be accounted a-geometrical y becaufe they are not perform'd by 
the Sole aid of Ruler and Compafs-, which he fuggefts to be well 
obferv'd a Subtilij?imo Mathematico D. Carolo Reinaldino in Geo- 
metra fuo promote , dum tract At denovis illis Lineis^ quas Medi- 
cez$ appeBat : Concerning which Author, he faith thus, p. 132. 
£ui autem defider at plenum Analyjees & *ALquationum doctrinam, 
txfpectet abfolutifimum Caroli Reinaldini Opus de Rejclutione & 
CvwpjQ fit tone Mathematical quod nunc fubpr do eft. It feems, that 
the Book will be three large Volums in folio * the firft whereof 
being Introductory, and containing the Algebra of the Antients, 
is already in England, 
And for the Confirmation of what hath beenaflerted, the Au- 
thor thus demonftrates, that no Cubick ^/Equation (that is irre- 
ducible to a guadratick) can be refolvYfby the fole aid of Ruler 
and Compafs. For every Cubick ^Equation hath either but one 
or three real roots, which if they could be found by the faid fole 
aid of Rule and Compafs, or by the Interferon of a Circle and a 
Right Line, then a Right Line fhould cut a Circle either in one 
Point or three 5 either of which is moft abfurd. And for the 
like xeztonz Cubick v£quation> having three real roots, can ne- 
ver be reduced to a pure zy£qua{ion, which hath but one onely 
.root 5 for in thefe equations, Reduction (hall no wife profit, for- 
afmuchas'tisimpoflible, by aid thereof to change an Imaginary 
root into a real one, and the Converfe. 
As to the Argument of the Book it felf,it contains xhefe feve- 
jal Heads, 
I. The Menfuration of fundry Solids, with General Methods 
to thatpurpofe* concerning whicfythe Author faith, p. 123. 
Totusnamque Archimedis Tractates de Sphtra & Cflindro facile 
demonfiraturexhujus 3. ad modumhujus 46. & aliquot fequenti- 
um : Liber de Cenoidibus & Sphtreidibus, &tota Luca Valeriido* 
ctrina^ex hujus 21. T ota Guldini, tfohannis de la Faille, & An- 
drea Tacqueti doctrina, exhujus^^. & aliquot fequentium. And 
as a Corollary of Prop. 62. he Cubeth or meafureth either of 
the Segments of a Parabolical Conoid cut with a Plain, parallel 
to the Axis. Hence we obferve, that fuppofing fuch a Seg- 
ment ? again cut with a Plain, ere& to the former Plain, the f re- 
f vfition may be well apply 'd to the Guaging of Cask part due, 
when 
