C 2 42 ] 
of. And this appeared to me fo obvious, that I 
wondered, neither the learned author, who feems to 
have the thing much at heart, nor any body elle 
fince the publication thereof, law it. 
Let the equation to be refolved, be a-\-bx -\-cxx 
'-\-dxXx, &c. — o. 
Upon the line Z Z, as a bafe, in either the firft or 
fecond figure, draw the lines S S and R R perpen- 
dicu’ar thereto, at any diftance taken at pleafure from 
each other. Then upon the line S S in either figure. 
Tab. VIII. fet off the lines O A, AB, BC, CD, &c. 
proportionable to the coefficients a, b> c , d , &c. in 
the equation, remembering to take each line upwards 
from the extremity of the lafb, when the coefficient, 
it is to reprefent, is affirmative ; but downwards from 
the faid extremity, when the coefficient is negative. 
Then through the extremity of the laft of the lines 
OA, AB, BC, &c. which in our cafe is D, draw 
the line D c, parallel to the bafe Z Z, and through c, 
where Dc interfeds RR, draw^C ; and parallel to 
SS, and at any diftance from it taken at pleafure, 
draw MM : then parallel to D c, and where C c in- 
terfeds M M, draw the line^^j through A where 
this laft line interfeds RR, draw b B; parallel alfo to 
D c, and where b B interfeds MM, draw la and 
through a, where la interfeds RR, draw a A. This 
done, let SS, RR and Cr, be fuppofed to reprefent 
three rulers with grooves or notches cut quite through 
them, of fuch form as is reprefented Fig. 3. 
and let thofe rulers be fcrewed down in their refpec- 
tive places S S, RR, and C<r, to a plane or frame of 
fufficient fize. 
Then 
