26 G. H. COST JORDENS 



proprietatibiis liDjus 'ciirvae facile eruitur ejiis aequatio; est enim «G = «a + oG ; 

 no est ex aequatione circuli = \/{^ax — x.-^:, oG autem , uti facile demonstrari p*- 

 test, est = arcui Bo; 



ergo j = «G = no -j- oG = t/(2fl« — .r^) + arc. Du 



= •!/( 2i7.r — .-(- ) -{- arc. sin. V (:«:<;— .t^) 

 ?it BP parallela basi AH; porro B/3 = yS = j' ; /3y = BS = .r, tunc difFerentiaTe 

 spatii Bj3:>' est =: .rfi^j, ergo xdy — x .d(^\/ (j.ax — x"') + arc. B)j); si nunc ordinata 

 in circulo generatore respondens abscissae x ponatur = v; erit : 

 C^.arc. B;,)^ = («'«)* -1- (rfv)2 



= idxy 4- id.\/("-ax-x''-):?- 



= (dxy + (^f^^^^^S 



\ 2.( 2/7.V — • .X ) i ' 





= (^..)^ + 



(2/7.V— .X-='jJ 

 2(J* — x' 



(a^ — 2ax + x')(dxy 



lax — x'^ 



_ (dx^i lax -~x'- + a'^ — lax + j= ) 



~ (dxY •, ; adeoque 



^ aax — .V 



^.arc. Bw = «^*- ~ ^r^; vidimus autem esse 



\/(iax — x-) 



xdy = X X rf.(VC=«^ — ^) + "c. By) 

 = :v (rf.VCaa^--^) + ''•arc. B.j ) 

 = i- ( I (2ax - .r*) ~" s -(<3 — ^) dx + d. arc. B» > 



= - ( v/(.ir-.v-) '^" + v(=.xZ7«) ^') 



na — x . cij.T — .r^ 



«/* = -rr^ ^. i^x 



~ V/(2fl*— .r^) y(2ax — x-) 



= V(2ax— *^) i/j:, adeoque 



J^dy =fdx y/iiax — x") =Jvdx. 

 Igitur arca By^ = BijS (i), adeoque quum boc semper locum habeat, quocunque 



9U- 



