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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. "
New Plane and Solid Geometry - Page 138
by Webster Wells - 1908 - 298 pages
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...other as their altitudes ; parallelograms having equal altitudes are to each other as their bases ; any two parallelograms are to each other as the products of their bases by their altitudes. 368. The area of a triangle is equal to one-half the product of its base by its altitude. 369. Cor....
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Elements of Geometry, Part 1

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...386. COR. I. Parallelograms having equal bases and equal altitudes are equivalent. 387. COR. II. — Any two parallelograms are to each other as the products of their bases and altitudes. Hint, — Let the areas of the parallelograms be P and P' , their bases b and b' ' ,...
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...386. COR. I. Parallelograms having equal bases and equal altitudes are equivalent. 387. COR. II. — Any two parallelograms are to each other as the products of their bases and altitudes. Hint. — Let the areas of the parallelograms be P and f, their bases b and b' ., and...
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Elements of Geometry: Plane geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...386. COR. I. Parallelograms having equal bases and equal altitudes are equivalent. 387, COR. II.—Any two parallelograms are to each other as the products of their bases and altitudes. Hint.—Let the areas of the parallelograms be P and f, their bases b and b', and altitudes...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...— area of R = a X b, provided U is the unit of area. R axb = axb. 380 U ixi [Two rectangles are to each other as the products of their bases by their altitudes.] But — = area of R. U 374 [The area of a surface is the ratio of that surface to the unit surface.]...
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Plane Geometry

George D. Pettee - Geometry, Modern - 1896 - 272 pages
...Proposition XI, Bk. II, and Proposition X, Bk. Ill PROPOSITION III 242. Theorem. Any two rectangles are to each other as the products of their bases by their altitudes. Appl. Cons. Dem. b Prove M = abN~a'b' Construct rectangle P, as indicated Ma — = — Pa' | 1 M ab...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...respectively ; and p a second parallelogram, with a and b its altitude and base respectively. COR. 1.—Two parallelograms are to each other as the products of their bases by their altitudes. For P= A X B, and p — a X b ( 229). COR. 2.— Two parallelograms having equal bases are to each...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...other as their bases. 2. Two parallelograms having equal bases are to each other as their altitudes. 3. Any two parallelograms are to each other as the products of their bases by their altitudes. PROP. V. THEOREM. '312. The area of a triangle is equal to one-half the product of its base and altitude....
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...equal altitudes are equivalent, because they are all equivalent to the same rectangle. 253. COR. 2. Any two parallelograms are to each other as the products of their bases by their altitudes; therefore, parallelograms having equal bases are to each other as their altitudes, and parallelograms...
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...two parallelograms having equal bases are to each other as their altitudes. 260. Cor. IV. Show that any two parallelograms are to each other as the products of their bases by their altitudes. 261. Cor. V. Can you show how to find the area of any triangle? 262. Cor. VI. Can yon show that triangles...
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