i5o 



DE PJRTITIONE 



f. 47. Qiicmadmodum lu(flenus omnes numcroj. 

 integros ad p.irtes conftituen ias a.lmilimu? , ita partium con- 

 ditionc limitanda numenis qiweftioiium in inSnitum augcri 

 poflfet : cui negoiio , cum methodus ccrta ad huiusmodi 

 qu:iertioncs refolucndas fit tradita , non diutius immorabi- 

 mur. Sufficiat ex praeccdcute iiifigncm proprietatem par- 

 titionis in partes impares annotafle. Cum fit ; 



(.-f-x)(,^x»)(,-Hx»)('-+-x*) etc— (7_xX.-Jc»X.— »»X«-*'Xr-.c») ftcV 



quac formula cx aequationc in §. XLIV. cxhibita (pontc 

 fluit , hinc fequitur, quemuis numcrum totidcm modis cx nu- 

 meris foiis imparibus per additionem produci pofle , quot 

 modis idem numerus omnino in partcs inter fe inacqualcs 

 difpcrtiri polfit. Sic cum numerus 10 dcccm modis in 

 partes inaequales difpertiri pofllt , qui modi funt : 



10 — 

 10 — 

 10 — 



10 



2 



10 — I -+- 2-1-7 



10 = I -f- 3 -h 5 



10 ir: I 4- 4 -h 5 



10 ir: 2 -f- 3 -+- 5 



io:z:i-i-2-i-3-1-4 

 idcm numcrus 10 quoquc dcccm modis cx foHs nu- 

 meris imp.iribus pcr additioncm produci potcfl , hoc 

 modo 



10= 3-+-7 

 10 — 4-4-(J 



1 0—— I -f* I -f- ' -f- 1 -f- '-+-'-+■> -t- ' -4- '"+- ' 



10 i-f-i-»-i-f-iHh'-t-'-f-'-f-» 



10 — — i-f-i-Hi-f-i-t-i-f^j 



10~i-f-p 



:'-f-j-f-j-+-i 



: I -f- 1 -+- I -»- ' -f- ; -f-l 



.■-»-i-f-i-^i 



§. 48. Rclidis autcm Iiis fpcciilationibus progrcdi- 

 or ad inuclligandum , quomodo quisquc numcnis cx tcr- 

 minis progrcfllonis Gcomctricac i, 2, 4, 8, i5, 32, 



ctc. 



