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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

Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...follows that: (1) Triangles having equal bases and equal altitudes are equal. (2) Two triangles are to each other as the products of their bases by their altitudes. (3) Triangles having equal altitudes are to each other as their bases. (4) Triangles having equal bases...
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Robbin's New Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...equal bases are to each other as then" altitudes. Proof : ('."). 370. COROLLARY. Any two triangles are to each other as the products of their bases by their altitudes. Proof : (?). PROPOSITION VI. THEOREM 372. The area of a trapezoid is equal to half the product of the...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...respectively. What is the ratio of If to T? AREAS OF POLYGONS PROPOSITION II. THEOREM 329. Two rectangles are to each other as the products of their bases by their altitudes. Hypothesis. Rectangle M has base b and altitude a ; rectangle N has base b' and altitude a'. Conclusion....
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Helps in school

William Emer Miller - Mnemonics - 1920 - 124 pages
...hypotenuse of a right angle is equal to the sum of the square on the other two sides. Two rectangles are to each other as the products of their bases by their altitudes. In the illustration below the bases and altitudes are emphasized to remind you of the fact that they...
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Miller's Mind Training for Children: A Practical Training for ..., Volume 3

William Emer Miller - Mnemonics - 1921 - 120 pages
...with others. Another example of emphasizing the important lines as in the Theorem : Two rectangles are to each other as the products of their bases by their altitudes. In the illustration below the bases and altitudes are emphasized to remind you of the fact that they...
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A Geometry Reader

Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...a unit of length. Det.: To prove that R -=- U or R is equal to ab. Proof: As any two rectangles are to each other as the products of their bases by their altitudes, we have R : U = (a) (b) : (1)(1), or in fractional form, -yr-' ~ i~~T> or R=a&- (See 250.) QED Perhaps...
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