| Charles Davies, William Guy Peck - Mathematics - 1872 - 602 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** base» and altitudes. 4. The sections made in the same prism by secant parallel planes are equal polygons.... | |
| Adrien Marie Legendre - Geometry - 1874 - 500 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...having equal altitudes are to each other as their** buses. B PROPOSITION XV. THEOREM. Two triangular pyramids having equal bases and equal altitudes, are... | |
| William Chauvenet - Geometry - 1875 - 390 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. Any two prisms having equivalent bases and equal altitudes are equivalent. PYRAMIDS.... | |
| William Chauvenet - Geometry - 1875 - 466 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 other as their** base's; and any two prisms are to each other as the product* of their bases and altitudes. Any two... | |
| William Guy Peck - Conic sections - 1876 - 376 pages
...of the given prism is equal to the product of its base and altitude, which was to be proved. Cor. 1. **Any two prisms are to each other as the products of their bases** and altitudes. Cor. 2. Two similar prisms are to each other as the cubes of their homologous edges.... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...that is the entire base by the altitude of the prism. QED 544. COROLLARY. Prisms having equivalent **bases are to . each other as their altitudes ; prisms...bases ; and any two prisms are to each other as the** product of 'their bases and altitudes. Any two prisms having equivalent bases and equal altitudes are... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...that is the entire base by the altitude of the prism. QED 544. COROLLARY. Prisms having equivalent **bases are to each other as their altitudes ; prisms...other as their bases : and any two prisms are to each** "'""r as the product of their bases and altitudes. Any two '» urns havi- ^nt bases and equal altitudes... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...323. Cor. 2. Parallelograms having equal bases are to each other as their altitudes ; parallelograms **having equal altitudes are to each other as their bases ; and any two** parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.... | |
| Elias Loomis - Conic sections - 1880 - 452 pages
...their ba&es. For the same reason, prisms having equivalent bases are to each other as their altitudes ; **and any two prisms are to each other as the products of their bases** and altitudes. PROPOSITION xu. THEOREM. Similar %irisms are to each other as the cubes of their homologous... | |
| George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...323. Cor. 2. Parallelograms having equal bases are to each other as their altitudes ; parallelograms **having equal altitudes are to each other as their bases ; and any two** parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V.... | |
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