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" ... triangles are to each other as the products of their bases by their altitudes. "
Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ... - Page 562
by Charles Davies, William Guy Peck - 1859 - 592 pages
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 490 pages
...226. Cor. Parallelograms having equal bases are to each other as their altitudes, and parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION VI....
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 490 pages
...226. Cor. Parallelograms having equal bases are to each other as their altitudes, and parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION VI....
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...226. Cor. Parallelograms having equal bases are to each other as their altitudes, and parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION VI....
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 320 pages
...226. Cor. Parallelograms having equal bases are to each other as their altitudes, and parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION VI....
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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 239 pages
...522. COR. 2. — Pyramids having equivalent bases are to each other as their altitudes; such as have equal altitudes are to each other as their bases; and, in general, pyramids are to each other as the products of their bases and altitudes. ELEMENTARY SOLID GEOMETRY....
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872
...522. COR. 2. — Pyramids having equivalent bases are to each other as their altitudes; such as have equal altitudes are to each other as their bases; and, in general, pyramids are to each other as the products of their bases and altitudes. ELEMENTARY SOLID GEOMETRY....
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New Elementary Geometry: With Practical Applications; a Shorter Course, Upon ...

Benjamin Greenleaf - Geometry - 1873 - 176 pages
...188. Cor. Parallelograms having equal bases are to each other as their altitudes, and parallelograms having equal altitudes are to each other as their bases ; and, in general, parallelograms are to each other as the products of their bases by their altitudes. THEOREM VI. 189....
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New Elementary Geometry with Practical Applications

Benjamin Greenleaf - Geometry - 1874 - 176 pages
...188. Cor. Parallelograms having equal bases are to each other as their altitudes, and parallelograms having equal altitudes are to each other as their bases; and, in general, parallelograms are to each other as the products of their bases by their altitudes. THEOREM VI. 189....
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 398 pages
...QED 325. COROLLARY 1. Triangles having equal bases and equal altitudes are equivalent. 326. COR. 2. Triangles having equal bases are to each other as...having equal altitudes are to each other as their bases ; any two triangles are to each other as the product of their bases by their altitudes. PROPOSITION...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 443 pages
...triangle is equal to one half of the product of BC by AD. Therefore the area of a triangle, etc. Cor. 1. Triangles having equal altitudes are to each other as their bases, and triangles having equal bases are to each other as their altitudes. Cor. 2. Equivalent triangles whose...
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