| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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