io6 



5. 12. Haec autem formLila fi fupra et infra mul« 



tiplicetur per -/2 — V i^ -^ ^^)> ita in duas partes difcer- 

 petur, vt lit 



Cum igitur fit • 



2 s <: 

 I — j4 



erit 



/1^ = M^:-Atang.^, 

 iicque prodibit ifta aequatio memorabilis: 



/ 27^/^2 — zz: i i Ldii — A tans;. s 



, I ^ •/ 2+/(i4-s4]-f-(s — 1'?-/2 _f_ 1 A. tans' ^•/ i^ 



4 ■/2 + v'(H-s4H-(sH-i)sy'2 2 O' ■/2-i-y'lH-54) — ii -/2 * 



vbi notaffe iuuabit efle 



A tang. ^ = 2 A tang. ^^^ l 



Verum li has partes coniungere vellemus, in formulas fere 

 inextricabiles illaberemur. Olim autem , cum huiusmodi 

 formulas tra£taffem, iam incidi in hanc integrationem : 



f s s_d^ — t I s -/2-1-/(1 + s ^) I A tanp" ^ '^'^ 



J (I — x4") ■/ I -4- s'» 4 -/2 I — ss 4/2 0*yn4-s4)' 



ynde pro noftro cafu fit 



f QssdsVQ I 7 y /2-+-/(i -f-s4) I A *^„-. ^ /2 ~ 



J (i_54)-/,i^,4) 2 ^ I— XS 2 ^ l-^llig- ^(i_^_,4) ^ 



cuius expredionis confenfus cum ante inuenta, propter ra- 

 dicalium complicationem , minus facile perfpici poteft. 



Alia Refolutio. 



Formulae propofitae V — f —^ . 



(i -f-a;) /(2 XX — 1) 



§. 13. Vtamur hic fubftitutione modo memorata 



y (2 X X — i) — s, vt fit X iz: ]/l±i!^ atque iam vidimus 



for^ ; 



