26 Johannes (I) Bernoulli. 



-, ■ adx ^yx dx -ay dx + a dxVZax - x. 



V2 ax -xx 2a x -xx 



Reducta aequatione habetur yx-ay=0 et proinde x = a. 



Per modum 2. Quia 



adx ., 77 -aadx 2 + axdx 2 



dy = — . ent ddy = —= - =0. 



VZax -xx 2aa -xx V2ax - xx 



Ideoque -aa + ax = et x = a. 



[32] Sic ad determinandum punctum flexus in Conchoide Nico- 

 meclis per methodos quas attulimus, oportet ut Natura Conchoi- 

 deos habeatur per aequationem, quae relationem explicet inter 

 abscissam et applicatam. 



Sit ergo (Fig. 25) AE = a EF = b AD--=x BD = y erit BG = a 

 DE = a-x, Quia DE • EF :: BG • GF erit 



GF = üb Ergo GE = VZabbx-bbxx . 

 a-x a - x 



Sed GF-GE::BF- BD id est 



a& V2abbx-bbxx , /s — ««+«*-«« „, 



vel a • V 2 a x - x x : : — - ' -'2A 



a - œ a-x « - x 



ideoque 



S ^VS^ + Ä^ 



eju.sque différent. 



aabdx a dx - x dx , 



dy= ,— + •",.- dx:: ?/ 



a« -2ax + xxV2ax -xx V2ax-xx 



a + b - x 



' = ~ a ^T^ — V2ax -xx) • f. 



Erit ergo 



ab -bx + aa - 2 a x + x x in 2 a x -xx 



aab + C:a - x 



Ponatur jam ut Calculus eo facilior evadat a-x=z et erit 



bz + zz in aa -zz aa bz + aa zz -bz 3 - z x 



t 



aab +z z aab +z z 



2aabz + aa zz -bz 3 -az 3 -a 3 b ,, . 



et t-x = t-a + z = — — ; =— — = Maximo. 



aab + z 6 



Ideoque illius differentiale erit 



2a 4 6& dz + 2a*bz dz -3aa bb zz dz -4aa bz 3 dz -aaz i dz 



D : a ab + z 3 



