...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...

...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...

...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...

...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...

...demonstrations. (Cours de Geometrie Ele'mentaire, par Vincent et Bourdon.) PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as...denote 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...

...colleges, is just as remarkable for the vicious method referred to as any other. The theorems, that ' the circumferences of circles are to each other as their radii, and the areas are to each other as the squares of the radii,' are thus disposed of by the author in question...

...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...

...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;...

...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...

...and B P. Now, what can we prove with reference to this geometrical figure, byjpure geometry ? Because the circumferences of circles are to each other as their radii (and this you have admitted), we can prove, First : — That the circumference of the circle X : the circumference...