460 Proceedings of Royal Society of Edinburgh. [july is, 
says — “ Hctec de Opere Bezoldino in universam, quod plurimis 
adhuc Lectoribus nostris ignotum erit , dicta suffciant. Nunc 
Regulam ipsam proponam .”. . . . The seventeen pages which 
follow, contain a tolerably close Latin translation of the Regie 
generate pour calcider . , and the Methode pour trouver . . . , 
pp. 172-187, §§ 198-223, which have been expounded above. 
Cramer’s rule is next given, the second mode of putting it being- 
in words, and the first as follows: — 
“ Sint plures Incognitse z , y, x , w , &c. totidemque Aequa- 
tiones simplices indeterminate 
A 1 = Zh + Y l y + XL: + W % + &c. 
A 2 = Z 2 z + Y 2 y + X 2 x + W 2 w + &c. 
A 3 = Z% + Y 3 y + X 3 x + W hv + &c. 
A 4 = ZH + Y 4 y + X% + W% + &c. 
Ac. Ac. Ac. Ac. Ac. &c. 
Erit, , positis terminorum signis, ut praecipitur in 
fine Tabulse, pag. seq. 
AYXWVUT (vn. 3.) 
_ Permut (1, 2, 3, 4, 5, 6, 7, ) 
Perrnut (1, 2, 3, 4. 5, 6, 7, ... . .) 
ZYXWYUT ” 
The similar expressions for y , x, w, v, u, t, are given, and then the 
“ regula signorum .” After an illustrative example, the question of 
the sequence of the signs is taken up. 
“ Quod si itaque +%/(!, 2, 3, . . ., n) denotet signorum 
vicissitudines, quibus hie afficiuntur Permutationum a numeris 
1, 2, 3, . . . n singulse species, et-sp(l, 2, 3, . . . n) signa 
contrarict vel opposita : appatet fore 
sp(l,2) = +*fif(l) -^(0 
s^(l, 2, 3 ) =+^(1,2) -^(1,2) +sg( 1,2) 
sg( 1, 2, 3, 4)= + sp(l, 2, 3) - sp(l, 2, 3) + ^(l, 2,3)-sg(l, 2, 3) 
unde, quia S£/(l) est +, facile eruitur 
sp(l, 2) esse H — 
sg(l, 2, 3) . ... -\ + 4 — 
6^(1, 2, 3, 4). . . .+ + + + + + 
+ -f + -t- + + 
