...Conversely, 2. The diameter equals the square root of the quotient obtained by dividing the area by .7854. 3. The areas of two circles are to each other as the squares of their diameters. NOTE.—The area of an ellipse equals the product of its twodiameters as factors...

...2Rw. Cor. 2.—The diameter is equal to the circumference divided by 3.14159, or D = — THEOREM XXII. The areas of two circles are to each other as the squares of their diameters. The same construction being used as in the last theorem, it may be shown as before,...

...more difficult. APPLICATION TO SIMPLE QUESTIONS IN THE ELEMENTS OF GEOMETRY. 1. The surfaces of any two circles are to each other as the squares of their radii. Let S, S7 be the surfaces of any two circles, and R, B/ their radii. These surfaces, we know, are the limits...

...indefinitely ; and the area of the circle is the limit of the areas of these polygons. PROPOSITION VIII. The circumferences of two circles are to each other as their radii, and their areas are to each other as the squares of their radii. Corollary I. The circumferences of circles...

...^r, b = irs2 (p. 124, No. 1). mu « rt Tl3' r2 Therefore - = — - = --• b TT.S- s3 In other words, the areas of two circles are to each other as the squares of their radii. 10. How is the circumference, and also the area, of a circle changed if the radius is doubled ? trebled...

...circumference. 425. COR. 2. The area of a circle equals IT times the square of its radius. 426. Con. 3. The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and PJ the radii, 427. COR. 4. Similar arcs, being like parts...

...their radii. Then o = wr, b = 7rs8 (p. 124, No. 1) . Therefore « = ^='l b irs2 s3 In other words, the areas of two circles are to each other as the squares of their radii. 10. How is the circumference, and also the area, of a circle changed if the radius is doubled ? trebled...

...hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. 2d. The areas of two circles are to each other as the squares of their radii, diameters, or circumferences. 1. The two sides of a right-angled triangle are 3 and 4 feet ; what is...

...Theorem. Similar arcs are as their radii. 220. Theorem. Arc of n° = •-£- X 2irr. ouO 222. Theorem,. Two circles are to each other as the squares of their radii, or of their diameters. 223. Theorem. Similar sectors are to each other as the squares of their radii....

...Theorem. Similar arcs are as their radii. 220. Theorem. Arc of n° = £- X 2irr. ooO 222. Theorem. Two circles are to each other as the squares of their radii, or of their diameters. - 223. Theorem. Similar sectors are to each other as the squares of their radii....