to each other as their...
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Elements of Solid Geometry

William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...prisms are to each other as the product oj their bases by their altitudes; prisms having equivalent bases are to each other as their altitudes; prisms...equal altitudes are to each other as their bases. THE PYRAMID. 638. A pyramid is a polyhedron, one of whose faces, called the base, is a polygon, and...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 220 pages
...V=BH. QED 800. Cor. I. Prisms having equivalent bases equal altitudes are equivalent. and 801. Cor. n. Any two prisms are to each other as the products of their bases and their altitudes. 1. 2. 3. 4.. 5. 6. REASONS 54, 15. 612. 732. 797. 54,2. 309....
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 pages
...be drawn from these statements ? Write the proof in full. 540. COROLLARY 1. Prisms having equivalent bases are to each other as their altitudes; prisms...equal altitudes are to each other as their bases. Write the proof in full. 541. COROLLARY 2. Prisms having equivalent bases and equal altitudes are equivalent....
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Solid Geometry

John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 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...equal altitudes are to each other as their bases; and prisms having equivalent bases and equal altitudes are equivalent. These relations are indicated thus:...
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Solid Geometry

Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...of the bases of the A prisms X h. 6. .:V=bh. 6. Ax. 9. O..ED 552. COB. 2. Prisms having equivalent bases are to each other as their altitudes ; prisms...equal altitudes are to each other as their bases. EXERCISES: GROUP 103 If b denotes the area of the base, and h the altitude, find the volume of the...
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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...equivalent. COR. II. Prisms having equivalent bases which lie in parallel planes are equivalent. COR. III. Any two prisms are to each other as the products of their bases and altitudes. COR. IV. Two prisms having equivalent bases are to each other as their altitudes. •...
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