 | 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... | |
 | 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... | |
 | 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... | |
 | New York (State). Legislature. Senate - Government publications - 1897 - 1306 pages
...Prove 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
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It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle. 
