| Edward Brooks - Geometry - 1868 - 294 pages
...expression for the volume of a frustum of a cone is (*& -f nr* + *B X r) X i .2". 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... | |
| Eli Todd Tappan - Geometry - 1868 - 432 pages
...generated by 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 Greenleaf - 1868 - 338 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.** BOOK IX. B The oblique lines CA, CB, CE are equal, being radii of the sphere ; therefore they are equally... | |
| Robert Potts - 1868 - 410 pages
...two great circles of a sphere, is measured by the arc of a great circle which joins their poles. ,35. **Every section of a sphere made by a plane is a circle** : and if two parallel planes cut a sphere so that the sections are equal, they are equidistant from... | |
| Benjamin Greenleaf - 1869 - 516 pages
...PROPOSITION I. — THEOREM. 516. Every section of a sphere made by a plane is a circle. Let ABE be a **section made by a plane in the sphere whose centre is C. From the** centre, C, draw CD perpendicular to the plane ABE; and draw the lines CA, CB, CE, to different points... | |
| Isaac Stone - Educational tests and measurements - 1869 - 278 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. vm. 6. The solidity of a sphere is equal to its surface multiplied by a third of its radins.... | |
| Isaac Stone - Educational tests and measurements - 1869 - 276 pages
...4. The solidity of a Cone is equal to its base multiplied by a third of its altitude. PBB VIII. 5. **Every section of a sphere, made by a plane, is a circle.** P. VII. B. vm. 6. The solidity of a sphere is equal to its surface multiplied by a third of its radius.... | |
| William Thomas Read - Nautical astronomy - 1869 - 154 pages
...of the sphere on which the circle is drawn. 11. All great circles bisect one another. 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... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...of the circle; and this diameter* is called the axis of the circle. PROPOSITION VII.— THEOREM. 28. **Every section of a sphere made by a plane is a circle. Let** abc be a plane section of the sphere whose centre is O. All the straight lines Oa, Ob, etc., drawn... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...all the diameters aie also equal, and each double of the radius. 3. It will be shown (Prop. I.), that **every section of a sphere made by a plane is a circle.** A great circle is a section made by a plane which passes through the center of the sphere. Any other... | |
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