'EX DATO TERMim CENERALL xt 



Si iam porro x clcmcnto dx aiigcatur, vcl x abcat in 

 X -h a dx ; tum loco j liabebitur j -f- 2 dj-^- ddy. Atqiie 

 fi .V dcmio elcmcnto dx crcfcatjj transibit in /-{-3 <(/ 

 -^ "^ddy-^-d^y ., vbi cocfficientcs limt iidcm qui in po- 

 teftitibus binomii. £x his fcquitur fi loco .v ponntur 

 x-\-mdx tum y abire in lianc formam: j-V-^^dy-^ 

 ^^ddy-{-i^^-^^dy-^ etc. 



§. 5. Sit iam ad noftrum inftitutum m riumerus 

 iijfinite m.ignus, quo wa^.v quantitatem finitam (ignificare 

 queat; erit valor, quemj', pofito jv-f- w^.v loco x, ha- 

 bebit, ilte: j-h -7^ -+--777^-4- -7x7 + rTTT^-Hetc. 

 Si nunc fiat mdx — a feu ;//~^,indiietj', fi pro x po- 



natur .v -h ^ , hnnc formam J -1- r^i -H ."TTd^ 4- m: a^ 

 -i- ecc. in qua omnes termini fuut finitae magnitudi- 

 nis. 



§. 6. Hanc ipfim fcricm , quae valorem ipfuis y 

 transmutatum exhibet, fi loco .v ponatur x-f-^, pri- 

 mus produxit C/.Tay/or in Methodo Increm. inu. eamque 

 ad .multos egregios vfus accommodauit. Sequitur fciii- 

 cct primum cleuatio binomii ad quamcunque dignita- 

 tem. Vt fi quaeratur vaior ipfius (x-\-aj^ ponoj—v'"^ 

 eritque ix-]-a f valor ipfius j , fi loco .v ponatur .v -\- a 

 Cum igitur fit dy — mx^~^dx:, d'y — m(m — i)x 



,m — t 



7nax^~^ 



dx^ et ita porro erit {x~{-a)^~x"^-\ -i- 



m{m — I ^a"- x'^^- 



■-\- etc. 

 1.2 



B 2 



