 | 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 perpendicular... | |
 | United States. Congress. Senate - United States - 1880 - 1304 pages
...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";... | |
 | Henry McCormick - Geography - 1885 - 424 pages
...The diameter of a sphere is a straight line drawn through the center and terminating in the surface. Every section of a sphere made by a plane is a circle. If an orange be cut into two parts, each cut surface is a circle. A great circle of a sphere is one... | |
 | Charles Davies - Geometry - 1886 - 352 pages
...linear dimen sions. THKOREM XX. Every sect1on oj a sphere, made by a plane, 1s a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular to the plane AMB, and also draw the lines CA, CM, &c., to the points... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...sphere. In this case the sphere is circumscribed about the polyedron. 316 PROPOSITION V. THEOREM. 623. Every section of a sphere made by a plane is a circle. P Let ABC be a plane section of the sphere APC. To prove that ABC is a circle. Let 0 be the centre... | |
 | Education - 1886 - 636 pages
...pyramid is onethird of a triangular prism of the same base and altitude. ' ' 10. (80) Demonstrate that "every section of a sphere made by a plane is a circle." achy ILLINOIS SCHOOL JOURNAL. [DECEMBER, 1 ILLINOIS SCHOOL JOURNAL A MONTHLY EDUCATIONAL MAGAZINE.... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...plane of the circle; and this diameter is called the axis of the circle. PROPOSITION V.—THEOREM. 22. Every section of a sphere made by a plane is a circle. 1st. If the plane passes through the centre of the sphere, the lines joining points on the perimeter... | |
 | George Anthony Hill - Geometry - 1888 - 200 pages
...sphere. In Fig. 169 OA is a radius, and AOB is a diameter. AP 3. Define great circles and small circles. Every Section of a sphere made by a plane is a circle. If the plane pass through the centre, the circle is called a great circle ; in all other cases the... | |
 | George Anthony Hill - Geometry - 1888 - 202 pages
...sphere. In Fig. 169 OA is a radius, and AOB is a diameter. AP 3. Define great circles and small circles. Every section of a sphere made by a plane is a circle. If the plane pass through the centre, the circle is called a great circle ; in all other cases the... | |
 | De Volson Wood - Geometry, Analytic - 1890 - 372 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 fi be a vector perpendicular to the plane, d the scalar of S, r the radius of the sphere, p the vector... | |
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THEOREM. Every section of a sphere, made by a plane, is a circle. 
