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" Rectangles of the same altitude are to each other as their bases, and rectangles of the same base are to each other as their altitudes. 245. "
An Elementary Treatise on Plane and Solid Geometry - Page 73
by Benjamin Peirce - 1865 - 150 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...of the prism of which ABC is the base and SO the altitude. 415. Corollary n. Two triangular pyramids of the same altitude are to each other as their bases, and two triangular pyramids of the same base are to each other as their altitudes. THEOREM. Fig. 214. 416....
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...finally, the solidity of a cylinder is equal to the product of its base by its altitude. Cor. 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of the same base are to each other as their altitudes. Cor. 9,. Similar cylinders are to...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...solidity of a cylinder is equal to the product of its base by its altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders of the same base are to each other as their altitudes. 518. Corollary n. Similar cylinders...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...Every pyramid is a third of a prism of the same base and same altitude. 418. Corollary n. Two pyramids of the same altitude are to each other as their bases, and two pyramids of the same base are to each other as their altitudes. 419. Scholium. The solidity of...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...x AD (Prop. V.) ; hence that of the trian- B gle must be |BC x AD, or BC x ŁAD. Cor. Two triangles of the same altitude are to each other as their bases, and two triangles of the same base are to each other as their altitudes. And triangles generally, are to...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...242. Corollary. The rectangle ABCD is, consequently, by art 240, to the unit of surface, as AB X AC le unity( or as the product of its base multiplied by...altitudes. 245. Theorem. Any two parallelograms ABCD, Area of the Parallelogram. ABEF (fig. 128) of the same base and altitude are equivalent. Demonstration....
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...of the prism of which ABC is the base and SO the altitude. 415. Corollary n. Two triangular pyramids of the same altitude are to each other as their bases, and two triangular pyramids of the same base are to each other as their altitudes. THEOREM. Fig. 2H. 416....
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1841 - 186 pages
...to each other as the products of their bases by their altitudes. 387. Corollary. Pyramids or cones of the same altitude are to each other as their bases ; and those of equivalent bases are to each other as their altitudes. 888. Corollary. Pyramids or cones of...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...equal to BCxAD (Prop. VII.); hence that of the triangle must bo JRCxAD, or BCXJAD. Cor. Two triangles of the same altitude are to -each other as their bases, and two triangles of the same base are to each other as llieir altitudes. And triangles generally, are...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...finally, the solidity of a cylinder is equal to the product of its base by its altitude, Cor. 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of the same base are to each other as their altitudes. Cor. 2. Similar cylinders are to each...
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