creafc or dimlnijlli the unknown Root of Equation, as to render 
it a whole number (or leffe differing therefrom, than any Error af- 
fign*d,) andby y^/^^r^ Geurds Method of Aliquot farts to find 
the fame,and thereby the Root fought although it beaMixc 
Number, FraiSion, or Surd. 
Probably this naay fympathife with what is promifcd by the 
teamed Hudknlm in AnntxU Cemetri^ Cartefian^^ v^h^rQ bo- 
fa th, he intended not then to publifli certain Rules, he had ready; 
whereof> one was. To find out all the irrational Roots both of 
Literal and Numeral Equations. This mud be underftood when 
foch Roots .are fof ible -r f^i^ 'tis certain, there are infinite Equati- 
ons> whofeRoots are no ways explicable, either in whole or mixt 
numbers^ Fradlions or Surds, and can be nootherwife explain'd, 
but by a quam pro^cime. 
The Author of this Narrative confidering, that the 
mck Sections m^y hQ projQded from lefler Circles placed on the 
Sphere, and thence ea% (otherwife than hitlierto hath been 
handled)? defcribed by Points, and that by their Tnterfediions 
fome Spherick Problem is determined, accordingly he found, that- 
this following Problem according to the various Scituation of 
the Eye, and of the Projecting Plain, would take in all Cafes, 
Thc Diftancesef anunknom Star are given from tm Stars of 
hm&rm declination andEight-Afcenfion y the Declination 4Hd Right" 
Afctnfwn of the mknown S^ar is resjiuirfd* 
And faith, he hath obferved, tkat, admitting the Mecha- 
liifme of dividing the Periphery^ofa Circle into any number of 
equal partSjOr (which is* equivalent) the Ufe.ofa Line of Chords, 
that this Problem, wherever the Eye bepkc'd, may berefolved 
fey Plain Geometry, and yet the Eyefhall be foplac'd> as to de- 
xerminit by the Interfeftions of the Conick Se^^ioas 5 C0nf<^- 
quently thofe Points of Fnt€rfe£l-i0n(the Species and Pofition 
of the figures being^given )raay be found without defcribing any 
in©fe Points than thofe fought^ and the Lengths of Ordinates 
tailing from thencfi on the Axes oi either figure calculated by 
mixt Trigoiaometry:, and hence likewise the Roots of all Ci^- 
kck and ^/-^'«^^rrf^/V* Equations fourid by Trigonometrp 
For giving from the MefolaU mentfenki the Scheme that 
finis thefe Roots^, it will then^l^e required to fit thofe Sectivrjsima 
Coms:^ which have tkeir Fertex^cithm' ia theCeneerj^ oracr af^ 
^ %i)«d point IE the Sui^aee of the Sphere jr to which they- 
