 | Ireland commissioners of nat. educ - 1834 - 370 pages
...multiplying the area of the base by one-third of the height. t In solid Geometry it is proved that every cone is the third part of a cylinder having the same base and altitude ; but the solidity of a cylinder is found by multiplying the area of its base by its altitude ; therefore... | |
 | Commissioners of National Education in Ireland - 1841 - 136 pages
...the area of th base by one-third of the height. (Page 87.) 66. In solid Geometry, it is proved that every cone is the third part of a cylinder having the same base and altitude ; but the solidity of a cylinder is found by multiplying the area of its base by its altitude ; therefore,... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...of the cone is equal to one third of the product of its base multiplied by its altitude. Cor. 1. A cone is the third part of a cylinder having the same base and the same altitude ; whence it follows : 1st, That cones of equal altitudes are to each other as their... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...of the cone is equal to one third of the product of its base multiplied by its altitude. Cor. 1 . A cone is the third part of a cylinder having the same base and the same altitude ; whence it follows : 1st, That cones of equal altitudes are to each other as their... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...solidity of the cone is equal to one third of the product of its base multiplied by its altitudeCor 1 A cone is the third part of a cylinder havIng the same base and the same altitude ; whence it follows : 1st, That cones of equal altitudes are to each other as thei:... | |
 | Euclides - 1855 - 270 pages
...pyramid AB С G is equal (V. Ax. 2) to the pyramid DEFH. Therefore the bases, &c. QED PKOР. X. THEOREM A cone is the third part of a cylinder, having the same base and altitude. Let a cone and a cylinder have the same base, viz., the circle AB С D, and the same altitude. The... | |
 | C. Davies - 1867 - 342 pages
...solidity of the cone is equal to one third of the product of its base multiplied by its altitudeCor 1 A cone is the third part of a cylinder having the same base and the same altitude ; whence it follows : 1st, That cones of equal altitudes are to each other as their... | |
 | Samuel Earnshaw - Differential equations, Partial - 1881 - 602 pages
...of * See Moritz Cantor's Euclid und uin Jahrhundert p. 2 (Zeitachrift. f. Math. n. Physik. Suppl I. 1867). circles are as the squares of their diameters...circumscribed to a sphere. The editio princeps of the Srot^eta was published at Basel in 1533 [p. 82] : the Arabic version at Rome in 1594. The Oxford Grseco-latin... | |
 | George Johnston Allman - Geometry - 1889 - 266 pages
...diameters, XII. 2 : A pyramid is the third part of a prism having the same base and same height, XII. 7 ; A cone is the third part of a cylinder having the same base and same height, XII. 10; Spheres are to each other in the triplicate ratio of their diameters, XII. 18.... | |
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... solidity of the pyramid will still be equal to one third of the product of the base multiplied by the altitude, whatever be the number of sides of the polygon which forms its base- • hence, the solidity of the cone is equal to one third of the product... 