JDE SERIEBFS QFIBVSDAM CONSIDERAT. 6i 



^ — 1.2.3 8 • ^'° — ^ — ^9 -^r- U ~ j9 -^- etc. 



1.2.3 ....9 • ^" ^ .^ 5'0 -+- I 



T , 1 50-C5t TT" T » II 



Tvr — ^i^jTp- "^'^ — T 1 I I I 



^^^ I .2>3.-.I • -'^ — . I ^ 3^2 -I- j 



N=: ^^2iz^ .fd = I 



i.2.3....ia - ^ 



lo -i- yio-t- etc. 

 '» -i- ^i-H etc. 

 '2 -f- jiz-\- ctc. 



oi4 — A 3IJ -t- jij -t- /ij-i- etc. 



0=:SSf-^=^-^-^- +^* + ^* etc. 



§. II. Denotant hic litterae A, B, C, etc. nu- 

 merales tantiim coefficientes potellatum t: per poteftates 

 binarii diuiiarum : quarum valores etii (iitis commode ex 

 iege data definiri poflunt , tamen alia lex poteft exhiberi, 

 quae magis ad calculum videtur expedita. Confidero lci- 

 licet feriem A + B ;s -4- C ;q;* -f- D s' +' E ^* -|- etc. 

 cuius fumma , quae tantisper defignetur littera s , eft per 

 §• S. == i5it:if , ob j/ = I. Qiiod fi igitur ex hac ae- 

 quatione s zn. ' !!^4a^ ^^^^^ ipfi"s s in ferie exprimatur ^ 

 quae iecundum potelbtes ipfius z progrediatur , prodire de- 

 bebit ipfa feries A-f-B5;-+-C;s*-4-D.cj'-4- etc. NuUa . 

 enim alia feries fimilis formae puta P -h Q_^ -h R s* -|- S .s* 

 H- etc. aiTignari poteft aequalis illi A -f- B5; -f- Cs* 

 -H D5;3 -f- etc quin fimul coefficientes poteftatum z con» 

 gruant , fitque P =z A ; Q.=: B ; R zz: C ; S = D, etc. 

 At vero exprimit \Ljuil^ tangentem arcus J -}- S feu erit 

 s — tang' A { J -h f ) et hancobrem conuertendo J -h 5 

 = A tang. i = / rzjin fumtisque diiferentialibus ob J con- 

 .ftans feu arcum 45 graduum, habebitur "^^==7::^ iiue 

 dz-^ ssdzzzz ^ds. Nunc ponatur szzA-\-Bz-\-Cz 

 ^-D;:'-4-Es*-i-etc. erit 



H 3 ^ds 



