 | Benjamin Peirce - Geometry - 1847 - 204 pages
...a sphere are equal ; and all its diameters are also equal, and double of the radius. 419. Theorem. Every section of a sphere made by a plane is a circle. Proof. From the centre C (fig. 178) of the sphere draw the perpendicular CO to the section AMB and... | |
 | Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...110 XIII. Examples Ill SPHERICAL TRIGONOMETRY. CHAPTER I. Р1ОЖ I. Definition of a sphere . 115 II. Every section of a sphere made by a plane is a circle 116 III. In a spherical triangle, any side is less than the sumí of the other two ) IV. The sum of... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...passing through the center, and terminated each way by the surface. 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 - 1850 - 332 pages
...FG will, at the same time, be the diameter of the circumscribed circle. PROPOSITION VIII. THEOREM. 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 perpendicularly... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...follows that similar cylinders are to each other as the cubes of the linear dimensions. THEOREM XX. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...follows that similar cylinders are to each other as the cubes of the linear dimensions. THEOREM XX. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular... | |
 | 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... | |
 | John Radford Young - Measurement - 1850 - 294 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... | |
 | 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 - 400 pages
...Treatise of 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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THEOREM. Every section of a sphere, made by a plane, is a circle. 
