| Benjamin Greenleaf - Geometry - 1861 - 628 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 whoso centre is C. From the centre, C, draw CD perpendicular... | |
| Benjamin Greenleaf - Geometry - 1862 - 520 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 centre is C. From the centre, C, draw CD perpendicular... | |
| Benjamin Greenleaf - Geometry - 1863 - 320 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... | |
| 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... | |
| Adrien Marie Legendre - Geometry - 1863 - 455 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, CA one of its radii, and AMB any section made by a plane : then will this... | |
| Eli Todd Tappan - Geometry, Modern - 1864 - 292 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.** 252 But if the section do not pass through the center, as DGF, then from the center C let CI fall perpendicularly... | |
| 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
...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... | |
| Benjamin Greenleaf - Geometry - 1866 - 328 pages
...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 centre is C. From the** centre, C, draw* CD perpendicular to the plane ABE; and draw the lines CA, CB, CE, to different points... | |
| 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... | |
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