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 Books Books Theorem. Every section of a sphere made by a plane is a circle. An Elementary Treatise on Plane and Solid Geometry - Page 132
by Benjamin Peirce - 1871 - 150 pages ## A Treatise on Plane and Spherical Trigonometry

Robert Woodhouse - Geometrical optics - 1819 - 264 pages
...called rectangular, isosceles, equilateral, in the same cases that a plane triangle is. PROPOSITION I. Every section of a sphere made by a plane is a circle. Let An Em be the plane, draw CO * perpendicular to it, which consequently, (by Euclid, Book XI. Def.... ## Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...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,... ## Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 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 the section, made by a plane, in the sphere whose centre is C. From the point C, draw CO... ## Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...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,... ## The Builder's Complete Guide: Comprehending the Theory and Practice of the ...

Charles Frederick Partington - Building - 1825 - 344 pages
...be circles, provided that the axis of the cylinder, or cone, tend to the centre of the sphere. For every section of a sphere made by a plane is a circle, and every section of a right cylinder, or cone, perpendicular to the axis, is also a circle. Let the... ## Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...circular sector as DCF, or FCH, describes a solid which is called a spherical sector. THEOREM. 452. Every section of a sphere made by a plane is a circle. Fig. 221. Demonstration. Let AMB (fig. 221) be a section, made by a plane, of the sphere of which C... ## The Principles of Analytical Geometry ...

Henry Parr Hamilton - Geometry, Analytic - 1826 - 326 pages
...the resulting expression reduced, we have which is the equation to a circle. Whence it appears that every section of a sphere, made by a plane, is a circle. 327. PROF. 5. To find the equation to a tangent plane drawn through a given point (x', y , z) of the... ## Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...circular sector, as DCF or FCH, describes a solid, which is named a spkericat sector. * THEOREM. 452. 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... ## A Synopsis of the Principal Formulae and Results of Pure Mathematics

Charles Brooke - Mathematics - 1829 - 358 pages
...(W. Ch. v; L. 72—84; Leg. 53—7; C. 559—615.) SPHEEICAL TRIGONOMETRY. (21.) General Principles. Every section of a sphere made by a plane is a Circle. The distance between the poles of two great circles is equal to the inclination of their planes. The... 