 | Roswell Chamberlain Smith - 1841 - عدد الصفحات: 324
...diameters of the circles. The same is true of the arcs and chords of similar segments. 57. Circles, or their areas are to each other as the squares of their radii, diameters ot circumferences. 58. To find the area of a regular polygon, or any regular figure : Multiply... | |
 | Roswell Chamberlain Smith - 1842 - عدد الصفحات: 320
...diameters of the circles. The same is true of the arcs and chords of similar segments. 57. Circles, or their areas are to each other as the squares of their radii, diameters or circumferences. 58- To find the area of a regular polygon, or any regular figure : Multiply... | |
 | Roswell Chamberlain Smith - 1843 - عدد الصفحات: 320
...diameters of the circles. The same is true of the arcs and chords of similar segments. 57. Circles, or their areas are to each other as the squares of their radii, diameters or circumferences. 58. To find the area of a regular polygon, or any regular figure: Multiply... | |
 | James Bates Thomson - 1844 - عدد الصفحات: 268
...become equal to the circle, and equal to each other. PROPOSITION X. THEOREM. The circumferences of circles are to each other as their radii ; and their areas are as the squares of their radii. Let the circumference whose radius is CA, be designated by circ. CA... | |
 | Elias Loomis - 1849 - عدد الصفحات: 252
...equal to the product of its arc AEB by half of AC. PKOPOSITION XIII. THEOREM. The circumferences of circles are to each other as their radii, and their areas are as the squares of their radii. Let R and r denote the radii of two circles; C and c their circumferences... | |
 | Roswell Chamberlain Smith - 1850 - عدد الصفحات: 314
...diameters of the circles. The same is true of the arc* and chords of similar segments. 57. Circles, or their areas are to each other as the squares of their radii, diameters or circumferences. 58. To find the area of a regular polygon, or any regular figure : Multiply... | |
 | Elias Loomis - 1858 - عدد الصفحات: 256
...equal to the product of its arc AEB by half of AC. PROPOSITION XIII. THEOREM. The circumferences of circles are to each other as their radii, and their areas are as the squares of their radii. Let R and r denote the radii of two circles ; C and c their circumferences... | |
 | Benjamin Greenleaf - 1862 - عدد الصفحات: 518
...of an infinite number of sides. BOOK VI. PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as their radii, and their...areas are to each other as the squares of their radii. Let C denote the circumference of one of j^ff \ B; the circles, R its radius 0A, A its area ; and let... | |
 | Benjamin Greenleaf - 1861 - عدد الصفحات: 638
...a polygon of an infinite number of sides. PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as their radii, and their...areas are to each other as the squares of their radii. Let C denote the circumference of one of A fl \ B / the circles, R its radius OA, A its area; and let... | |
 | Benjamin Greenleaf - 1863 - عدد الصفحات: 504
...a polygon of an infinite number of sides. PROPOSITION XIII. — THEOREM. 376. The circumferences of circles are to each other as their radii, and their...areas are to each other as the squares of their radii. Let C denote the circumference of one of A /! \ B /./ \\ 1 - i -r. A". \\ "*-•. " the circles, K... | |
| |
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 R and R' be the radii of the circles, C and C" their circumferences, S and S 
