 | James Smith - 1870 - 634 pages
...and B P. Now, what can we prove with reference to this geometrical figure, byjpure geometry ? Because the circumferences of circles are to each other as their radii (and this you have admitted), we can prove, First : — That the circumference of the circle X : the circumference... | |
 | 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... | |
 | 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... | |
 | 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).... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...within it ; hence, the perimeters of the polygons must coincide with the circumference of the circle, and be equal to it. 237. Scholium. Every circle, therefore,...denote the circumference of the other circle, r its radiua OB, A' its area ; then will C : C' : : R : r, and A : A' : : R* : r*. Inscribe within the given... | |
 | 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... | |
 | 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... | |
 | 1876 - 646 pages
...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. 1. If a straight line and a plane are parallel, the intersection... | |
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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... 
