 | 1876 - 646 pages
...are respectively equal to three faces similarly placed including a Jtriedral 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... | |
 | Robert Potts - Geometry - 1876 - 446 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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...a sphere, any circular sector, as ACD or DCE, describes a spherical sector. PROPOSITION I. THEOREM. Every section of a sphere made by a plane is a circle. Let ABD be a section made by a plane in a sphere whose centre is C. From the point C draw CE perpendicular... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...the sphere is inscribed in the cylinder or cone. GEOMETRY. BOOK VIII. PROPOSITION I. THEOREM. 678. Every section of a sphere made by a plane is a circle. Let the section ABC be a plane section of a sphere whose centre is 0. We are to prove section ABC a circle.... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...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... | |
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THEOREM. Every section of a sphere, made by a plane, is a circle. 
