1 1 



Solutio. 



Si hic immediate fubftitutioncm facere vcllemiis, iii 

 calculos fatis moleftos dclabeiemur, (juos ut evitemus , ob- 

 feivaffe iuvabit, foimulam i — 2 z cof. a -f- x % effe produc- 

 tLim ex his fadoribus : 



[ I — z (cof. X -4- ]/ -- 1 fin. x){i — z (cof. X— /—1 fin. a ) ] , 

 quorum ergo logarithmos invicem addi oporlct. 



TraQemus ergo primo formulam 



/ [ I — z (cof. a -J- / — 1 fin. a)]j 

 et com fit 



y (cof. t! -t- / : — I fin. ^' ) (cof. a -;- / — i fin. a) 

 — z ( cof. cc -I- y' — 1 fin. ) 

 quoniam in genere eft 



(cof. (3-1-1/ — 1 fin. (3) (cof. y -h "/ — J fin. y) 

 ~ cof. ( ^ -^ 'y )-}-]/— I fin. ((3 -h v) » e^i*^ 

 Z [i — z (cof.a -f- 1/ — I fin. a.)] 



~l[i j cof. (;i -4- e) -i- / — I fin. (a + f)].' 

 Hic ergo faSa comparatione erit 



a ~ I — y cof. (a -(- c ) et 5 ziz — y fin. (a H- ^) , 

 unde eius valor rcfolutus erit 



l[i — z (cof. a -f- / — I fin. a)] 

 - |/ [I- -vcof.(.H-e)^jj] -/- I Arc.tang. /_^^^;;-|\^ T 



Hinc altcra formula facile deducitur, fumendo angulum <x 

 negative, eritque 



l[i ~z (cof. a — ■/ — I fin. a)] 

 zr I / [ r - . ^ cof. (0 - .) -^yy] - /- 1 Arc. tang. //;,i;-!^^, ." 



B 2 Nunc 



