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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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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...and E', its altitude by h, and its volume by V, we shall have V - J * A (R2 + R'" + RR'). THEOREM vI. 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...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...are equal ; all the diameters are equal, and each is double the radius. 12. It will be shown (p. 7,) that every section of A sphere, made by a plane, is a circle : this granted, a great circle is a section which passes through the centre ; a small circle, is one...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...an axis. The distance from any point of the surface to tho centre is called a radius of the sphere. Every section of a sphere made by a plane is a circle, and all sections made by planes equally distant from the centre, are equal. A circle of the sphere...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...; all the diameters are also equal, and each double of the radius. 3. It will be shown (Prop. I.), that every section of a sphere made by a plane is a circle. A great circle is a section made by a plane which passes through the center of the sphere. Any other...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 474 pages
...and R', its altitude by h, and its volume by V, we shall have V = 1 * A (R2 + K" + RK'). THEOREM VI. 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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. — THEOREM. 515. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whoso centre is C. From the centre, C, draw CD perpendicular...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. — THEOREM. 515. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whose centre is C. From the centre, C, draw CD perpendicular...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. — THEOREM. 515. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whose center is C. From the centre, C, draw CD perpendicular...
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A Second Book in Geometry

Thomas Hill - Geometry - 1863 - 136 pages
...analogous to that in which they are used of a circle. 436. All radii of a sphere are, then, equal. 437. Every section of a sphere made by a plane is a circle. Proof. Let fall from the centre a perpendicular upon the plane. Join the centre to all parts of the...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...two great circles of a sphere, is measured by the arc of a great circle which joins their poles. 35. Every section of a sphere made by a plane is a circle : and if two parallel planes cut a sphere so that the sections are equal, they are equidistant from...
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