 | John Playfair - 1806 - 320 σελίδες
...same number of sides, inscribed in the circles ABD and GHK ; ABCDEF and GHIKLM are similar, and are to each other as the squares of the diameters of the circles ABD, GHK. Find N, O the centres of the circles ; join AN and BN, and GO and HO ; and produce AN and... | |
 | Charles Hutton - 1811 - 406 σελίδες
...and then it follows, that the spaces of the circles, which are the same as of the polygons, will be to each other as the squares of the diameters of the circles, c^. ED Corol. The spaces of circles are also to each other as the squares of the circumferences ; since... | |
 | Charles Hutton - 1812 - 620 σελίδες
...: FO + GH +HI, &t :: the diam. AL : the diam. KM (th. 72). (). E. 1). THEOREM XCI. Similar Figures Inscribed in Circles, are to each other as the Squares of the Diameters of those Circles. LET ABCDE, FCHIK, be two similar figures inscribed in the circles •whose diameters... | |
 | Jeremiah Day - 1815 - 388 σελίδες
...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... | |
 | Charles Hutton - 1816 - 610 σελίδες
...or spaces of two circles, and D, dineir diameters ; then A : a •. -. o* : d1. For (by theorem 91) similar polygons inscribed in circles are to each...polygons to be increased more and more, or the length of thesides to become less and less, the polygon approaches nearer and nearer to the circle, till at length,... | |
 | Charles Hutton - 1818 - 646 σελίδες
...or spaces of two circles, and D, tl their diameters ; then A : a : : oa : rf3. For (by theorem 91'i similar polygons inscribed in circles are to each...and less, the polygon approaches nearer and nearer lo the circle, till at length, by an infinite approach, coincide, and become in effect equal ; and... | |
 | Charles Hutton - 1822 - 616 σελίδες
...&c. : FO + OH + HI, &c. : : the diam. AL : the diam. FM (th. 72). 4. ED THEOREM XCI. Similar Figures Inscribed in Circles, are to each other as the Squares of the Diameters of those Circles: Let ABCDE, FGH1K, be two similar figures inscribed in the circles whose diameters are... | |
 | Jeremiah Day - 1824 - 440 σελίδες
...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... | |
 | Charles Hutton - 1825 - 608 σελίδες
...areas or spaces of two circles, and D d, their diameters ; then A : a : : oa : d*. For (by theorem 91) similar polygons inscribed in circles are to each...the circle, till at length, by an infinite approach, coincide, and become in effect equal ; and then it follows that the spaces of the circles, which are... | |
 | John Playfair - 1829 - 210 σελίδες
...polygons of the same number of sides, inscribed in the circles ABO, UHK.; they are similar, and are to each other as the squares of the diameters of the circles. 1. Find N, O the centres of the circles; join AN, BN, and GO, HO; produce AN and GO till they meet... | |
| |
The areas or spaces of circles are to each other as the squares of their diameters, or of their radii. 
