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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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Plane Geometry

Edward Brooks - 1901 - 278 pages
...regarded as bases, and their bases as altitudes. PROPOSITION III. — THEOREM. Any two rectangles are to each other as the products of their bases by their altitudes. Given. — Let R and R' represent two rectangles whose bases are respectively 6 and b', and altitudes...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...altitudes; triangles having equal altitudes are to each other as their bases; any two triangles are to each other as the products of their bases by their altitudes. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to...
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University of the State of New York Bulletin

Education - 1902 - 880 pages
...perpendicular to a chord bisects the chord and its subtended arc. 4 Prove that the areas of two rectangles are to each other as the products of their bases by their altitudes. 5 Prove that two regular polygons of the same number of sides are similar. Second 6 The base of a triangle...
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Bulletin

Education - 1902 - 780 pages
...perpendicular to a chord bisects the chord and its subtended arc. 4 Prove that the areas of two rectangles are to each other as the products of their bases by their altitudes. 5 Prove that two regular polygons of the same number of sides are similar. Second 6 The base of a triangle...
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Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903
...; two triangles having equal bases are to each other as their altitudes ; and any two triangles are to each other as the products of their bases by their altitudes. 200. Corollary 111. A triangle is equivalent to one-half a parallelogram having the same base and altitude....
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...AB' 284 QED BOOK IV. PLANE GEOMETRY. PROPOSITION II. THEOREM. 397. The areas of two rectangles are to each other as the products of their bases by their altitudes. Let R and R' be two rectangles, having for their bases b and b', and for their altitudes a and a',...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...sum of the bases of the A prisms X H. = BXH. Ax. 8. .'. V=BXH. Ax. l. QED 629. COR. 1. Two prisms are to each other as the products of their bases by their altitudes; prisms having equivalent bases and equal altitiides are equivalent. PYEAMIDS Pyramid 0 PYRAMIDS 631....
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...(WhyT) QED BOOK IV. PLANE GEOMETRY PROPOSITION II. THEOREM 382. ' The areas of any two rectangles are to each other as the products of their bases by their altitudes. Given the rectangles R and R', having the bases 6 and b', and the altitudes a and a', respectively....
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...QED 234 BOOK IV. PLANE GEOMETRY PRGPOSIT ION II . TH EG RKM 382. The areas of any two rectangles are to each other as the products of their bases by their altitudes. Given the rectangles R and Rr , having the bases 1) and V ', and the altitudes a and oJ ', respectively....
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Manual of the Free High Schools of Wisconsin

Wisconsin. Department of Public Instruction - Education - 1906 - 124 pages
...102. Two rectangles having equal bases are to each other as their altitudes. 103. Two rectangles are to each other as the products of their bases by their altitudes. 104-107. The theorems which give the areas of (1), the rectangle; (2), the parallelogram; (3), the...
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