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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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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 294 pages
...expression for the volume of a frustum of a cone is (*& -f nr* + *B X r) X i .2". THE SPHERE. THEOREM VII. Every section of a sphere made by a plane is a circle. Let C be the centre of a sphere whose radius is CA, and ADB any section made by a plane; then will this...
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 432 pages
...generated by the 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...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 338 pages
...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. BOOK IX. B The oblique lines CA, CB, CE are equal, being radii of the sphere ; therefore they are equally...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...two great circles of a sphere, is measured by the arc of a great circle which joins their poles. ,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...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...PROPOSITION I. — THEOREM. 516. 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 centre is C. From the centre, C, draw CD perpendicular to the plane ABE; and draw the lines CA, CB, CE, to different points...
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The Elementary and Complete Examiner: Or, Candidate's Assistant: Prepared to ...

Isaac Stone - Educational tests and measurements - 1869 - 278 pages
...The solidity of a Cone is equal to its base multiplied by a third of its altitude. P. 5. B. VIII. 5. Every section of a sphere, made by a plane, is a circle. P. VII. B. vm. 6. The solidity of a sphere is equal to its surface multiplied by a third of its radins....
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The Elementary and Complete Examiner: Or, Candidate's Assistant: Prepared to ...

Isaac Stone - Educational tests and measurements - 1869 - 276 pages
...4. The solidity of a Cone is equal to its base multiplied by a third of its altitude. PBB VIII. 5. Every section of a sphere, made by a plane, is a circle. P. VII. B. vm. 6. The solidity of a sphere is equal to its surface multiplied by a third of its radius....
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The theory of navigation and nautical astronomy, together with the elements ...

William Thomas Read - Nautical astronomy - 1869 - 154 pages
...of the sphere on which the circle is drawn. 11. All great circles bisect one another. Proposition I. Every section of a sphere, made by a plane, is a circle. Fig. 10. Let the sphere BFD be cut through in one direction by the plane surface BODE, then the section...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...of the circle; and this diameter* is called the axis of the circle. PROPOSITION VII.— THEOREM. 28. Every section of a sphere made by a plane is a circle. Let abc be a plane section of the sphere whose centre is O. All the straight lines Oa, Ob, etc., drawn...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...all the diameters aie also equal, and each double of the radius. 3. It will be shown (Prop. I.), that every section of a sphere made by a plane is a circle. A great circle is a section made by a plane which passes through the center of the sphere. Any other...
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