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" ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude. "
Elements of Plane and Solid Geometry - Page 179
by George Albert Wentworth - 1877 - 398 pages
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...necessary to suppose P and Q parallelograms to prove this. (See also th. 19.) THEOREM LX. Rectangles are to each other as the products of their bases by their altitudes. For, in the last figure, let the two rectangles P and Q be unequal, and be placed as before. Then (th....
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...other as their bases. •.' ~ ' • . PROPOSITION I. THEOREM. Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to sayf as: the products of their three dimensioiis. For, having placed the two solids AG,...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...denotes its ratio to the unit of surface. 241. Theorem. Two rectangles, as ABCD, JlEFG (fig. 127) are to each other as the products of their bases by their altitudes, that is, ABCD : AEFG = AB Proof, a. Suppose the ratio of the bases AB to AE to be, for example, as...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...each other'as the cubes oi their homologous edges. as their altitudes ; and pyramids generally are to each other as the products of their bases by their altitudes. Scholium. The solidity of any polyedron may be found by dividing it into pyramids, by planes passing...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...3. Two pyramids having equivalent bases are to each other as their altitudes. Cor. 4. Pyramids are to each other as the products of their bases by their altitudes. Scholium. The solidity of any polyedral body may be computed, by dividing the body into pyramids ;...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...AG : sol. AK : : ABx AD : AOxAM. PROPOSITION X. THEOREM. 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. For, baring placed the two solids AG, AZ,...
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Iconographic Encyclopaedia of Science, Literature, and Art, Volume 1

Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...base, are to each other as their altitudes ; of the same altitude, as their bases ; and generally, parallelograms are to each other as the products of their bases by their altitudes. The areas of two squares are to each other as the squares of their sides. The areas of two similar...
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Young Scientist: A Practical Journal for Amateurs, Volume 1

1851 - 716 pages
...base, are to each other as their altitudes ; of the same altitude, as their bases ; and generally, parallelograms are to each other as the products of their bases by their altitudes. The areas of two squares are to each other as the squares of their sides. The areas of two similar...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...altitudes AD, s \ base AM. GEOMETKY. PROPOSITION XIII. THEOEEM. Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is, as the products of their three dimensions. Having placed the two solids AGj AZ, so that...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...as their bases. 190 GEOMETRY. PROPOSITION XIII. THEORESt. Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is, as the products of their three dimensions. E H M — Having placed the two solids AG, AZ,...
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