»fc8 ) iii ( Sfc*- 



hicque ante omnia requiritur vt iftac binae formulae integrabi- 

 lcs euadant, id quod euenict, fip, q, r,s talcs fuerint fimcliioncs 

 binarum variabilium t et 7/, vt fit 



Praeterea vero valores fupra inuenti ita exprimentur, vt fit 



VQ_—duVpp-\-rr et VR — djV qq-\-ss. 

 Tum vero anguli, quo clemcntum PQ ad axem inclinatur, tan- 

 gens erit z: - : at vero anguli, fub quo clementum P R ad axera. 

 inclinatur, tangens —~ ; denique anguli QPR tangens erit 1L~&. 



§. 9. His igitur denominationibus introdudis ad reprae- 

 fentationem perfeclam requirercntur tres fequentes conditiones: 



I. pp-\-rrzzi: II. qq-\-sszz cof.y ; 111.1 = -?-. 

 Hinc ergo, fi fiat - r: tang. C|5, erit - —— cot. Cf), ita vt fit 

 r~p tang. Cp ct s — — q cot. <p , 



vndc binae priores conditiones dant 



pp — cof. <$>' et q q — fin. (£)' cof. «\ 

 atque hinc deducimus 



p — cof. <P ct q — — fin. Cj) cof. a 

 hincque porro 



r zz: fin. Cj) et s zz cof. Cj) cof. u. 

 His igitur valoribus fubftitutis integrabiles reddi debent hae 

 duae formulae : 



d x z~ du cof.Cp — ;//fin.Cj)cof. u et 

 d y zzdu fin. (p + <//cof.Cj)cbf. « 

 ad quod cum requiratnr vt fit 



d p dj7 e £ djr d_s 



d t d u d } d u ' 



oricntur hae duae acquationcs 



I. -(^)fin.Cp=fin^fin.(I)-(^)cof.«cof.Cf> 

 II. (Jf)cof.(t)=:-fin.ttcof.Cp-(^)cof.«fin.(p. 



Hinc 



