[ 55 ° ] 
of equal Girelbs, and w circles in each row, the 
number of interftices- formed by all tlie rows is 
zm — 2 X n — 1 . Now, when the circles are in- 
finitely fmall, their diameters are infinitely fmalL 
Therefore,, the fpace which they cover being, of finite 
magnitude, it is necefTary, that both the number of 
circles in each row, and the number of rows, that 
is,- that each- of the numbers, m and fliould be 
infinitely great. But when m and n are each in- 
finitely great, zm — 2*x n — i, that is,, the num- 
ber of interdices, becomes ultimately zmn\ and the 
interdkes being all equal one to another, if the area 
of one be called P„ the fam of their areas will bo 
zvm X P. But the number of circles in n rows, 
each rov/ confiding of 7n circles, is mn'y. ajid the 
circles being equal, if the area of one be called A, 
the dim of their areas will be mn x A. " Hence the 
fpace covered by all the circles is to the fpace covered 
by all their interftices, when the magnittftie of each 
circle is infinitely diminidied, and the number of 
them fb infinitely augmented, as that they diaFl 
cover a fpace of finite magnitude, ultimately, as 
to 2W72xP, that is, as A to 2 P, or as 
^ A to P, that is, as £ the area of one circle to the 
whole area of one interdice. 
Cafe 2 . Now, fuppofe, that unequal numbers of 
circles are ranged along the feveral lines AG, HP,, 
QX, &c. which mud always be the cafe, if the 
figure of the fpace, in which they are contained, be 
any other than a parallelogram ; and let the number 
upon AG be the greated of all, and call that num- 
ber, as before, m. If from the row HP, the ex-’ 
tremc 
