vsLrycd ill terms ot Jigns. After \\ieSynthe(u our Author 
fliews the analyfis or methodhy which he found this Rule, 
viz. a jP^r<3J^o/^ beingdefcnbed, and z point in its //^//2 
given inpojition, he exprefles 2 ways, the radius of a ^>r- 
r/^ palling through the Vertex of any diameter^ i. e. by 
pofition of the given Center , and application of the 
iorefaid propriety to exprefs the ratio of the radius to 
the given lines of the parabola: So having an Equatiou 
of \dimenJions^ and rejeding equal on both fides, hede- 
preflfes it to ^.Cubicy but adjoyning to it a quantity for 
, the Homogene of the comparifon, the Equation fubfifts 
in a Biquadratic, having all its terms , if the Circle be 
fuppofed to pafs not thro the vertex of the diameter , but 
thro a point which being joynd with the Vertex ^ndCenter 
may terminate a right angled triangle. 
This Equation he compares with another like it and 
equal to itj tliQii by equating the Coeffiae?its of thefe 2 
Equations he prefently difcovers the central Rule ^ whofe 
univerfal extent appears in BiquadraticEquations zSeSttd 
under all their -P^ro^/V degrees ; for all the other cafes 
where any terms are wanting, are but Corollarys or 
more compendious Conftrudtions deriv'd from the ge- 
neral rule. £0 that the invention of the rule feems as 
much due to the laQ: Equation of the Coefficients, as to the 
forefaid propriety , which is demonftrated by Archimedes 
in the Section of a parabolic Conoidhy aplane parallel to 
the axis, and is particularly ufed by Slufius inhis Analy- 
tics , who thereby conflrLidts a Biquadratic Equation 
keeping zS\. \t% terms. But then the Analyfis ot Slufius 
by breaking the Equation into 2 others to find 2 places 
is very different firom that whereby our Author found 
his r^w^r^/ rz^/^ ; then which nothing can be expedl- 
ed more eafie, fimple, or univerfal ; feeing any Fara- 
hola being once for all defcribed, will give all the roots 
true and falfe, of any Equation without redudion or 
any alteration. 
\JE^KKArvM. p, 51 8.; line the lafl, read Ntibigenum. . , 
OXFORD, Printed at the THE^T^ET?, an'd are to be fold 
hy Mo fes Tin, at the A97gtf^ and Samuel Smith, at the Prmces 
Arms in St. T^^ul's ChHrch-jard LONDON. 1(584, 
