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" THEOREM. Every section of a sphere, made by a plane, is a circle. "
Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ... - Page 196
by James Bates Thomson - 1844 - 237 pages
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Syllabus of Geometry

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...
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Elements of Geometry

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—...
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Documents of the Senate of the State of New York, Volume 11

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...
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Elements of Geometry

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 —...
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Elements of Geometry

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...
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Plane and Solid Geometry

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...
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Plane and Solid Geometry

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...
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Solid Geometry, Volumes 6-9

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...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

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...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

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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