| Silvestre François Lacroix - Calculus - 1816 - 720 pages
...demonstrated that the convex surface of a right cone is equal to the area of a circle, whose radius is a **mean proportional between^ the side of the cone, and the radius of the circle,** which, constitutes its base: that the surface of a sphere ^quadruple the area of one of its great circles,... | |
| Thomas Leybourn - Mathematics - 1819
...the other focus. 14. The radius of a circle whose area is equal to the surface of a given cone is a **mean proportional between the side of the cone and the radius of** its base. Required a proof. io. An I»" 1 ) part of a hollow paraboloid with its vertex downwards is... | |
| Thomas Leybourn - Mathematics - 1819
...cosine is a maximum. 14. The radius of a circle whose area is equal to the surface of a given cone is a **mean proportional between the side of the cone and the radius of** its base. Required a proof. . i¿. Compare the absolute forces in the centre and circumference of a... | |
| Etienne Bézout - Calculus - 1836 - 195 pages
...Archimedes demonstrated that the convex surface of a right cone is equal to a circle which has for **its radius the mean proportional between the side of the cone and the radius of the** base, that the whole surface of a sphere is equal to that of four of its great circles, and that the... | |
| Etienne Bézout - Calculus - 1836 - 195 pages
...Archimedes demonstrated that the convex surface of a right cone is equal to a circle which has for **its radius the mean proportional between the side of the cone and the radius of the** base, that the whole surface of a sphere is equal to that of four of its great circles, and that the... | |
| ALBERT TAYLOR BLEDSOE, A.M., LL.D. - 1886
...demonstrated that the convex surface of a right cone is equal to the area of the circle which has for a **radius the mean proportional between the side of the cone and the radius of the circle of the base** ; that the total area of the sphere is equal to four great circles; and that the surface of any zone... | |
| Archimedes - Geometry - 1897 - 326 pages
...the radius of the base. By Prop. 14, the surface of the cone is equal to a circle whose radius is a **mean proportional between the side of the cone and the radius of the** base. Hence, since circles are to one another as the squares of their radii, the proposition follows.... | |
| T. L. HEATH - 1897
...the radius of the base. By Prop. 14, the surface of the cone is equal to a circle whose radius is a **mean proportional between the side of the cone and the radius of the** base. Hence, since circles are to one another as the squares of their radii, the proposition follows.... | |
| Archimedes, Sir Thomas Little Heath - Mathematics - 2002 - 377 pages
...the radius oft/me base. By Prop. 14, the surface of the cone is equal to a circle whose radius is a **mean proportional between the side of the cone and the radius of the** base. Hence, since circles are to one another as the squares of their radii, the proposition follows.... | |
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