C 306s ) 
Operations , he faith he hath delivered the Principles noc 
only 9f meafuring the Magnitudes and Diftances of places 
Inacccffible ^ of making the Map of a place or a province 5 
Qf finding the Sinm*$ , Tangents and Secants of all Angles; 
but in (hort, df coming to the Knowledge of what ever ap- 
pertains to this part of Geometry. 
In his Preface promifcth to give us, mxt ^ his Algebra, 
his Do(ftrine of Conical Seftions, Sphericks and Staticks* 
bur, above all, to eftabliflb Five or fix General Rules, whence 
afterwards , by way of Corollaries , may be drawn ihe de- 
monftration of an Infinity of Propoficions , which pafs for 
great ones in Geometry : Where, he adds, (hall be found 
the nature andmeafure of Afymptoticj^rpzcct^ as the moit 
admirable knowledge in the World ^ thofe fpaces being of 
an extent aftaally infinite , comprifed between two lines, 
which being infinitely prolonged do never meet i but of 
whichyctitmay bedemDnftrated, that they are equal to a 
Circle or another determined figure 3 fo that Infinite it felf, 
as immeofe and innumerable as it is, may notwithftanding 
be reduced to a calculus and to a Geometrical meafure , 
and that the Mind of Man, being greater than it, is capable 
to comprehend it ; For fince Imagination cannot attain fo 
far as to rcprefent unto us what is Infinite; the demonftfa- 
tion, we make of the nature and proprieties of this iramenfe 
and infinite Afympotick extenfion, convinceth us at the fame 
time, that we have within us a power capable to reprefent 
unto us this infinite Extenfion. For, Jaithhey as, for mea« 
furing with a Rule and Corapafs a Figure reprefentcd upon 
paper , I mufl have this Figure prelcnt to mine eyes and 
hands, that fo, by applying the Inftruments to its angles 
and fides, I may take all the dimenfions of ir, and fo de- 
termineits Magnitude; even fo, for taking with the rule 
of my Reafon the meafures of this Afymptotick fpace, I 
mufl: have an Idea thereof inwardly prefented to my Mind^ 
and this Mind by applying it felf, as it were , to this idea and 
Interior figure, muft take the dimenfions of it, determine 
its bignefs , and demonflrate all its proprieties , 
la 
