I rioi] 
a nd grounded thereupon ; not any way contrary or re- 
pugnant thereunto. 
Confe<}uent to this, is the Arithmetica Infinitorum, 
which depends alfo on the method of Exhauftions ; tak- 
ing that to be Equal, which is proved to differ by leis 
than any affignable Quantity. And a Vindication of the 
method of Demonftration therein uled. 
Andlaftly, the method of infinite 6'<?r/>/, ("as of late 
they have been called^ or continual Approximations ^ 
(grounded on the fame Principles ij arifing Principally 
from DivipQUy and Extraction of l^ots in Species ^ In- 
finitely ontinued. 
With federal Examples of the Application thereof, to 
the Squaring of Curve-lined Figures,Red:ifying of Curve 
Lilies, Pla iitng of Curve Surfaces, and many other per- 
- plexed Inquiries. 
Which is an Arithmetic^ of Infinites upon Infinites-. 
For when as the §^otient of Divifion, or the ^ot cx- 
trad:ed in Species » doth not Terminate, but run on 
Infinitely, (much after the manner of fome ordinary 
Fractions, when reduced to Decimals;) an Infinite Se- 
ries of thefe ("continued as far as is thought neeeffary,) 
is CoUeded according to the method, in the Arithme- 
tick of Infinites, for Terminated Magnitudes. 
This was introduced by Mr. I/aac Newton, and hath 
been purfued by Mr. Nicholas Merfator, and others. 
And it is of great nfe for Re(Stifying of Curve Lines, 
Squaring oi Curve-lined Figures, and other abftrufe 
Difficulties in Geometry ; efpecially where the Enquiry 
doth not end in a determinate Proportion, explicable 
according to tlae commonly received ways of Notation. 
And on this occafion, is inferred a Difcourfe of Infinite 
TrogreJJions Geometrical ^ (which when deereafing, be 
come Equivalent to Finite Magnitudes,^ firft uled by 
Archimedes, andlince purfued hj Torricellius, San-Vin" 
cent, Tacquet, and others. With the Refult of two or 
more fuch Progreffions compounded. Several 
