...—«,-, s a6which proves the proposition. Cor.—Since circles are similar figures, it follows that the areas of two circles are to each other as the squares of their circumferences, or of their diameters. Exercises (5). 1. The sides of a triangle are 9, 10,...

...circumferences of two circles are to each other as their radii, or as their diameters, and their areas are to each other as the squares of their radii, or as the squares of their diameters. Cor. 2. Because similar sectors and similar segments are like parts of the circles to which they belong,...

...Circumferences of circles are to each other as their radii, or as their diameters ; and the circles as the squares of their radii, or as the squares of their diameters. For circles are regular polygons of an infinite number of sides (44) ; and if the circumferences of...

...following proportions should be observed. They are sometimes useful in the solution of problems : — (1) The areas of two circles are to each other as the squares either of their circumferences or of their diameters. For circles are similar figures. (2) Either the...

...2' + 31 + 4' + . . . . + n' = 2n' + 3n'+n. "ireU known form, etc. 1. -. O. But these elements are to each other as the squares of their radii, or as the squares of their distances from the vertex of the cone. If, then, B denote the base of the cone, H its height, b any...

...Circumferences of circles are to each other as their radii, or as their diameters ; and the circles as the squares of their radii, or as the squares of their diameters. For circles are regular polygons of an infinite number of sides (44); and if the circumferences of...

...We find that the areas are to each other as the numbers i, 4, 9, 16, etc. That is, — The areas of circles are to each other as the squares of their radii (or their diameters) . § 214. Problem. — To transform a given circle into a square. By computation....

...PROPOSITION XIII. THEOREM. 1. The circumferences of two circles are to each other as their radii. 2. The areas of two circles are to each other as the squares of their radii. First. — Inscribe in the two circles whose radii are OB and CA two regular similar polygons. Let...

...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,...