 | William Chauvenet - Geometry - 1871 - 380 pages
...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...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' their areas. Inscribe... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...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...are to each other as the squares of their radii. Let R and R' be the radii of the circles, C arid C' their circumferences, S and S' their areas. Inscribe... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...and s. PROPOSITION XV.— THEOREM. 37. The circumferences of two circles are to each other as their and their areas are to each other as the squares of their radii. Let jR and R' be the radii of the circles, C and C' their circumferences, S and S' their areas. Inscribe... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...polygons. For the apothems are to each other as the sides of the polygons (351). 3TÍ 1. COR. 2. — The circumferences of circles are to each other as their radii, and as their diameters ; since they may be considered as regular polygons of the same number of sides (352).... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...3.1422236 3.1417504 3.1416321 3.1410025 3.1415951 3.1415QJ3 3.1415928 3.1415927 PROPOSITION XIII. THEOREM. The circumferences of circles are to each other as their radii, and the areas are to each other as the squares of their radit. Let C and 0 be the centres of two circles... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...within it ; hence, the perimeters of the polygons must coincide with the circumference of the 'cjrclc, and be equal to it. 237. Scholium. Every circle, therefore,...denote the circumference of the other circle, r its radius OB, A' its area ; then will C:C'::R:r, and A : A' : : R? : r*. Inscribe within the given circles... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...4096 3.1415914 3.1415933 8192 3.1415923 3.1415928 16384 3.1415925 3.1415927 PROPOSITION XIII. THEOREM. The circumferences of circles are to each other as their radii, and the areas are to each other as the squares of their radii. Let C and 0 be the centres of two circles... | |
 | Benjamin Greenleaf - Geometry - 1875 - 204 pages
...circumscribed polygons are regular, and have the same number of sides, they are similar (Thco. I ) ; therefore, by increasing the number of the sides,...their radii. Let C denote the circumference of one of A f "^ B the circles, R its radi us OA, A its area; and let C' denote the circumference of the other... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...and s. PROPOSITION XV.—THEOREM. 37. The circumferences of two circles are to each other as tiieir radii, and their areas are to each other as the squares of their radii. Let Pk and R' be the radii of the circles, C and C" their circumferences, S and S' their areas. Inscribe... | |
 | Harvard University - 1876 - 554 pages
...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 line in extreme and mean ratio. 9. To find a fourth proportional... | |
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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 ^ the circles, R its radius OA, A its area; and let C... 
