 | Charles Hutton - 1831 - 632 pàgines
...or spaces of two circles, and D, d, their diameters ; then A : я : : D3 : d*. For (by theorem 91) similar polygons inscribed in circles are to each...other as the squares of the diameters of the circles. away its half, and then the half of the remainder, and so on, until there be obtained an arc cd less... | |
 | Jeremiah Day - 1831 - 520 pàgines
...the latter is found in the table ; and from the properties of similar figures, the two segments are to each other, as the squares of the diameters of the circles. We have then the following rule : To find the area of a circular SEGMENT by the TABLE. Divide the height... | |
 | Jeremiah Day - 1831 - 418 pàgines
...the latter is found in the table ; and from the properties of similar figures, the two segments are to each other, as the squares of the diameters of the circles. We have then the following rule : To find the area of a circular SEGMENT btj the TABLE. Divide the... | |
 | William Grier - 1832 - 366 pàgines
...in the same ratio as the diameters of the circles in which they are inscribed. 74. Similar figures inscribed in circles, are to each other as the squares of the diameters of those circles. 75. The circumferences of all circles are to each other as their diameters. 76. The... | |
 | William Grier - 1836 - 384 pàgines
...in the same ratio as the diameters of the circles in which they are inscribed. 73. Similar figures inscribed in circles, are to each other as the squares of the diameters of those circles. 74. The circumferences of all circles are to each other as their diameters. 75. The... | |
 | William Ritchie - 1836 - 198 pàgines
...polygons having the same number of sides in two given circles, they showed that these polygons were to each other as the squares of the diameters of the circles. The same ratio was also shown to exist between similar circumscribing polygons. By continually doubling... | |
 | Jeremiah Day - 1838 - 416 pàgines
...the latter is found in the table ; and from the properties of similar figures, the two segments are to each other, as the squares of the diameters of the circles. We have then the following rule : To find the area of a circular SEGMENT by the TABLE. Divide the height... | |
 | William Grier - 1842 - 320 pàgines
...in the same ratio as the diameters of the circles in which they are inscribed. 73. Similar figures inscribed in circles are to each other as the squares of the diameters of those circles. 74. The circumferences of all circles are to each other as their diameters. 75. The... | |
 | Charles Davies - 1850 - 238 pàgines
...same ratio as AL to FM, we have (Bk. III. Th. xii), BOOK IV. Proportions of Polygons. THEOREM XXIII. Similar polygons inscribed in circles are to each...other as the squares of the diameters of the circles. Let ABODE, FGNIK, be two polygons inscribed in the circles whose diameters are AL and FM: then will... | |
 | Charles Davies - 1850 - 218 pàgines
...same ratio as AL to FM, we have (Bk. III. Th. xii), BOOK IV. Proportions of Polygons. THEOREM XXIII. Similar polygons inscribed in circles are to each...other as the squares of the diameters of the circles. Let ABODE, FGNIK, be two polygons inscribed in the circles whose diameters are AL and FM: then will... | |
| |
The areas or spaces of circles are to each other as the squares of their diameters, or of their radii. 
