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" It will be shown that every section of a sphere made by a plane is a circle... "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 245
των William Chauvenet - 1872 - 368 σελίδες
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The Theory of Navigation and Nautical Astronomy: Together with the Elements ...

William Thomas Read - 1869 - 176 σελίδες
...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...

The Elementary and Complete Examiner: Or, Candidate's Assistant: Prepared to ...

Isaac Stone - 1869 - 278 σελίδες
...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....

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 380 σελίδες
...the centre. A sphere may be generated by the revolution of a semicircle ABC about its diameter A Cas an axis; for the surface generated by the curve ABC...its centre is the foot o of the perpendicular Oo let fall from O upon the plane of the section. 29. Corollary I All great circles, as ABC, ADCE, are equal;...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 380 σελίδες
...every diameter is double the radius, all the diameters are equal. 26. Definition. It will be shown that every section of a sphere made by a plane is a circle ; and as the greatest possible section is one made by a plane passing through the centre, such a section...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 302 σελίδες
...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...

An Elementary Geometry

William Frothingham Bradbury - 1872 - 124 σελίδες
...of a sphere are equal ; all the diameters are equal, and each is double the radius. THEOREM XIV. 58. Every section of a sphere made by a plane is a circle. Let ABD be a section made by a plane cutting the sphere whose centre is C ', then is ABD a circle. Draw...

Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1872 - 464 σελίδες
...frustum, and a mean proportional between them; which was to be proved. PROPOSITION VII. THEOREM. Any section of a sphere made by a plane, is a circle. Let C be the centre of a sphere, CA one of its radii, and AMB any section made by a plane: then will this...

Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - 1873 - 288 σελίδες
...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...

A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 472 σελίδες
...twice the radius. ELEMENTARY SOLID GEOMETRY. CIRCLES OF THE SPHERE. PROPOSITION L 533. Theorem. — Every section of a sphere, made by a plane, is a circle. P DEM. — Let AFEBD be a section of a sphere whose centre is O, made by a plane ; then is it a circle....

Solid geometry and conic sections

James Maurice Wilson - 1873 - 178 σελίδες
...semicircle describes a circle whose plane 1s at right angles to AB, and centre lies in AB. THEOREM 35. Every section of a sphere made by a plane is a circle. Let a plane RQR' cut the sphere whose centre is O ; then shall the section be a circle. Draw ON perpendicular...




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