. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. E V O I. U T E. rate CD-;, fine I G = f> and arc FG = *. Now by 35 E. 3. I G =i)lx Il'V, that is, t = 2tty â y J I > ^~-\ i ; and by yâf\$ the fluxion of which equation is j = the nature of the cycloid, arc 1) G == G 13 ;'and there- fore, arc F G = G I + AC, or AC c arc F G â G Is that is, r â ~. â j- =r (by fubftituting for s its above value) z â j a y â y J 2 ; and the fluxion of .. ⢠1 ⢠* . ⢠⢠3 y â a y this equation, making x = I, is 1 = « + - But k = s^+y ay - r U (b
. The cyclopaedia; or, Universal dictionary of arts, sciences, and literature. Encyclopedias and dictionaries. E V O I. U T E. rate CD-;, fine I G = f> and arc FG = *. Now by 35 E. 3. I G =i)lx Il'V, that is, t = 2tty â y J I > ^~-\ i ; and by yâf\$ the fluxion of which equation is j = the nature of the cycloid, arc 1) G == G 13 ;'and there- fore, arc F G = G I + AC, or AC c arc F G â G Is that is, r â ~. â j- =r (by fubftituting for s its above value) z â j a y â y J 2 ; and the fluxion of .. ⢠1 ⢠* . ⢠⢠3 y â a y this equation, making x = I, is 1 = « + - But k = s^+y ay - r U (by writing for j its above value), + f\ = v aj 1 which, fubflituted 1 «j -J»- j 2tfy i, makes the above equation 1 fo â a \ - * 8 «>-/!£ that 18, and. equation (the fluxion of y being negative), pyy â f zay-â _ a ⢠J- ⢠2 a j' - j--"\ â 'â (by writing for _y its equal), ; f Now, by fubftituting â-ââ 2 12 that "^^ for v% and â for y, f â¢we have ' + . 2 a \ B« = x1, and n b = y, when, by 47 E. 1 B b -s *' V ^* . â will be = x'''+' »i~*\iJ *' " + y' = B F or B ;⢠; and B b I b. n y y' + y rs\>, y +/" : v :â-= -, , x'' \ y \ri : : B C : C F, that is, \ = C F or C r ; the in- crement of which is rfj that is, fuppofmg x' to be inva- y" -i-yy" x x7* +/â â ] i - y'y'xjy'^ riable) , *ZZZHi__ _ 2y" +/* + y«"y" ^TT - rf. Again, the triangles E £ b and E r / being fimilar, B b - r f: R b â ⢠(BE - r E, or) r B : B E ; that is, («f« +.y/)| _. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Rees, Abraham, 1743-1825. London Longman, Hurst, Rees, Orme & Brown
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Keywords: ., bookcentury1800, bookdecade1810, booksubjectencyclo, bookyear1819
