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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

## A Treatise on Plane and Spherical Trigonometry

Robert Woodhouse - Geometrical optics - 1819 - 470 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. 3.)...

## Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 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 - 394 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,...CO perpendicular to the plane AMB ; and different A| lines CM, CM to different points of the curve AMB, which terminates the section. The oblique lines...

## Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 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 - 342 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: Designed for the Use of Students

Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 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...