 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...6. The radius of a circle is 4: find the area of the inscribed square. Proposition 8. Theorem. 433. The circumferences of two circles are to each other...circles are to each other as the squares of their radii. Hyp. Let C and 0' be the Oces, R and It' the radii, and S and S' the areas of the two Os. To prove... | |
 | Edward Albert Bowser - Geometry - 1891 - 424 pages
...perimeter of a regular inscribed polygon of double the number of sides. Proposition 8. Theorem. 433. Tlie circumferences of two circles are to each other as...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... | |
 | 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... | |
 | Yale University - 1892 - 200 pages
...right angle ? Why ? 5. On a given straight line to construct a polygon similar to a given polygon ? 6. 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. II. — SOLID AND SPHERICAL GEOMETRY.... | |
 | William Chauvenet - 1893 - 340 pages
...as the number of sides of the polygons is indefinitely increased. PROPOSITION VIII.—THEOREM. 18. 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. Let J2 and R' be the radii of the circles,... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...of two circles, R and R' their radii, and D and D' their diameters. Then, I . 5*1 = =»!. That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. 373. COR. III. A sector is the same part of the circle that its... | |
 | 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 of their radii, or as the squares of their diameters. 373. COR. III. A sector is the same part of the circle that its... | |
 | 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... | |
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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 R 
