...the pyramid is the spherical polygon intercepted by the same planes. Proposition I. — Theorem. 515. 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 centre, C, draw CD perpendicular...

...follows that similar cylinders are to each other as the cubes of the linear dimensions. THEOREM XX. Every section of a sphere, made by a plane, is 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...

...analogous to that in which they are used of a circle. 436. All radii of a sphere are, then, equal. 437. Every section of a sphere made by a plane is a circle. Proof. Let fall from the centre a perpendicular upon the plane. Join the centre to all parts of the...

...analogous to that in which they are used of a circle. 436. All radii of a sphere are, then, equal. 437. Every section of a sphere made by a plane is a circle. Proof. Let fall from the centre a perpendicular upon the plane. Join the centre to all parts of the...

...frustum, and a mean proportional between them ; which was to be proved. PROPOSITION VII. THEOREM. Any section of a sphere made ~by a plane, is a circle. Let G be the centre of a sphere, GA one of its radii, and AMB any section made by a plane : then will this...

...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. —THEOREM. 515. Every section of a sphere made by a plane is a circle. The oblique lines CA, CB, CE are equal, being radii of the sphere ; therefore they are equally distant...

...follows that similar cylinders are to each other as the cubes of the linear dimon»ions. THEOREM XX. Every section of a sphere, made by a plane, is 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...

...one point; and at that point the radius of the sphere will be perpendicular to the line or plane. 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...

...motion of a straight line, every possible section of it is a curve. SECANT PLANES. 744. Theorem.— Every section of a sphere made by a plane is a circle. But if the section do not pass through the center, as DGF, then from the center C let CI fall perpendicularly...

...and a lino passing through tho centre and meeting the surface in two opposite points, is a diameter. Every section of a sphere, made by a plane, is a circle. A section through the centro is termed a great circle of tho sphere; any other, a small circle. A sphere...