 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...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... | |
 | John Gummere, Ezra Otis Kendall - 1854 - 484 σελίδες
...a small circle about the pole jp, at a distance equal to the obliquity of the ecliptic. Then, since the distance between the poles of two great circles is equal to the angle they make with each other, if we suppose the obliquity of the ecliptic to continue the same,... | |
 | Charles Davies - 1854 - 436 σελίδες
...lQPxOBxPCx«. hence, the solidity of the frustum of the cone is equivalent to PROPOSITION VII. THEOREM. Every section of a sphere, made by a plane, is a circle. Let AMB be any section made by a plane, in the sphere whose centre is C: then will it be a circle.... | |
 | George Roberts Perkins - 1856 - 460 σελίδες
...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. Let AMB be the section, made by a plane in the sphere whose centre is C. From the point C draw CO perpendicular... | |
 | Charles Davies, William Guy Peck - 1857 - 608 σελίδες
...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 - 1858 - 256 σελίδες
...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 - 1860 - 472 σελίδες
...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. Let AMB be the section, made by a plane in the sphere whose centre is C. From the point C draw CO perpendicular... | |
 | Benjamin Greenleaf - 1862 - 518 σελίδες
...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. — THEOREM. 515. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whose centre is C. From the centre, C, draw CD perpendicular... | |
 | Benjamin Greenleaf - 1861 - 638 σελίδες
...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. — THEOREM. 515. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whoso centre is C. From the centre, C, draw CD perpendicular... | |
 | Benjamin Greenleaf - 1863 - 504 σελίδες
...the pyramid is the spherical polygon intercepted by the same planes. PROPOSITION I. — THEOREM. 515. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whose center is C. From the centre, C, draw CD perpendicular... | |
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THEOREM. Every section of a sphere, made by a plane, is a circle. 
