SL2T 



/Z3. / (I + 3'j = ^ (I + rF -t- ^ + •••••) H-nii^iV, ^ « 



■~"8(11»— x*J ^ B'» ^^3 (B'*-!-»»**) "^ S(Ji4-hnax2)ii "^ *''• 



Quae scrics semper valdc convergit, nisi n in infinitum abeaty 

 vel cllipsis sit infinite oblongaj et vel tum scries nostra crit 

 ! -f_ I -^ I _}- S -4- etc. Plerisque vero casibus , inprimis autem, 

 quando sphaerois elliptica tellurem rcpraesentat , ubi eccentrici- 

 tas n est admodum exigua, prioribus tribus terminis acquics- 

 cere possumus. Ponamus adhuc B' — x^ zzz q*y ut sit 

 B* 4- n* jr* zz: A' B' — «'3'*? tunc scries nostra 4ianc induet for- 

 mam- — 2i^J Ca -H "' '"' ~^'' -|- J1L1Ej=-£)- -|- ctc.) = 



B^-a^ n^^jj _. «2^32 __!il51±i__ -4- mB^^qdq , ^^^ 



—^~ 'zq '^ 2B» 6^(A2B3— n«q2J ' 6 (A^ B^ — n* 5«) 



Quare cum sit /- ,^.,fl,.^., - ^^ ^^^' 7 (A^B^'-n»,^) ^ series no- 

 stra integrata praebet: 



Const. - ^^^' log. q -H ^'g -4- ^?-!-^ log. v-(A»B»-n^,^ 



U »» ^ 4 B* 6 A* q 



— II log.(A'B' — «'(/'). 



Quoniam area evanescit quando jr ~ o seu (|f =: B , integrale 



completum est 



2 °' ^ 4 ^l^ 6 A» ^* B^ 12 ^' B4 



Restituto nunc valorc (7*= V (B' — x*), reperitur area LMD 



- S = -" ^ "' log -_5_ -52 loe b^-*-"'« '-^"' f JL Ioz i^i^ltin^- J^Ll 



2 o"v(it_xS) 12 °' B4 s «■ 3A* *'By(B* — **) 2 B" ' 



^uae formula adhuc est per tangentem anguli a multiplicanda. 



i X7. 



