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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
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An introductory treatise on mensuration, in theory and practice

John Radford Young - Measurement - 1850 - 12 pages
...the sphere; and a line through the centre meeting the surface in two opposite points is a diameter. Every section of a sphere, made by a plane is a circle ; a section through the centre is called a great circle of the sphere, any other a small circle. A...
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The Elements of Astronomy: Or, The World as it Is, and as it Appears

Anna Cabot Lowell - Astronomy - 1850 - 412 pages
...All the radii of a sphere are equal ; all the diameters are also equal, and double the radius. 2. Every section of a sphere made by a plane is a circle. If a sphere is cut by a plane which passes through the centre, the section is called a great circle...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...Archimedes himself in an edition of his works.] CHAPTER VII. THE CONE, CYLINDER, AND SPHERE. PROPOSITION I. Every section of a sphere made by a plane is a circle. 1 . Let the plane pass through the centre 0 of the sphere : then all lines drawn from the centre in...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...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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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 235 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....point C draw CO perpendicular to the plane AMB ; and draw lines CM, CM to different points of the curve AMB, which terminates the section. The oblique lines...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 444 pages
...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 - 234 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 - 443 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....point C draw CO perpendicular to the plane AMB ; and draw lines CM, CM to different points of the curve AMB, which terminates the section. The oblique lines...
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