[ 2 4 + 3 
always to be eftimated on a fcale on which the 
affumed line D c is unity. 
Demonjl. Since the lines OA, AB, BC, &c. are 
to be taken proportional to the coefficients a, b, c , See. 
let us fuppofe the firft of them, viz. OA, to be 
taken equal to the firft coefficient a, or to any part of 
it taken at pleafure ; fuppofe for inftance, to the n tJ * 
part, that is, to ^ j then, to preferve the above-men- 
tioned proportionality, the next viz. AB will be 
b c d 
equal to — , BC will be equal to — , and C D to — , 
&c. Call OQ or its equal DP, xj then D c, as above- 
mentioned, being taken equal to unity. Pc will be 
equal to 1 — x, and DC being equal to and the 
triangles DCcandPy<r being fimilar, we have this 
proportion, viz. 1 : 1 — x : : : - n ~ = P q or D k ; 
but kP is equal BCq-CD — T)k , that is, to ~ 4--^- 
— ——— '» that is, to i and by fimilar triangles, 
as kb: qb:: kP : qr, that is, in fymbols, as 1 : 1 — x 
: : — — i = qr or kl i but A / is equal 
to AD— T>k— kj, that is, in fymbols, to -^4*' 
d — dx c-bdx — cx — dxx 
that is, to 
b-\-c x + d x x 
and by fimilar triangles, la :ra:: A / : rs j in fym- 
. , b-\-cx-\-dxx b+cx+dxx — bx — exx — dxxx 
bols i : i —x : : : 
n n 
—rs j Q s therefore, which by the figure is equal to 
qp 
