e«-itq"e ^^^, - 4^, , pofito z - —^ , et fubftitutio. 

 iie fada, liQrum ditferentialium aequalitas mox inuotefcet. 



§. 33. Dum fupra §. 23. 24, oftendimus effe 

 pro Hyperbola: 



P i_ g ( P -)- co/. (P ) ( p -f- cof. 4/ ) _ 



pofito 



p V / />» _ T ^ ■^'" - ^ — l-hP CO/.>f< 



c "^ ^«= ^/,-hecoJ.$ ji;i.> » 



ct pro ellipfi: 



/",y (h V( ' + » e co/. J -f- e- ) I /~ J j, V_LL±Il£^^±f ' ^ 

 J » H^ ( .-Hecoj". CpJ^ ^^.' ^ ( i -f-ecoj.xj/)' 



r^ g^ ( ■' -f- coJ ^J ) ) ( f - f-co/. vjy ) 



e- — 1 * ( 1 -f- e coj. >p j ( 1 -f. e coj. vfT) ' 



pofito 



y C I _ ^= ) _ /'t. — e+i£/-> 

 \ / e-(-coj.cp /"i.'ip ' 



valorem conftantis C nondum dcfiniuimus , quare reftat , 

 \t id hic expediamus. Definietur autcm ille valor com- 

 jnodiflime ex fuppofitione (p — vp , tum fcilicet erit pro^ 

 priori cafu eV [e^ — i ) fin. (I)' — ( i -f- £- cof (^)- , ideoque^^ 

 f y (f'- i) rr: I -f- 2 f cof Cp-hf cof. Cp'(e-i-y(^?-i)), 

 vnde deducitur: 



cof Cp 



V ( ( e V (e^ — ■ ) — ' )(e»-f-pV(f^-i ) -f-ei ) 



e-f-V(e'-'i) - — ^eCe-f-Vre*— ■ )) ' 



haec autem formula aliquanto fit concinnior, fi locp e ip/ 

 compurum introducatur fin, X zz J , tum enim erit.:^ 



cof 0' ( I -+- cof X ) -+- 2 fm. X cof (^— cof X — fin. X' 

 et proinde 



cof(p*-+-2tang.iXcofCp — ^-^li^i^', ob -|iA- - tang. | X , 



hincque cof 0^-4-2 tang. \ X cof Cp — '.sL^^-^zi , 



A£ta Acad. Imp. Sc. Tow. II. P. I. N quam- 



