AY — Z — V(-^x-^yy)y crit ur=:^/3, ita rt ifte angulus 

 metiarur logarichmum dilbntiae AY = 2, quae ergo lineae erunt 

 fpiralcs logarithmicae redas fingulas A Y fub angulo cuius 

 tangens — 5 fecautcs. 



Exempliim 2. 



§. 45. Sint curuae fecantes omncs circuli axem AX 

 in A normaliter fecantes, hac aequatione: y-}/ {2 a x^-xx) y 

 contenti , ericque a nz ^^^^^ hincquc differentiando 



Tnde fit p = x' — yy ^t q =.-!.. Cum igitur in gcncrc inucntJ 



fit haec acquatio: 



d^(q-}-^p) — dxi^q~^p)y 



crit pro hoc cafu 



dj[2xj^^(xx — yj^^zzzdx^z^xj-xx-^jy)^ fnie 

 2 ( jf A- — jj' ^dj — zSxj^dx — ijj — xx) dx — 2 xj dj, 



§. ^6. Quoniam autem haec aequatio cft homogenca, 

 (latim ponatur ^ ~ r j:, vt fit dy — t d x-\- x d t ^ et aequatio 

 nofba hanc induet formam: x d t-^ ''^*^ jyr — ■ '-^x Ynde fit 



X i 1 -i-i 1 M 5 I — I ) 



quac fradio in duas partes refoluta praebec 



ix »t<it , Sit 



X t-T-n it — .1 



cuius integrale manifefto eft 



lx = —I(i-htt)-{-I(St—x)-\-if 

 fiuc jr — "'^^-" , ct rcmtuto yalorc /r-2L, crit jr-l *'^^'V ^ 

 qunc rcducirur ad hanc formam; jr x h-^/ = <• (?7- r) , qnae 

 acquatio, vt iam fupra cft oftcnfum, coraplcditur infiiiitos cir- 



D 3 culos 



