JLGORITHMI SINGVLARIS. 6$ 

 et generaliter : 



(*,*....*)(*. ...*,/>*»>»)- (*•• .£)(#,*• • •*,/,»,») 



zz -4- 0$ ») 

 vbi fignorum, vel fuperias, vel inferius, valet, prout in 

 primo •vinculo numerus indicum fuerit, vel par, vel 

 impar. 



27. Ratio autem huius formulae ex fupra reper- 

 tis flicile deriuatur. Si enim ponatur : 

 (a.b....k,l>m)[b..k i l t m,n)-(b..k>I,m)(a i b..k,l.mjt)zA. 



{a,b kj)(b..k l l,m,n)~(b... k I)(a t b.. fe,7,*»,»)-B 



(a t b k)(b..kj 1 m,n)~(b k)(a,b .kJ,m,n)zC 



jnanifemim eft, elTe A zz m B -f- C. At eft Azz+i: 

 et B — -f- n j ldeoque C — ± 1 -4- m n zr H^ (w.«) , 

 vbi de ambiguitate fignorum tenenda funt praecepta 

 fuperiora. 



28 Si ordo indicum in his formulis inuertatur s 

 cae fient : 



(* y)(a,b..,.y t z)-(a,b...y,z)(a,b...y)zzo 



(a,b....y) (b, c. . . .y y Z)-(a,b.. .y. z) 'b,c . . j)zz± 1 

 (a,b.c...y)(c,d .. y t z)-(a t b...y t z)(c,d . y)~±(a) 

 {a,b,cd. y)(d t e. . y,z)-(a y b...y % z)(d,e. . .y)z=±(a,b) 

 (a t b J c\de.y)(e t f..,.y,z)-(aJ...y t z)(eJ...y)z±(a,bc) 

 (a 1 b....y)(j,g... .y>z)-(a,b...y,z){f.g .y)~±(aj t cj) 

 vbi figna valent fuperiora, fi numerus indicum in fecun- 

 do vinculo futrit par, contra autem valent infenora. 



TonUX.Nou.Comm. I aj>. Si 



