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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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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...and PD2.Ť Hence the solidity of the frustum of the cone is measured by iŤOP x (OA2+PD2+ AO x PD). PROPOSITION VII. 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 perpendicular...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...radii of 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. Demonstration. From the centre C (fig. 178) of the sphere draw the perpendicular CO to the section...
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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 and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 359 pages
...PD). PROPOSITION VII. 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 perpen- ť, dicular to the plane AMB ; and different lines CM, CM, to different points of the curve...
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Arithmetical Spyglass and Teacher's Assistant: Intended as a Key and ...

Charles Waterhouse - Arithmetic - 1842 - 166 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 Geometry and Trigonometry

Geometry - 1843 - 404 pages
...175 PROPOSITION VII. 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 CU perpen- A dicular to the plane AMB ; and different lines CM, CM, to different points of the curve...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...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 perpendicu- A, lar to the plane AMB ; and different lines CM, CM, to different points of the curve...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...circular 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 perpend icular...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 244 pages
...occurs in this volume, is used to denote because ; when applied in algebraic notation. 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 perpendicu-...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...occurs in 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 perpend...
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