( PsO 
kind th« Rtsil^ may fin4 Examples in SriggU AmtkmetkA Loga- 
rithmie^ d Trigonometm Bri^mnim^ r«bting to Logarithmes » 
Sin^s, and the Powers of an. Arithmetical Progreffion : But the 
method there delivered maybe rendred more eafy and general, 
viz. by aid of a Table of figurat Numbers, by deriving 
Generating diffcreiices /^/^^k, from thok given % a dodrine? 
that eafily iSows from ,M^r<r4Wx Logarithmotechma 3 and of 
ufe in the tafe in hand , fliould we fuppofe thefe Powers and 
their Coefficients vnknown, or a Table of Squares and Cubes 
wanting, and give nothing more^than a few Hejolvends belonging 
to equal Moments or Spaces. And this may likewife be of 
good ufe in Guaging j when having the Contents of a Solid ^ 
for every j. laches, more or leffe, given^ without knowing the 
dimenfions of the Figure, and even in moft Cafes* when the dif- 
ferences are Progresfive of one kind, without knowing the Fi- 
gure it felf 3 having nothing: given but its Contents at feveral 
equal Parallel diftances, each fuch diftance may be fubdivided , 
and made as many as yon pleafe^and the refpedive Contents 
found by this general Method of Interpolation.* 
*N:ta. Author (M. Coi- After one Root is obtained , the 
lins) hiveing expim'l Mercators Methods, of HudHenius and others will 
themj with Exmpks , haib JifiS' ipofc , and confequently all of them. 
kfon^"mdm\7th^^^ It is eafy, by a T/i^/^ of figurate 
^^^Ti(^%!"^3^%iaSs'^ Numbers to give the fum of any fuch 
gures bj mm Divifion(or Propor- Rank Or any term in it relating to a 
fion^j^Uchias 'tisihtu iiiuftrA' Roots-, but^ r^^/^i'^r/^ 5 giving the i^^- 
ted) m not ^Qem t<t extend farr ft, [vend to End the Root, coms to an 
enough. Tim bath already been com- °^T^ • j-rr i l rj 
muniuted, fome. Months ftnce, n Equation as difficult as that propofed 5 
(erne of the Members of thsV^.to- aS in D» Wallis Ms Chapter of Fi' 
ckty,47!dmd)beexp€^€dhereafter. gyj-ateV^^mj^bers. 
7. Some affirm , they can give good Approaches for the ob« 
taining a Root of any /«ifr^ power, ^jfi^-f^^ Equarion^orforthe 
finding of any of the mean Proportionals in any Rank between 
two ex treams given, ■'■ 
S, Others pretend to have found out a method (incited there- 
to by an example Jlbert Gerards Invention Nouuelle en^lgebre 
a Jmfierdam i62fi.) fo much, by comparing of Equations;^ toin- 
Pp pp 2 creafe 
