20 MEMOlRSofthe 
exceeding thiiinefs, many of thole atoms may Hill lie one over the 
other. 
Oft/^e feverql Species of infinite Quantities, and their Ratio's 
to each other t, by ^Ifr. Edm. Halley. Phil. Tranf. N° 195. 
p. 5 5(?. 
THAT all magnitudes infinitely great, or fuch as exceed 
any affignable quantity, are equal amongft themfelves. tho' 
it be vulgarly received as a maxim, is not yet lb common, as it is 
erroneous; and the reafon of the miftake Teems to be, that the 
mind of man conning to contemplate the extenfions of what exceeds 
the bounds of its capacity, and of which the very idea does 
include a negation of limits, it comes to pals that we acquielce 
generally, and it luffices to lay, fuch a quantity is infinite: But 
if we examine this notion more narrowly, we fhall find, that there 
are really befides infinite length, and infinite area, no lefs than 
three feveral forts of infinite lolidity ; all which are quantities 
fui generis, having no more relation to each other, than a line 
hath to a plane, or a plane to a Iblid, or a finite to an infinite 5 
but that amongft themlelves, each of thofe fpecies of infinites are 
in given ratio's will plainly appear: And 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 pointy in which cale, the one, which is a begin- 
ning infinity, is the half of the whole, which is the aggregate of 
the beginning and ceafing infinity ^ or, as we may lay, ^of infinity 
a parte ante and a parte foft-^ which is analogous to eternity, in 
which there is always as much to follow as is already paft, trom 
^ny point or moment of duration^ nor doth the addition or fub- 
itraftion of finite length, or fpace of time, alter the cafe either in 
infinity or eternity, fince neither the one nor the other can be any 
p rt of the whole: As to infinite furface or area, any righe line, 
infinitely extended both ways on an infinite plane, does divide that 
infinite pkne into equal parts, the one to the right, and the other 
to the left of the laid line 5 but if from any point in luch a plane, 
two right lines be infinitely extended, (o as to make an angle, the 
infinite area, intercepted between thole infinite right lines, 
is to the whole infinite plane, as the arch of a circle, on the 
pointofconcourlc of thole lines, as a centre, intercepted between 
the faid lines, is to the circumference of the circle 5 or as the 
degrees of the angle to 560°, for inftance, two right lines, 
meeting at a right angle, do include, on an infinite plane, 
^ quarter of the whole infinite area of fuch a plane: But if 
tWQ 
