17^ SVBSIDIVM 



Quotie? ergo n efl: numerus integer , pro fradis enim 

 haec redudio minus commode inftitui potcft, lequentes 

 obtinebuntur redudiones : 

 ifin.vp — fjn. v{y 

 a fm. v|>'''— — cor. 2 \4> -f i. 2, 

 :i.fin.vj>'i=:— fin. s^^+afin. \j^ 

 8fin. v}>*:= + coC4\|v' — 4.cof. 2 \[/-i- 1.6 

 i<Sfin.vj^'r=:+ fin.5 v}y— 5fin. 3\|y+iofin. v|/ 

 • 3 2 fin. v{>''r=:— cof. 6 vfy + 6cof 4 \|/ — 1 5 cof 2 v[/ +- ;. 20 



<J4fin.v|^'— — fin.7v|y + 7fin. ^v}/ — 21 fin.3\]^ + 35 fin.Cf) 

 X 28 fiu. vjy'— +co(. 8 v|> ~ 8 cof 6 v|y 4- 2 8 cof. 4; v|v - 56 cof 2 v|> +I.70 



etc. 



Pro valoribus autem negatiuis ipfius n habcbitur : 



-fl^^ — -ffin. v|/+ fin.3\{>+ fin.5^+ fm- 7^+ fin. 5)v|^+etc. 

 — i-^— _cof2v{y-2Cof4.vly— ^cof dv^y-^-cof 8v{./— scof lovj/- etc. 

 -— :r-fin.3v{>-3fm.5v{y- 6fin.7\|/-iofin. 9\{y-i5fin. 1 1 v|y- etc. 

 — .-^r+-cof+\{^+4.cof(5\{>+iocof8\[/+2ocof rov[/+53cor.i>2v|./+etc. 

 '_L,^— +fin.5\'/+5fin.7^+i5rin.9vly+35fin:iivi/+7ofm.i3v{y+etc. 

 etc. 



Hinc ergo qnadrupliccs formulae gcncniles cliciuntur, 

 prout n fuerit numerus foim:\e vel ^m^ vcl xw— i> vcl 

 4/« -2, vel 4W — 3» eaequc cruut : 

 2.*'"-'fin.\}>*'"— cof 4?n\l^-4W/cof (4?;/-2^v{y+^^^]7^-cof [^m-^] y\f 

 -t!te--i^--cof(V;/-6)vl^ 



, 4.ni(<m — .Xt.TT!— 1] . (om-f-i 



+"»' 1. 2. 5 » 2"! 



«♦" 



