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" It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle. "
The Principles of Analytical Geometry: Designed for the Use of Students - Page 253
by Henry Parr Hamilton - 1826 - 326 pages
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The elements of plane trigonometry

John Charles Snowball - 1837 - 322 pages
...INDEX. CHAPTER I. ON CERTAIN PROPERTIES OF SPHERICAL TRIANGLES. AВТ. ГЛОК 1. DEF. A Sphere 1 2, 3. Every section of a sphere made by a plane is a circle 1 4. Objects of SPHERICAL TRIGONOMETRY 2 6. Def. POLES and Axis of a circle 3 8. The Pole of a circle...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...the diameters also are equal, and each double of the radius. 439. It will be demonstrated, art. 452, that every section of a sphere made by a plane is a circle. This being supposed, we call a great circle the section made by a plane which passes through the centre,...
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Arithmetical Spyglass and Teacher's Assistant: Intended as a Key and ...

Charles Waterhouse - Arithmetic - 1842 - 180 pages
...spherical polygon is a part of the surface of a sphere terminated by several arcs of great circles. 30. Every section of a sphere made by a plane, is a circle ; hence, a great circle is the section made by a plane which passes through the centre, and a small...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...sector, as DCF or FCH, describes a solid, which is named a spherical sector. PROPOSITION I. THEOREM. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere, whose centre is C. From the point C, draw CO...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845 - 542 pages
...this volume, is used to denote because; when applied in algebraic notation. 4 PROPOSITION I. THEOREM. Every section of a sphere, made by a plane, is a circle. Let j\MB be a section, made by a plane, in 'the sphere, whose centre is C. From the point G, draw CO...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...sector, as DCF or FCH, describes a solid, which is named a spherical sector. PROPOSITION I. THEOREM. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere, whose centre is C. From the point C, draw CO...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - Mathematics - 1846 - 500 pages
...any line passing through the centre and bounded by the surface is called a diameter of the sphere. 3. Every section of a sphere made by a plane is a circle. Let EDF be any such section of a sphere, of which the centre is O. Draw OC from O perpendicular to...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...that all the diameters are equal, and each double of the radius. 3. It will be demonstrated (Prop. 1) that every section of a sphere made by a plane is a circle ; this being assumed, A great circle of a sphere is the section made by a plane passing through the...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...FG will, at the same time, be the diameter of the circumscribed circle. PROPOSITION VIII. THEOREM. Every section of a sphere, made by a plane, is a circle. Let AMB be the section, made by a plane in the sphere whose B/ centre is C. From the point C, draw...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...a sphere are equal ; and all its diameters are also equal, and double of the radius. 419. Theorem. Every section of a sphere made by a plane is a circle. Proof. From the centre C (fig. 178) of the sphere draw the perpendicular CO to the section AMB and...
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