...semicircle describes a circle whose plane 1s 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...

...whose bases are the two bases of the frustum, and a mean proportional between them. THEOREM VII. 353. 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 center, C, draw CD perpendicular...

...third. 8. A triangular pyramid is one-third of a triangular prism of the game base and altitude. 9. Every section of a sphere made by a plane is a circle. 10. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite...

...positions are parallel to iach other, and whose center remains constantly upon he axis. JJow, since every section of a sphere made by a plane is a circle, we may take the equations of a sphere and a plane as the two equations of the circle which generates...

...passing through the centre, and terminated on both sides by the surface. It is equal to two radii. 16. Every section of a sphere made by a plane is a circle. (For proof, consult some work on geometry, as Chauvenet's Geometry, p. 245.) MOUNTING AND OPERATING...

...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...

...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...

...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...

...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...

...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....