which troubled all Gmii^ The Solution of which Probleme la 
Geometry may be compared to that with the giving of the 
Cube-root of any Number propofed in Arithmetick : For, ia 
Arithmetick, the firft of two continual Proporri' n Js bttvveea 
znUm and any Number proipokd^ls the Cube-root oi that Nain- 
ber^^^d the Unit in Arithmetick is reprefented b} ■ Lincia Geo- 
meirvj^vhich is one of the Extreams. 
Concerning this Probleme, the Author declares himfelf to be 
none of chofe, that fearch for that which cannot be found ^to wit^ 
to perform it by f.ight Lines and a Cirde. 'Ti$ true indeed, it may 
be fo done, to wit, by tryalsand profers > as, who cannot in that 
manner divide an Arch into three Equal parts < Butfuchik/^r^^- 
m[mes zx^zccomitA ageometricks and fuch operations may be 
well refembled to the vulgar Rule of Falfe Fofttion in Arithme- 
tick, which cannot give an abfolute true Refolution of one of 
the meaneft of Queftions, when the thing fought is Multiplex of 
it felf, or Involved 5 for inftance, what Number is that, which, 
mukiplyed in it felf makes 9 5 who I^oweth it not to be 3 ^ But 
who can find it to be abfolutcly fo by the aid of the ordinary 
rules of Falfe Tofttion^ wherein the Extraction of a Square Reot 
is not prefcribed i 
The Author obfervefj, that amongft thofe, that folve this Pro- 
bLeme by the Conick SeSiions^ thty feem to have afforded fewer 
Effedions thereof, than there have been Ages, fince it was firft 
propofed. Very few by ayd of a Circle and an Hyperbola or Para- 
bola : by a Circle and Blliffis none, that he could obferve to have 
been publiflied. 
The which the Author confidering , and ftudying how to 
fapplyjhe found out not osely one, bat infinite fuch EfFcdlions, 
and that not in one Method,but many 5 ' following the guidance 
of which Methods, by the like felicity he hath conftruCled all 
folid Problems infinite ways, by a OW/^ and an EMiffts oxHy- 
ferhola. 
I. His general Methods for finding two Means, by a Circle 
and cither an HjperboU or Bllipfis^ are laid down in Prop. 1,2,1^, 
and in this 16 Prop, he flieweth to do it with any Slliffis and a 
Circle. 
z. Particular Effeiiions for finding but one or both of the 
Means^ 
