| William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...greater or less than the radius. COB. 3. Spheres of equal radii or of equal diameters are congruent. VI. **Theorem. Every section of a sphere made by a plane is a circle.** HYPOTH. ABC is a plane section of the sphere, whose centre is M. To BE PROVED. ABC is a circle. PROOF.... | |
| De Volson Wood - Geometry, Analytic - 1882 - 360 pages
...sphere, and equations (1), (2), (3), of Article 386 will be the equation of a tangent plane. EXAMPLES. 1. **Every section of a sphere made by a plane is a circle. Let** 5 be a vector perpendicular to the plane, d the scalar of 5, r the radius of the sphere, p the vector... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...the arcs of the same great circles on opposite sides of the sphere. Proposition 1. Theorem.—Every **section of a sphere made by a plane is a circle. Let** ABC be any section of a sphere made by a plane; it is a circle. Take D, the centre of the sphere, and... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...of a sphere are equal; all the diameters are equal, and each is double the radius. THEOREM XXVI. 92. **Every section of a sphere made by a plane is a circle. Let** ABD be a section made by a plane cutting the sphere whose centre is C; then is ABD a circle. Draw CE... | |
| George Anthony Hill - Geometry - 1880 - 348 pages
...are circles differing in size, the largest being that which passes through the centre of the orange. **Every section of a sphere made by a plane is a circle.** If the section passes through the centre of the sphere, it is called a great circle ; in all other... | |
| French Ensor Chadwick - Merchant marine - 1880 - 222 pages
...SENIOR PUPIL TEACHERS — SIXTH YEAH. SPHERICAL TRIGONOMETRY. (Time allowed, 3 hours.) 1. Prove that **every section of a sphere made by a plane is a circle.** 2. In spherical triangle ABC, given a — 87° 10' 15", ft = 62° 36' 45", and c=100° 10' 15"; find... | |
| Charles Scott Venable - 1881 - 380 pages
...points. The demonstration is exactly the same as that of Proposition III., Book II. PROPOSITION II. **THEOREM. Every section of a sphere, made by a plane, is a circle. Let** AMD be a section made by a plane in the sphere whose centre is C. From the point C, draw CO, perpendicular... | |
| Education, Higher - 1881 - 504 pages
...zenith, the zenith distance and altitude of a star, arimuth, solstice, oblate spheroid. 6. Prove : **Every section of a sphere made by a plane is a circle.** Any two great circles bisect the one the other. 7. Explain the causes of solar and lunar eclipses.... | |
| Edward Olney - Geometry - 1883 - 352 pages
...is a Diameter. The diameter is equal to twice the radius. CIRCLES OF THE SPHERE. PROPOSITION I. 649. **Theorem. — Every section of a sphere made by a plane is a circle.** DEMONSTRATION. Let AFEBD be a section of a sphere, whose centre is O, made by a plane; then is the... | |
| F. B. Stevens - Examinations - 1884 - 202 pages
...are respectively equal to three faces similarly placed including a triedral angle of the other. 9. **Every section of a sphere made by a plane is a circle.** 10. Between what two limits does the sum of the angles of a spherical triangle lie? Write expressions... | |
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