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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

Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...greater or less than the radius. COB. 3. Spheres of equal radii or of equal diameters are congruent. VI. Theorem. Every section of a sphere made by a plane is a circle. HYPOTH. ABC is a plane section of the sphere, whose centre is M. To BE PROVED. ABC is a circle. PROOF....

The Elements of Coordinate Geometry: In Three Parts: 1. Cartesian Geometry ...

De Volson Wood - Geometry, Analytic - 1882 - 360 pages
...sphere, and equations (1), (2), (3), of Article 386 will be the equation of a tangent plane. EXAMPLES. 1. Every section of a sphere made by a plane is a circle. Let 5 be a vector perpendicular to the plane, d the scalar of 5, r the radius of the sphere, p the vector...

The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...the arcs of the same great circles on opposite sides of the sphere. Proposition 1. Theorem.—Every section of a sphere made by a plane is a circle. Let ABC be any section of a sphere made by a plane; it is a circle. Take D, the centre of the sphere, and...

An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...of a sphere are equal; all the diameters are equal, and each is double the radius. THEOREM XXVI. 92. Every section of a sphere made by a plane is a circle. Let ABD be a section made by a plane cutting the sphere whose centre is C; then is ABD a circle. Draw CE...

A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 348 pages
...are circles differing in size, the largest being that which passes through the centre of the orange. Every section of a sphere made by a plane is a circle. If the section passes through the centre of the sphere, it is called a great circle ; in all other...

Report on the Training Systems for the Navy and Mercantile Marine of England ...

French Ensor Chadwick - Merchant marine - 1880 - 222 pages
...SENIOR PUPIL TEACHERS — SIXTH YEAH. SPHERICAL TRIGONOMETRY. (Time allowed, 3 hours.) 1. Prove that every section of a sphere made by a plane is a circle. 2. In spherical triangle ABC, given a — 87° 10' 15", ft = 62° 36' 45", and c=100° 10' 15"; find...

Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 pages
...points. The demonstration is exactly the same as that of Proposition III., Book II. PROPOSITION II. THEOREM. Every section of a sphere, made by a plane, is a circle. Let AMD be a section made by a plane in the sphere whose centre is C. From the point C, draw CO, perpendicular...

The Cambridge Examiner, Volume 1

Education, Higher - 1881 - 504 pages
...zenith, the zenith distance and altitude of a star, arimuth, solstice, oblate spheroid. 6. Prove : Every section of a sphere made by a plane is a circle. Any two great circles bisect the one the other. 7. Explain the causes of solar and lunar eclipses....