 | Adrien Marie Legendre - 1852 - عدد الصفحات: 436
...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 - 1854 - عدد الصفحات: 436
...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 - 1855 - عدد الصفحات: 628
...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 - 1863 - عدد الصفحات: 464
...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 - 1868 - عدد الصفحات: 284
...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 - 1871 - عدد الصفحات: 380
...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 - 1872 - عدد الصفحات: 464
...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 - 1872 - عدد الصفحات: 382
...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 - 1872 - عدد الصفحات: 124
...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 - 1872 - عدد الصفحات: 262
...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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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... 
