 | John Radford Young - 1827 - 246 sivua
...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 - 1837 - 216 sivua
...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,... | |
 | Benjamin Peirce - 1847 - 204 sivua
...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... | |
 | George Roberts Perkins - 1847 - 326 sivua
...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... | |
 | George Roberts Perkins - 1850 - 332 sivua
...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 - 1852 - 436 sivua
...of their diameters. 151 PBOPOSITION XIV. THEOEEM. Similar arcs are to each other as their 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 will and AB : ACB DE :: DOE CA For,... | |
 | Charles Davies - 1854 - 436 sivua
...diameters. BOOK V. 151 PROPOSITION XIV. THEOREM. Similar arcs are to each other as their 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 A CB DOE... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 sivua
...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... | |
 | 1861 - 420 sivua
...equal to the radius. 3. Book V, Proposition XIV. Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii. 4. Book VI, Proposition IV. If a straight line be perpendicular to two straight lines at their point... | |
 | Benjamin Greenleaf - 1862 - 532 sivua
...: 4 R3 : 4r3. PROPOSITION XIV. — THEOREM. 379. Similar arcs arc to each other as their radii; and similar sectors are to each other as the squares of their radii. Let AB, DE be similar arcs ; А С В, DOE, similar sectors ; and denote the radii С A and 0 D by... | |
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Similar arcs are to each other as their radii; and similar sectors are to each other as the squares of their radii. 
