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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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A Treatise on Plane and Spherical Trigonometry

Robert Woodhouse - 1819 - 264 σελίδες
...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. 3.)...

Elements of Geometry

Adrien Marie Legendre - 1819 - 208 σελίδες
...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 J1MB (Jig. 221) be a section, made by a plane, of the sphere of which...

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1822 - 367 σελίδες
...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 perpendicular...

The Builder's Complete Guide: Comprehending the Theory and Practice of the ...

Charles Frederick Partington - 1825 - 304 σελίδες
...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

Adrien Marie Legendre - 1825 - 224 σελίδες
...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...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 σελίδες
...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,...

A Synopsis of the Principal Formulae and Results of Pure Mathematics

Charles Brooke - 1829 - 358 σελίδες
...(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...

A Syllabus of a Course of Lectures Upon Trigonometry, and the Application of ...

Henry Pearson - 1833 - 137 σελίδες
...the centre, the equation of the sphere is the same for all positions of the rectangular axes. 208. Every section of a sphere made by a plane is a circle. Let the inclination of the cutting plane to the plane of xy be 0; and let us assume the common section...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 σελίδες
...solidity of the frustum of the cone is measured by i«OP 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...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1837 - 159 σελίδες
...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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