 The circumference of a circle is the limit which the perimeters of regular inscribed and circumscribed polygons approach when the number of their sides is increased indefinitely ; and the area of the circle is the limit of the areas of these polygons.  A Treatise on Algebra - Page 162by James Edward Oliver, Lucien Augustus Wait - 1887 - 412 pagesFull view - About this book
 | William Chauvenet - Geometry - 1871 - 380 pages
...inscribed and circumscribed polygons approach when the number of their sides is increased indefinitely; and the area of the circle is the limit of the areas of these polygons. Let AB and CD be sides of a regular inscribed and a similar circumscribed polygon ;... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...inscribed and circumscribed polygons approach when the number of their sides is increased indefinitely; and the area of the circle is the limit of the areas of these polygons. Let AB and CD be sides of a regular inscribed and a similar circumscribed polygon;... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...than from each other; therefore this difference may be made less than any assignable quantity. Hence the area of the circle is the limit of the areas of both polygons. THEOREM XIV. 4 i. A circle is a regular polygon of an infinite number of sides. any assignable... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...than from each other; therefore this difference may be made less than any assignable quantity. Hence the area of the circle is the limit of the areas of both polygons. THEOREM XIV. 44. A circle is a regular polygon of an infinite number of sides. any assignable... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...and circumscribed polygons approach when the number of their sides is increased indefinitely ; and the area of the circle is the limit of the areas of these polygons. Let AB and CD be sides of a regular inscribed and a similar circumscribed polygon (v.... | |
 | James Morford Taylor - Algebra - 1889 - 400 pages
...be always less, always greater, or alternately less and greater than its limit. If a regular polygon be inscribed in a circle, and another be circumscribed...their sides be doubled again and again, the area of each of these polygons will approach indefinitely near to, but can never equal, the area of the circle,... | |
 | William Chauvenet - 1893 - 340 pages
...and circumscribed polygons approach when the number of their sides is increased indefinitely ; and the area of the circle is the limit of the areas of these polygons. Let AB and CD be sides of a regular inscribed and a similar circumscribed polygon (v.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...inscribed and circumscribed polygons approach when the number of ilicir sides is doubled indefinitely ; and the area of the circle is the limit of the areas of these polygons. GIVEN — P and/ the perimeters, R and r the apothems, 5 and j the areas, respectively,... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...inscribed and circumscribed polygons approach when the number of their sides is doubled indefinitely; and the area of the circle is the limit of the areas of these polygons. GIVEN — P and/ the perimeters, R and r the apothems, 5 and s the areas, respectively,... | |
 | Harvard University - Geometry - 1899 - 39 pages
...and circumscribed polygons approach when the number of their sides is increased indefinitely ; and the area of the circle is the limit of the areas of these polygons. THEOREM X. The lengths of the circumferences of two circles are to each other as the... | |
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