 | Adrien Marie Legendre - 1863 - 464 pàgines
...triangular pyramid is equal to one-third of the product of its base and altitude. PROPOSITION XVII. THEOREM. The volume of any pyramid is equal to one-third of the product of its base and altitude. Let S-AB CDE, be any pyramid : then is its volume Aqual to one-third of the product of... | |
 | Eli Todd Tappan - 1864 - 288 pàgines
...volume of the prism ; that is, one-third of the product of its base by its altitude. VOLUME OF PYRAMIDS. 702. Corollary. — The volume of any pyramid is equal...sum of their bases forming the given, base (653). SIMILAR POLYEDRONS. 239 volumes of two prisms of equal altitudes are to each other as their bases.... | |
 | William Chauvenet - 1871 - 380 pàgines
...each other, and the given pyramid is one-third of the prism. 53. Corollary. The volume of a triangular pyramid is equal to onethird of the product of its base by its altitude. PROPOSITION XIX.— THEOREM. 54. The volume of any pyramid is equal to one-third of the product... | |
 | William Chauvenet - 1871 - 380 pàgines
...from its bases multiplied by its slant height. PROPOSITION VII.— THEOREM. 28. The volume of any cone is equal to one-third of the product of its base by its altitude. Let the volume of the cone be denoted by F, its base by B, and its altitude by H. Let the... | |
 | Eli Todd Tappan - 1873 - 288 pàgines
...volume of the prism ; that is, one-third of the product of its base by its altitude. VOLUME OF PYRAMIDS. 702. Corollary — The volume of any pyramid- is equal...other as their bases. The same is true of pyramids. 7O4. Corollary. — Symmetrical prisms are equivalent. The same is true of symmetrical pyramids. 71)5.... | |
 | Charles Davies - 1872 - 464 pàgines
...triangular pyramid is equal to one-third of the product of its base and altitude. PROPOSITION XVII. THEOREM. The volume of any pyramid is equal to one-third of the product of its base and altitude. Let S-AB CDE, be any pyramid: then is its volume equal to one-third of the product of... | |
 | William Chauvenet - 1872 - 382 pàgines
...each other, and the given pyramid is one-third of the prism. 53. Corollary. The volume of a triangular pyramid is equal to onethird of the product of its base by its altitude. PROPOSITION XIX— THEOREM. 54. The volume of any pyramid is equal to one-third of the product... | |
 | David Munn - 1873 - 160 pàgines
...prism. Let A = area of base, h = the height; . . A - , • A-iY. "~ A' Cor. i. — Hence it follows that the volume of any pyramid is equal to one-third of the product of its base by its altitude. triangular pyramids by passing planes through an edge, SA, and the diagonals, AD, AC, &c.... | |
 | Catherinus Putnam Buckingham - 1875 - 362 pàgines
...V=o, x=o, and hence C=o, and making x=h we have for the entire cone • that is, the volume of a cone is equal to one-third of the product of its base by its altitude, or equal to one-third of a cylinder of the same base and altitude. (247) To find the volume... | |
 | Catherinus Putnam Buckingham - 1875 - 374 pàgines
...x=o, and hence C=o, and making x=h we have for the entire cone V=«*'3 that is, the volume of a cone is equal to one-third of the product of its base by its altitude, or equal to one-third of a cylinder of the same base and altitude. (247) To find the volume... | |
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Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid... 
