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" ... is impossible. Cor. 3. The centre of a sphere, and the centre of any small circle of that sphere, are in a straight line perpendicular to the plane of the circle. Cor. 4. The square of the radius of any small circle is equal to the square of the radius... "
A Treatise on the Analytic Geometry of Three Dimensions - Page 276
by George Salmon - 1862 - 465 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...any small circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XL, C. l) : hence, circles which are equally distant from the centre, are equal ; and of...
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The elements of plane and spherical trigonometry. [With] Key

William Rossiter - 1868 - 186 pages
...is cut by a plane, the centre of the circle made by the section is found by drawing a perpendicular from the centre of the sphere to the plane of the circle. Сircles are said to be nearer to the centre of the sphere (and are greater) as this perpendicular...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...any small circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1) : hence, circles which are equally distant from the centre, are equal; and of...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...any small circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1) : hence, circles which are equally distant from the centre, are equal ; and...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...any small circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1): hence, circles which are equally distant from the centre, are equal ; and of...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...sphere. 586. COROLLARY II. The centre of any rirde of a sphere is the foot of the perpendicular drawn from the centre of the sphere to the plane of the circle. 587. COROLLARY III. The centres of all great circles coincide with the centre of the sphere, and all...
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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...the cone is equal to the area of that part of the sphere not included within the cone. Compute the distance from the centre of the sphere to the plane of the small circle. 78. The area of a certain small circle on a sphere of radius r is equal to the difference...
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Textbook Of Engineering Mathematics

Debashis Dutta - 2006 - 954 pages
...+ b2 + c2) (u2 + v2 + w2 - d) Proof. Since the plane ax + by + cz + e = 0 is the tangent plane then the perpendicular distance from the centre of the sphere to the plane ¡s equal to the radius of the sphere. ie, ie, a(- u) + b(- v) + c(- w) I аи + bv + cw - e I = ^/fl2...
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