 | Charles Hutton - Mathematics - 1811 - 406 pages
...prisms ; then will the prism CD be to the prism GH, as ABS to BE3 or AD' to EH'. For For the solids are to each other as the product of their bases and altitudes (th. 110, cor. 2), that is, as AC . AD to EG . EH. But the bases, being similar planes, are to each... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...prisms ; then will the prism CD be to the prism GH, as AB3 to EFS or AD' to EH". For For the solids are to each other as the product of their bases and altitudes (th. 1 10, cor. 2), that is, as AC . AIT to EG . EH. But the bases, being similar planes, are to each... | |
 | George Clinton Whitlock - Mathematics - 1848 - 340 pages
...+ b). h, becomes T = ±ah. Fig. 323. Cor. 3. Parallelograms are to each other, and triangles (149) are to each other, as the product of their bases and altitudes. Cor. 4. Parallelograms of the same or equal altitudes are (150) to each other as their bases. Cor.... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...that the solids are to each other as the cubes of any other homologous sides. Cor. Since cylinders are to each other as the product of their bases and altitudes (Th. xiv. Cor.), it follows that similar cylinders are to each other as the cubes of the linear dimensions.... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...that the solids are to each other as the cubes of any other homologous sides. Cor. Since cylinders are to each other as the product of their bases and altitudes (Th. xiv. Cor.), it follows that similar cylinders are to each other as the cubes of the linear dimensions.... | |
 | Charles Davies - Geometry - 1855 - 340 pages
...shown that the solids are to each other as the cubes of any other homologous edgesCor Since cylinders are to each other as the product of their bases and altitudes (Th- xiv- Cor-), it follows that similar cylinders are to each other as the cubes of the linear dimensions... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...altitudes, or having equal altitudes, are to each other as their bases. Generally, any two parallelopipedons are to each other as the product of their bases and altitudes. PA-RAM'E-TEK. [Gr. параметры, to measure with another thing]. A name given to a constant quantity... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...similar prisms; then will the prism CD be to the prism GH as AB3 to EF3, or as AD3 to EH3. For the solids are to each other as the product of their bases and altitudes (Prop. 5, Cor. 2) ; that is, as AC . AD to EG . EH. But the bases, being similar plsfties, are to each... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...BE; hence, the area of the parallelogram is equal to AB X BE. Therefore, etc. Cor. 1. Parallelograms are to each other as the product of their bases and altitudes. Cor. 2. Parallelograms having equal altitudes are to each other as their bases; and parallelograms... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...Cor. 1. A cone is equal to one-third of a cylinder having an equal base and an equal altitude. Cor. 2. Cones are to each other as the product* of their bases and altitudes. Cones having equal bases are to each other as their altitudes. Cones having equal altitudes are to... | |
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The volumes of two pyramids (cones) are to each other as the product of their bases and altitudes... 
