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XXIV. Directions for mating a Machine for 
finding the Roots of Equations univ erf ally ^ 
with the Manner of ufing it : By the Rev . 
Mr. Ro wning, to John Be vis, M. D. 
F. R. S. 
S I R, 
Read May 3 >TT^E R U SIN G a difcourfe in the me- 
I/7 °' Jh moirs of the Royal Academy at Peterf- 
hurgh, Tome vii. page 21 1, by the learned John 
Andrew de Segner, containing an univerfal method 
of difcovering the roots of equations, which you 
was fo kind as to recommend to my confideration* 
I found, that the author’s method, as youobterved to 
me, confifted in finding feveral ordinates of a para- 
bolic curve, fuch, that its abfcifTas being taken equal 
to any affumed values of the unknown quantity in 
the equation, the ordinates correfponding to thofe 
abfciflas, fhould be equal to the values of ali the 
terms in the equation (when brought to one fide) 
that is, in other words, in finding feveral ordinates of 
a parabolic curve defined by the equation propofed : 
in which cafe, as is well known, if a curve be drawn 
through the extremities of the faid ordinates, the 
points upon the axis, where the curve fhall cut it, 
will neceffarily give the feveral values of the real 
roots 
