TNTER SE COMPARAnDlS: 15 



Radices autem huius aequationis ope trifedtionis anguli 

 ita rcperientur , vt fumto v — lViss — ^t), et angulo 



$, cuius fit cofMUs, fcilicet cof. $z=.^;f^Vf)i 



ipfae radices futurae fint: 



XzvcoC.i(p'^s; ^zi-ycof^^oVs^j-^-f; ^^i^cof.f^C-iCpj-li 



30. Sed relidlis his , qnae ad radices fpedant , 

 vfum formulae inuentac accuratius perpendamus, ac pri- 

 mo quidem notatu maxime digna occurrit haec aequa- 

 tio differentialis : 



d_x djy 



V(A-+-Cxjc_hEjc*) — ' ■^{A-i~Cyy-i~Ey^] 



qulppe cui nouimus conuenire hanc aequationem intc- 

 gralem : 



jyVA(A-t-C fet-t-Efe*).4-feVA(A-f.C yy-hEy*) 



•* A — Ekkyy 



quae cum conftantem nouam k inuoluat ah arbitrio 

 noftro pendentem, erit rcuera integralis coropleta. 



31. Si pro hoc cafu ponamus /vu -h cl x -t- e I? 

 rzIT.jr, quia pofito j/ro fit x-k\ erit nji;z:n jk+n^. 

 Hinc fi fiat kzny, yt fit x=:'J-^}^=^^ ■ erit 

 Tl.x—2n.j\ ideoque ifte valor ipfius a: fatisfacit huic . 

 aequationi difFerentiali: 



dx 2dy 



quia autem nouam conftantem non compleditur , erit 

 is tantum int^grale incomplctum. 



32. Interim tamen et huius aequationis diffiren- 

 tialis facile integrale completum exhiberi poterit. Po« 

 natur enim 



d_v dz , 



V( A -hCyy-i- Ey*) V ( A -t- C z z -H E a*J 



eritaue v zj x: \-^,ckk-t~Ek*) - hk^/ \ [x-t-c zz-^-^z*) 



B 3. qvii^ 



