C 5 SO 
An Account of the fever al Species of Infinite Quantity, 
and of the Proportions they hear one to the other ^ 
OA It was read before the Royal Society , by 
E. Halley, 
THAT all Magnitudes infinitely great, or fuch 
as exceed any affignable Quantity, are equal 
among themfelves, though it be vulgarly received for 
a Maxim, is not yet fo common a9 it is erroneous } and 
the reafonof the Miftake (eems to be, That the Mind 
of Man, coming to contemplate the Extenfions of 
what exceeds the bounds of its Capacity, and of which 
the very Idea does include a negation of Limits 3 it 
comes to pafs that we acquiefce generally, andit fuf- 
fices to fay fuch a Quantity is infinite. 
But if we come more nearly to examine this Notion, 
v/e fhall find , that there are really befides infinite 
Length and infinite Area^ no lefs than Three feveral 
forts of infinite Solidity all of which are guantitates 
Jui generis, having no more relation or proportion the 
one to the other, than a Line to a Plane, or a Plane to 
a Solid, or a Finite to an Infinite : but that among them- 
lelves each of thofe Species of Infinites are in given 
Proportion^ is what I now intend to make plain , if 
poffible. 
But firft, infinite Length or a Line infinitely long is 
to be confidered either as beginning at a point, and fo 
infinitely extended one way, or elle both ways from 
the fame Point 5 in which cafe the one, which is a be- 
ginning Infinity, is the one half of the whole,which is the 
iumm of the beginning and ceafing Infinity, or as I may 
fay of Infinity a parte ante and a parte foft 9 which is 
analogous to Eternity in time or Duration, in which 
there is always as much to follow as is paft from any 
