 | Thomas Hill - Geometry - 1863 - 136 pages
...analogous to that in which they are used of a circle. 436. All radii of a sphere are, then, equal. 437. Every section of a sphere made by a plane is a circle. Proof. Let fall from the centre a perpendicular upon the plane. Join the centre to all parts of the... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 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. Let ABE be a section made by a plane in the sphere whose center is C. From the centre, C, draw CD perpendicular... | |
 | Euclides - 1864 - 448 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... | |
 | William Harris Johnston - 1865 - 478 pages
...and a line passing through tho centre and meeting the surface in two opposite points, is a diameter. Every section of a sphere, made by a plane, is a circle. A section through tho centre is termed a great circle of tho sphere ; any other, a small circle. A... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...a sphere when it contains only one point in common with the surface of the sphere. PROPOSITION' i. Every section of a sphere made by a plane is a circle Let AZBX be a sphere whose centre is O. Let XPZ be a section made by the plane XZ. From O draw OC perpendicular... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...generated by the motion of a straight line, every possible section of it is a curve. 8ECANT PLANE8. 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... | |
 | Edward Brooks - Geometry - 1868 - 284 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... | |
 | 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. BOOK IX. B The oblique lines CA, CB, CE are equal, being radii of the sphere ; therefore they are equally... | |
 | Robert Potts - 1868 - 434 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... | |
 | William Thomas Read - Nautical astronomy - 1869 - 176 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... | |
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Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C. 
