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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. "
Plane and Solid Geometry - Page 155
by Claude Irwin Palmer, Daniel Pomeroy Taylor - 1918 - 436 pages
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Hints, Theoretical, Elucidatory, and Practical, for the Use of Teachers of ...

Olinthus Gregory - Euclid's Elements - 1840 - 208 pages
...generally, since they are respectively equivalent to the rectangles of the same bases and altitudes. Hence, parallelograms are to each other as the products of their bases and altitudes. (6.) Farther, to measure an area is to determine R R' H h R' T B b .-. R r BH bh R BH or...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...x BE\ hence, the area of the parallelogram is also equal to AB x BE ; which was to be proved. Cor. Parallelograms are to each other as the products of their bases and altitudes. If their altitudes are equal, they are to each other as their bases. If their bases are...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...other as their bases ; parallelograms having equal bases are to each other as their altitudes; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.— THEOREM. 13. The area of a triangle is equal to half the product...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...each other as their bases; parallelograms having equal bases are to each other as their altitudes; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.—THEOREM. 13. The area of a triangle is equal to half the product...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...T) FO hence, the area of the parallelogram is also equal to AB x BE ; which was to be proved. Cor. Parallelograms are to each other as the products of their bases and altitudes. If their altitudes are equal, they are to each other as their bases. If their bases are...
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...algebraically, if a = AB and b = BC (a + b) (a — i) = a'' — b* _ Produce AB so that BD — B C. ACBD 42. Parallelograms are to each other as the products of their bases and altitudes. (10.) 43. . Parallelograms having equal bases are to each other as their altitudes; those...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...algebraically, if a = AB and 5 = BC (a -fb) (a — b) = a1 — b' Produce AB so that BD = BC. -**- CBD 42. Parallelograms are to each other as the products of their bases and altitudes. (10.) 43. Parallelograms having equal bases are to each other as their altitudes; those...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...x BE: hence, the area of the parallelogram is also equal to AB x BE ; which was to be proved. Cor. Parallelograms. are to each other as the products of their bases and altitudes. If their altitudes are equal, they are to each other as their bases. If their bases are...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 412 pages
...the area of the parallelogram is also equal to the product of AC and CK, which was to be proved. Cor. Any two parallelograms are to each other as the products of their bases and altitudes. If their bases are equal, they are to each other as their altitudes ; if their altitudes...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...other as their altitudes ; parallelograms having equal altitudes are to each other as their bases ; and any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 324. The area of a triangle is equal to one-half of th...
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