Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal... Elements of Geometry: Plane and Solid - Page 272by John Macnie - 1895 - 374 pagesFull view - About this book
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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, two prisms of the... | |
| Charles Davies - Geometry - 1854 - 436 pages
...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, two prisms of the... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...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. 5 lOvery prism... | |
| Adrien Marie Legendre - Geometry - 1863 - 464 pages
...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 altitudes. Prisms...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 - 284 pages
...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 altitudes; prisms...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
...common altitude, which is the base ABCDE of the given prism multiplied by its altitude. 39. Corollary. **Prisms having equivalent bases are to each other as...equal altitudes are to each other as their bases ; and** any two prisms are to each other as the products of their bases and altitudes. PYRAMIDS. 40. Definitions.... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...common altitude, which is the base ABCDE of the given prism multiplied by its altitude. 39. Corollary. **Prisms having equivalent bases are to each other as...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.... | |
| 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... | |
| Edward Olney - Geometry - 1872 - 472 pages
...; and prisms of the same or equivalent bases are to each other as their altitudes; and, in general, **prisms are to each other as the products of their bases and altitudes.** PROPOSITION XIL 491. Theorem. — The volume of a right cylinder of revolution is equal to the product... | |
| Edward Olney - Geometry - 1872 - 562 pages
...; and prisms of the same or equivalent bases are to each other as their altitudes; and, in general, **prisms are to each other as the products of their bases and altitudes.** PROPOSITION XH. 49 1. Theorem. — The volume of a cylinder of revolution is equal to the product of... | |
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