 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...the one arc to the other as the radius of the former to that of the latter. Cor. 3. Therefore also similar sectors are to each other as the squares of their radii, for each sector is to the circle as the arc to the circumference (Prop. XXIII. Cor. 2. B. VI) ; consequently... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...Definition. Similar sectors and similar segments are such as correspond to similar arcs. 287. Theorem. Similar sectors are to each other as the squares of their radii. JDemonstration. The similar sectors AOB, A'O'B' (fig. 136) are, by the same reasoning as in art. 97,... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...the one arc to the other as the radius of the former to that of the latter.. Cor.. 3. Therefore also similar sectors are to each other as the squares of their radii ; for each sector is to the ciflle as the arc to the circumference : consequently the one sector is... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...Definition. Similar sectors and similar segments are such as correspond to similar arcs. 287. Theorem. Similar sectors are to each other as the squares of their radii. Proof. The similar sectors AOB, A'O?B' (fig. 136) are, by the same reasoning as in § 97, the same... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...the polygons become equal to the ureas of the circles, and we shall have A : a : : R" : r\ Cor. 1. Similar arcs are to each other as their radii; and similar sectors are as the squares of their radii. For since the arcs AB, ab are . similar, the angle C is equal to the... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...the one arc to the other as the radius of the former to that of the latter. Cor. 3. Therefore also similar sectors are to each other as the squares of their radii; for each sector is to the circle as the arc to the circumference : consequently the one sector is to... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...and their areas are to each other as the squares of their diameters. 151 PBOPOSITION XIV. THEOEEM. Similar arcs are to each other as their radii: and...sectors are to each other as the squares of their radii. Let AB, DE, be similar arcs, and ACB, DOE, similar sectors: then will and AB : ACB DE :: DOE CA For,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...their areas are to each other as the squares oj ti1eir diameters. BOOK V. 151 PROPOSITION XIV. THEOREM. Similar arcs are to each other as their radii: and...sectors are to each other as the squares of their radii. Let AB, DE, be similar arcs, and ACB, DOE, similar sectors : then AB : DE :: CA : OD • and A CB DOE... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...the squares oj their diameters. PROPOSITION XIV. THEOREM. Similar arcs are to each other as tf1eir radii: and similar sectors are to each other as the squares of their radii. Let AB, DE, be similar arcs, and ACB, DOE, similar sectors : then AB : DE :: CA : OD; and ACB DOE CA... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...the polygons become equal to the ureas of the circles, and we shall have A : a : : R' : r\ Cor. 1. Similar arcs are to each other as their radii ; and similar sectors are as the squares of their radii. For since the arcs AB, ab are similar, the angle C is equal to the ingle... | |
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DE, are like parts of the circumferences to which they belong, and similar sectors, as A CH and 'D OE, are like parts of the circles to which they belong : hence, similar arcs are to each other as their radii, and similar sectors are to each other as... 
