| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...demonstrations. (Cours tie Gu'metrie Elemenlaire, par Vincent et Bourdon.) PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as...their radii. Let C denote the circumference of one of A f! \ B / the circles, R its radius OA, A its area ; and let C' denote the circumference of the other... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...regarded as a polygon of an infinite number of sides. BOOK VI. PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as...their radii. Let C denote the circumference of one of j^ff \ B; the circles, R its radius 0A, A its area ; and let C' denote the circumference of the other... | |
| Benjamin Greenleaf - Geometry - 1861 - 638 pages
...are to each other as the squares of their radii. Let C denote the circumference of one of A fl \ B / the circles, R its radius OA, A its area; and let...the circumference of the other circle, r its radius 0 B, A' its area ; then will C : C' : : R : r, and A : A' : : R2 : r1. Inscribe within the given circles... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...therefore, may be regarded as a polygon of an infinite number of sides. PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as...their radii. Let C denote the circumference of one of A /! \ B /./ \\ 1 - i -r. A". \\ "*-•. " the circles, K \j "---..... \\ its radius OA, |\ /J A its... | |
| Benjamin Greenleaf - Geometry - 1863 - 502 pages
...therefore, may be regarded as a polygon of an infinite number of sides. PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as...their radii. Let C denote the circumference of one of A // \ B / ^v /./ \ \ the circles, R its radius OA, A its area; and let C' denote the circumference... | |
| Benjamin Greenleaf - Geometry - 1866 - 328 pages
...demonstrations. (Cours de Geometrie Ele'mentaire, par Vincent et Bourdon.) PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as...the circumference of the other circle, r its radius 0 B, A1 its area ; then will C : C' : : R : r, and A : A' : : R2 : r\ Inscribe within the given circles... | |
| Benjamin Greenleaf - Geometry - 1868 - 340 pages
...regarded as a polygon of an infinite number of sides. BOOK VI. PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as...their radii. Let C denote the circumference of one of ^fi \ B, the circles, R its radius 0A, A its area; and let C' denote the circumference of the other... | |
| Benjamin Greenleaf - 1869 - 516 pages
...may be regarded as a polygon of an infinite mimber of sides. 159 PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as...circumference of one of the circles, R its radius 0A, A its area; and let C' denote the circumference of the other circle, r its radius 0B, A- its area;... | |
| Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...PROPOSITION XIII. THEOREM. The circumferences of circles are to each othe/ as their radii, and the areas are to each other as the squares of their radii. Let C and 0 be the centres of two circles whose radii are CA and OB : then will the circumferences be to... | |
| |