 | C. Davies - 1867 - 342 pages
...expression for the volume of a frustum of a cone is OR 2 + ^ + *R X r) X 3 H. THE SPHERE. THEOREM VII. Every section of a sphere made by a plane is a circle. Let C be the centre of a sphere whose radius is CA, and ADB any section made by a plane; then will this... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...all the diameters are equal, and each double of the radius. 3. It will be demonstrated (Prop. 1) that every section of a sphere made by a plane is a circle; this being assumed, A great circle of a sphere is the section made by a plane passing through the centre... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...expression for the volume of a frustum of a cone is (*It? -f nr* + icR X f) Xi S. THE SPHERE. THEOREM VII. Every section of a sphere made by a plane is a circle. Let G be the centre of a sphere whose radius is CA, and ADB any section made by a plane; then will this... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. — THEOREM. 515. Every section of a sphere made by a plane is a circle. The oblique lines CA, CB, 0 E are equal, being radii of the sphere; therefore they are equally distant... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...the motion of a straight line, every possible section of it is a curve. SECANT PLANES. 744. Theorem.- Every section of a sphere made by a plane is a circle. But if the section do not pass through the center, as DGF, then from the center C let CI fall perpendicularly... | |
 | Benjamin Peirce - 1868 - 200 pages
...of a sphere are equal; and all its diameters are also equal, and double of the radius. 419. Theorem. Every section of a sphere made by a plane is a circle. Proof. From the centre C (fig. 178) of the sphere draw the perpendicular CO to the section JIMB and... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...frustum, and a mean proportional between them; which was to be proved. PROPOSITION VII. THEOREM. Any section of a sphere made by a plane, is a circle. Let C be the centre of a sphere, GA one of ita radii, and AMB any section made by a plane: then will this... | |
 | William Thomas Read - Nautical astronomy - 1869 - 176 pages
...centre of every great circle is the centre of the sphere on which the circle is drawn. Proposition I. Every section of a sphere, made by a plane, is a circle. Fig. 10. Let the sphere BFD be cut through in one direction by the plane surface BODE, then the section... | |
 | Benjamin Peirce - Geometry - 1869 - 194 pages
...a sphere are equal ; and all its diameters are also equal, and double of the radius. 419. Theorem. Every section of a sphere made by a plane is a circle. Proof. From the centre C (fig. 178) of the sphere draw the perpendicular CO to the section AMB and... | |
 | Isaac Stone - Educational tests and measurements - 1869 - 272 pages
...The solidity of a Cone is equal to its base multiplied by a third of its altitude. P. 5. B. VIII. 5. Every section of a sphere, made by a plane, is a circle. P. VII. B. VIII. • 6. The solidity of a sphere is equal to its surface multiplied by a third of its... | |
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(1). Every section of a sphere made by a plane is a circle. Let 
