-*S=?^ ) 50 ( V^<- 



E — x"-x"-x''{i -jr* ) -.V*' ( r -.v') ( I -.v') 

 — .v*' ( 1 — ;v* ) ( I - .V ) ( I — jc* ) etc. 



\bi poteftates ipfius Jf lcnario crefciint. 



f. 7. Ciim lcx, qiia iftae opcrationes vlteriiis funt 

 conriiuiandae fatis Hr pcrrpicua , fi portremi valores pro 

 fingi'lis litttris A, B, C, 1), inuenii ordinc fublhtuantur, 

 pro fciie quatfita repericmu» feqnciitcm formam: 



S—i—x, —xx-{-x\ -f x' — x'\ -X'^ + X"f 

 4-.v='- A-'% - x^^-^-x", etc. 

 Hic i^itur tota quacllio huc rcducitur, vt ordo dcfiniatur, 

 cuo cxporentes potclhitum iplius x continuo vltcrius au- 

 gtutur, quandoquidcm cx opcrationibus in(l;tutis iam fatis 

 efl manifcnum fgna terminorum -f ct — ita altcrnatim 

 fe excipcrc, vt anibo gcminentur. 



§. 8. Quo igitur in hanc legcm inquiramuj, vidca- 

 mus ouomodo in finguiis httcris illi ntimcri fint orti. 

 Hunc in fincm primos faltcm cuiusquc littcrac tcrminos 

 in cius forma prima exhibitos ordinc difponamus 



A — Jf .v ( I — .V ) 

 B — x'(i-x V) 

 C — x"{i-x') 

 D — jr"(i-x*) 

 h^.v'''(i-.v') 

 ctc. 



7=34- 4-3 + 1+ 3 = 3 + 1 + 1 + 2 

 15 = 4+11-4+2+ 9-4 + 2+2^-7 

 26-54 2i:r5 + 3+ib = 5 + 3+3 + i5 

 40 = <5-f34=6-f4+30 = <5 + 4 + 4+26 



571:7 + 50 -7 + 5+ 45 = 7 + 5+5 + 40 

 etc. 



Hic fcihcct cx cuolutione litterae A vidimus, numcrnm 7 

 ojin cx aggrcgato 3 -f- 4 , tiim vcio 4 oriri cx i -H 3> 

 ac dcniqnc 3 cx i -h 2, quae ergo rcli^iutio dabit 



7 — 3 -H 4 = 3 --h I 4- 3 = 3 H- 1 -i- I +-2. 



At- 



