== (108) = 



§. 9« Hanc quidem formulam haud difTicultcr, pofito 

 ^Lrzl — j ct •;/(;/« — //) — « — u Sy ad rationalitatcm perdu- 



cerc ct pcr iogarithmos ct arcus circuhires intcgrare liceret, 

 vnde rcftituto valorc z pro quauis dillaiitia z angulum Cj) ali"'g- 

 nare pofTem.us; vcrum inde nihil circa naturam curuae parcret: 

 difHciliiirie enim foret ex illa acquatione vicilfim diftantiam z 

 pcr angulum (^ dcfinire , vti conftruAio curuae polhihit. Se- 

 quenti autem modo res fiiie vUa difficultatc perfici potelt. 



'^^^- ^'* §. lo. Ducatur re(fla Y S, normalis in diftantiam A Y, 



fig. 1. 



voceturquc anguhis, qucm curua cum tangcnte conllituit, fcili- 

 cct angulus A Y T — et angulus T Y S = 2 >4^, eritque Q — 

 2. \\j — 90". Tum vero ex triangulo AYT habcbitur fin. ^ r 

 ^1 = 2- = 1:=-% vnde colligitur z = — "—- =1 — - — - . liinc 

 autem fit 



a^ 1 n a 5 ^Jin. i \1/ -» j. 3 a i n 5 \}/ f/rt. i \J/ 



(I-t-7lC3j.2\j/)2 z i-t-n COf. 5 \|/ 



Vnde cum in genere pro elemento anguli (|) hanc inuencri- 

 mus cxprefiionem: d(p=: '^'' ,^, , ob —^ — — — ^ — 



tang. =; — cot. c ^4^, erit 



a (1) zr: — ^? cot. 2 v^ = — i!Litf?tl_^ . 



" z ' I -*- n coj. I \J/ 



Denique ctiam notetur Cjcmcntum arcus 



,— — ;; ~Z'a^ zna !) \J/ 



dS = ydZ''^ZZO(p =^ ^.-rncoj.z^,)' • 



§. II. Quo nunc angulum dcfiiiire queamus , cius 

 difFerentiale hoc modo repraefentemus: 

 d(b=z—zdKL-\ 1^^, 



cuius integralc cfl 



(p^C-.^+f^, 



)/.2\i» 



Pona- 



