| Edward Albert Bowser - Geometry - 1890 - 420 pages
...on which the student should draw the diagrams of spherical surfaces. Proposition 1 . Theorem. 664. **Every section of a sphere made by a plane is a circle.** Hyp. Let ACB be a plane section of the sphere whose centre is 0. To prove that ACB is a Q. Proof. Draw... | |
| George Albert Wentworth - Geometry - 1888 - 466 pages
...each other when their surfaces have one, and only one,- point in common. PROPOSITION I. THEOREM. 685. **Every section of a sphere made by a plane is a circle. Let** 0 be the centre of a sphere, and ABD any section made by a plane. To prove that, the section ABD is... | |
| William C. Bartol - Geometry, Solid - 1893 - 112 pages
...tangent to the sphere. The polyedrou is then circumscribed about the sphere. PROPOSITION XXVI. 173. **THEOREM. Every section of a sphere made by a plane is a circle.** The section through the centre is a circle (166). Let ABC be any section not through the centre 0;... | |
| William Chauvenet - 1893 - 340 pages
...a circular cone passes through the centres of all the sections parallel to the base. PROPOSITION V. **Every section of a sphere made by a plane is a circle.** Corollary T. The axis of a circle on a sphere passes through the centre of the circle. Corol/nry II.... | |
| George Clinton Shutts - Geometry - 1894 - 412 pages
...only one point, as О and S, Fig. 3. 624. The point at which the line, FIG. 3. PROPOSITION IX. 625. **Theorem. Every section of a sphere made by a plane is a circle. Let** the plane MN intersect the sphere 0 in the section AS B. To prove that the section ASB is a circle.... | |
| Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...product of its slant height by the sum of the perimeters of its bases. PROPOSITION IX. PROPOSITION X. **Every section of a sphere made by a plane is a circle.** PROPOSITION XI. Two intersecting great circles of a sphere bisect each other. PROPOSITION XII. Three... | |
| Webster Wells - Geometry - 1894 - 400 pages
...this case the sphere is said to be circumscribed about the polyedron. PROPOSITION V. THEOREM. 581. A **section of a sphere made by a plane is a circle. Let** ABC be a section of tie sphere APC made by a plane. To prove ABC a circle. Let O be the centre of the... | |
| Michigan. Department of Public Instruction - Education - 1895 - 686 pages
...Can there be a spherical triangle whose sides are 78°, 113° and 31° ? Explain. 3. Demonstrate— **Every section of a sphere made by a plane is a circle.** 4. Demonstrate — The diagonals of a paral lelopiped bisect each other. 5. Demonetate — The angle... | |
| John Macnie - Geometry - 1895 - 390 pages
...both ways by the surface. 585. COR. All diameters of a sphere are equal. PROPOSITION V. THEOREM. 586. **Every section of a sphere made by a plane is a circle.** Given : A plane section ABC of a sphere whose center is O ; To Prove : ABC is s, circle. 1°. If the... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...line drawn through the centre and terminated at both ends by the surface. PROPOSITION IX. THEOREM 8O3, **Every section of a sphere made by a plane is a circle** whose centre is the foot of the perpendicular from the centre of the sphere on that plane. p' GIVEN... | |
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