| 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... | |
| Charles Taylor - Mathematics - 1881 - 486 pages
...* Bee Sloritz Cantor's Euclid und tein Jahrhundert p. 2 (Zeitschrift. f. Math. n. Physik. Suppl 1. 1867). circles are as the squares of their diameters...circumscribed to a sphere. The editio princeps of the Erot^cta was published at Basel in 1533 [p. 82]: the Arabic version at Rome in 1594. The Oxford Graeco-latin... | |
| Charles Taylor - Mathematics - 1881 - 512 pages
...Moritz Cantor's Euclid and $ein Jahrhundert p. 2 (Zcitscluift. f. Hath, u, Fhysik. Suppl I. 1807). circles are as the squares of their 'diameters (prop....altitude* (prop. 10), and the volumes of spheres are aa the cubes of their diameters (prop. 18). In the 13th book, which is a sequel to the 4th, it is shewn... | |
| 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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