| George Albert Wentworth - Mathematics - 1896 - 68 pages
...and R and r are the radii of its bases, and H is its altitude, BOOK VIII. THEOREMS AND PROBLEMS. 685. **Every section of a sphere made by a plane is a circle.** 686. Cor. 1. The line joining the centre of a sphere to the centre of a circle of the sphere is perpendicular... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 374 pages
...straight line drawn through the centre and terminated at both ends by the surface. PROPOSITION IV. **THEOREM 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. GIVEN—... | |
| New York (State). Legislature. Senate - Government publications - 1897 - 1306 pages
...that two triangular pyramids having equivalent bases and equal altitudes are equivalent. 13 Prove that **every section of a sphere made by a plane is a circle.** 14-15 Prove that the area of the surface of a sphere is equal to the product of its diameter by the... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...line drawn through the centre and terminated at both ends by the surface. PROPOSITION IX. THEOREM 803. **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. GIVEN —... | |
| George Washington Hull - Geometry - 1897 - 408 pages
...equally distant from every point in the circumference of the circle. PROPOSITION I. THEOREM. 56(>. **Every section of a sphere made by a plane is a circle.** Given—ADB a section of a sphere made by a plane. To Prove—ABED a circle. Dem.—Draw OP perpendicular... | |
| James Howard Gore - Geometry - 1898 - 232 pages
...a plane figure whose boundary is the intersection of its plane with the surface of the sphere. 479. **Every section of a sphere made by a plane is a circle** (see 334). When the plane passes through the centre, the section is called a Great Circle. 480. Every... | |
| George Albert Wentworth - Geometry - 1899 - 500 pages
...each other when their surfaces have one, and only one, point in common. PROPOSITION I. THEOREM. 743. **Every section of a sphere made by a plane is a circle. Let** 0 be the centre of the sphere, and ABD any section made by a plane. To prove that the section ABD is... | |
| George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...only one, point in common with the surface of the sphere. THE SPHERE. PROPOSITION 1. THEOREM. 743. **Every section of a sphere made by a plane is a circle. Let** 0 be the centre of the sphere, and ABD any section made by a plane. To prove that the section ABD is... | |
| Harvard University - Geometry - 1899 - 39 pages
...cone is equal to one third the product of its base and its altitude. BOOK IX. THE SPHERE. THEOREM I. **Every section of a sphere made by a plane is a circle.** Corollary I. All great circles of the same sphere are equal. Corollary IL Every great circle divides... | |
| Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...Spheres having the same centre and one point m common must coincide throughout. PROPOSITION I 583. The **section of a sphere made by a plane is a circle. Let** O be the centre of the given sphere and A, B, C three points on the section made by any plane L. It... | |
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