 | 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... | |
 | French Ensor Chadwick - Merchant marine - 1880 - 222 pages
...square. 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... | |
 | 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... | |
 | 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... | |
 | Charles Scott Venable - 1881 - 380 pages
...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
...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... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...square. Si MOR PUPIL TEACHEHS — SIXTH YEAR. SPHERICAL TRIGONOMETRY. (Timo allowed, 3 hours.) 1. Prove that every section of a sphere made by a plane is a circle. 2. In spherical triangle А В С, given a = 87° 10' 15", Ь = 62° 36' 45", and с = 100^ 10' 15";... | |
 | James Maurice Wilson - Conic sections - 1885 - 180 pages
...semicircle describes a circle whose plane is at right angles to AB, and centre lies in AB. THEOREM 35. Every section of a sphere made by a plane is a circle. Let a plane RQR' cut the sphere -whose centre is O ; then shall the section *' be a circle. Draw ON... | |
| |
It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle. 
