 S' denote the areas of two © whose radii 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.  New Plane Geometry - Page 168by Webster Wells - 1908 - 298 pagesFull view - About this book
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...Proposition 8. Theorem. 433. The circumferences of two circles are to each other as their radii, and the areas of two circles are to each other as the squares of their radii. Hyp. Let C and C' be the Oces, R and R' the radii, and S and S' the areas of the two Os. To prove C... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...equal to the area of four great circles. 791. COR. 2. The areas of the surf/,ct.s of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 792. COR. 3. The area of a zone is iqual to the product of its altitude by the circumference of a great... | |
 | George Anthony Hill - 1891 - 206 pages
...their radii. Then a = nr', b = wx- (p. 124, No. 1.) Therefore a = ^ = ?f. b 7TS2 S3 In other words, Me areas of two circles are to each other as the squares of their radii. 10. How is the circumference, nnd also the area, of a circle changed if the radius is doubled? trebled?... | |
 | Horatio Nelson Robinson - Arithmetic - 1892 - 428 pages
...II. The hypotenuse is equal to the square root of the sum of the squares of the other two sides. III. The areas of two circles are to each other as the squares of their radii, diameters, or circumferences. IV. The base or perpendicular of a right-angled triangle is equal to... | |
 | Horatio Nelson Robinson - Arithmetic - 1892 - 428 pages
...II. The hypotenuse is equal to the square root of the sum of the squares of the other two sides. III. The areas of two circles are to each other as the squares of their radii, diameters, or circumferences. IV. The base or perpendicular of a right-angled triangle is equal to... | |
 | George Albert Wentworth - Algebra - 1892 - 312 pages
...sides, or the squares of their radii, or the squares of their apothems. The areas of two circles are as the squares of their radii, or as the squares of their diameters. 323. If a rod 3 ft. high casts a shadow 2 ft. long, how high is a tree which casts a shadow 60 ft.... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...spheres upon which they are situated. COmpare § 206. ^ 308. COR. 3. The surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. V ^ 309. COR. 4. The area of a zone is equal to the product of its altitude % the circumference of... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...circles, _E and R' their radii, and D and D' their diameters. Then S vR ^ R * ' S' ! That is, tfAe areas of two circles are to each other as the squares...their radii, or as the squares of their diameters. 373. COR. III. A sector is the same part of the circle that its arc is of the circumference. Hence,... | |
 | John Tilden Prince - Arithmetic - 1894 - 160 pages
...Can you show that circumferences of circles are to each other as their radii ? 13. Can you show that areas of two circles are to each other as the squares of their radii ? 14. Can you draw an ellipse ? Can you show that the sum of the distances of every point in the boundary... | |
 | Webster Wells - Geometry - 1894 - 400 pages
....A. Ji (§ 320.) ,.'2 That is, the areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems. PROPOSITION VI. THEOREM. 351. The area of a regular polygon is equal to one-half the product... | |
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