...OM, and 2 thus r— will approach unity. OD (The argument continues the same as in I.) 441. THEOREM. The circumferences of two circles are to each other as their radii. Given : Two © whose radii ,..• P' are -B and R' and circumferences, C and c' respectively. To Prove...

...circumference and area. Ex.3. The diameter of a circle is 25. Find the circumference and area. 447. THEOREM. The areas of two circles are to each other as the squares of their radii, and as the squares of their diameters. To Prove: S : S' = .B2: R'2= D2: D'Z. ... S:s'=R2:R'2=tf: D'2...

...be indefinitely increased, OD will approach 0.ET, and OE thus .will approach unity. OD 441. THEOREM. The circumferences of two circles are to each other as their radii. Given : Two © whose radii are B and B' and circumferences, C and C' respectively. To Prove : C : C'...

...— PROPORTIONAL AREAS The areas of two squares are to each other as the squares of their lengths. The areas of two circles are to each other as the squares of their diameters. Observe that the ratio of the areas of the above squares is î (or }). But the...

...are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. 339. Let s be the area, and c the arc, of a sector of a O, whose...

...the apothem of a regular polygon inscribed in a circle whose radius is OA'. PROP. XIII. THEOREM 331. The circumferences of two circles are to each other as their radii. Proof. 1. Inscribe similar regular polygons whose perimeters are P and P, in ® whose radii are R and...

...the apothem of a regular polygon inscribed in a circle whose radius is OA'. PROP. XIII. THEOREM 331. The circumferences of two circles are to each other as their radii. To Prove = - (1) Proof. 1. Inscribe similar regular polygons whose perimeters are P and P', in ® whose...

...hundred and fourteen square miles. And this progression in size would be due to the geometrical fact that the areas of two circles are to each other as the squares of their radii. The steam railways can do much in distributing the population, but their general use is limited in...

...volume of a body of gas (F) is inversely proportional to the pressure (P). (d) The areas (A and A') of two circles are to each other as the squares of their radii (R and R1). (e) The number of men (m) is inversely proportional to the number of days (d) required...

...yd., SC = 85 yd., CD = 22 yd., AD = 80 yd., and diagonal BD = 91 yd. PROPOSITION XV. THEOREM. 489. The circumferences of two circles are to each other as their radii. Given C and C', the circumferences, and R and R', the radii, respectively, of two Os. To prove g =...