VII. Concerning the Proportion of Mathematical 
Points to eych other. By the Honourable 
Francis Robartes Efy; Vice-Prefident of the 
Royal Society. 
I T has heretofore pafs’d for a current Maxime, That 
all Infinites are equal. 
Divines and Metaphyficians have not fcrupled to 
ground many of their Arguments on that Foundation. 
The Polition neverthelefs is certainly erroneous, as 
Dr. Halley abundantly has fhown in the PhilofophicaL 
Tranfaftion for Oftober 1696. He there gives divers In- 
ftances of infinite quantities which are in a determinate 
finite proportion one to another, and fome infinitely 
greater one than another. , 
The like may be obferv’d of infinitely fmall quantities 
{viz.') Mathematical Points,) as the following Propofi- 
tions will make appear, 
PROP. I. Fig. 1. 
Jbe Points of contaU between Circles and their Tangents 
are in Subduplicate proportion to the Diameters of the 
Circles. — — — — r -■ f 
Let two Circles adch , afbg y touch one another 
from within at the point a. Draw the Tangent p a q, 
arid parallel to it the line m n. From the point a draw 
the Diameter a c. 
Let 
