 | James Elliot - 1852 - 106 pages
...whole circle of which EGF forms a part, and c, that of the circle forming the base of the cone. Since the circumferences of two circles are to each other as their radii, C:c::CB:ED, and £ C:1<;::CB:AB. But C: arc EGF :: 360° : Z ECF (Euc. vi, 33). .-. £ C-:£arcEGF::90°:ZECG.... | |
 | George Salmon - Conic sections - 1855 - 376 pages
...indefinitely near lines of equal length are at right angles to the line joining their extremities. Ex. 2. The circumferences of two circles are to each other as their radii. If polygons of the same number of sides be inscribed in the circles, it is evident, by similar triangles,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...quantity. Therefore, the area of the circle is the common limit of S and s. PROPOSITION XV.— THEOREM. 37. 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,... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...the areas of the polygons will become ultimately equal to the area of either of them. PROPOSITION 3i. 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. Let a regular polygon... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...quantity. Therefore, the area of the circle is the common limit of S and «. PROPOSITION XV— THEOREM. 37. 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,... | |
 | 1876 - 646 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.... | |
 | Harvard University - 1876 - 554 pages
...upon that side. 6. Similar polygons are to eaoli other as the squares of their homologous sides. 7. 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. PROBLEMS. 8. To divide a given straight... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...areas are to each other as the squares of their apothems (P. 1, Cor. ), which was to be proved. Cor. 1. The 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... | |
 | George Anthony Hill - Geometry - 1880 - 348 pages
...doubled, trebled, quadrupled, etc., c will be doubled, trebled, quadrupled, etc. ; in other words, — The circumferences of two circles are to each other as their radii, or as their diameters. § 210. An arc may be measured in degrees, minutes, and seconds (angular measure),... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...indefinitely ; and the area of the circle is the limit of the areas of these polygons. PROPOSITION VIII. 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. Corollary I. The circumferences of... | |
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The circumferences of two circles are to each other as their radii. Given C and C" the circumferences of two © whose radii are R and R', respectively. 
