| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since **any two prisms are to each other as the products of their bases** and altitudes, if the altitudes be equal, they will be to each other as their bases simply; hence,... | |
| Charles Davies - Geometry - 1854 - 436 pages
...the solidity of any polygonal prism, is equal to the product of its base by its altitude. Cor. Since **any two prisms are to each other as the products of their bases** and altitudes, if the altitudes be equal, they will be to each other as their bases simply; hence,... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 630 pages
...prisms, are to each other as the products of perimeters of their bases and altitudes. The volumes of **any two prisms are to each other as the products of their bases** and altitudes. 4. The sections made in the same prism by secant parallel planes are equal polygons.... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...was to be proved. Cor. Any two prisms are to each other as the products of their bases and altitudes. **Prisms having equal bases are to each other as their...equal altitudes are to each other as their bases.** B PROPOSITION XV. THEOREM. Two triangular pyramids having equal bases and equal altitudes^ are equal... | |
| Edward Brooks - Geometry - 1868 - 294 pages
...etc. Cor. 1. Any two prisms are to each other as the products of their bases and altitudes. Cor. 2. **Prisms having equal bases are to each other as their...equal altitudes are to each other as their bases.** THEOREM VII. Similar triangular prisms are to each other as the cubes of their homologous edges. Let... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...the base ABCDE of the given prism multiplied by its altitude. 39. Corollary. Prisms having equivalent **bases are to each other as their altitudes ; prisms...prisms are to each other as the products of their bases** and altitudes. PYRAMIDS. 40. Definitions. A pyramid is a polyedron bounded by a polygon and triangular... | |
| Charles Davies - Geometry - 1872 - 464 pages
...two prisms are to each other as the products of their bases and altitudes. Prisms having equal basea **are to each other as their altitudes. Prisms having...equal altitudes are to each other as their bases.** PROPOSITION XV. THEOREM. Two tr1angular pyramids having equal bases and equal altitudes, are equal... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...the base ABCDE of the given prism multiplied by its altitude. 39. Corollary. Prisms having equivalent **bases are to each other as their altitudes ; prisms having equal altitudes are to each** othef as their bases ; and any two prisms are to each other as the prod i of their bases and altitudes.... | |
| William Frothingham Bradbury - Geometry - 1872 - 124 pages
...three dimensions. 71. In a cube the square of a diagonal is three times the square of an edge. 72. **Prisms are to each other as the products of their bases by their altitudes.** (25.) 74. Polygons formed by parallel planes cutting a pyramid are as the squares of their distances... | |
| William Frothingham Bradbury - Geometry - 1872 - 256 pages
...three dimensions. 71. In a cube the square of a diagonal is three times the square of an edge. 72. **Prisms are to each other as the products of their bases by their altitudes.** (25.) 73. Prisms \vith equivalent bases are as their altitudes; with equal altitudes, as their bases.... | |
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