fnfimte Divisibility of Matier. 104 
be made up of sueh indivisible portions, a surface of lines, and 
asolid ofsurfaces ;a circle,therefore, filled with the peripheries 
of other lesser circles cutting a diameter, shows nothing more 
than the assumption itself, which is, that points have exten- 
sion and that a given line is made up of such points. But 
that a point has any parts, or dimensions, or that a line has 
any breadth, or thickness, is directly contrary to the very defi- 
nitions of geometry. Points, lines, and surfaces are merely 
the terms, or limits of extension, and constitute no part of that 
species of magnitude of which they are the limits. No num- 
ber of points can constitute a line, and if we even suppose 
that to be infinite, such a condition would not give to them 
any other property than that included in the definition, viz : 
an infinite number of boundaries of no magnitude. From the 
same definitions, it results, that evenan infinite number of peri- 
pheries of lesser concentric circles, would not fill or make 
up the area of a given circle. The supposition of the author 
is, therefore, mathematically inconsistent, and impossible. 
I know full well, that the notion of indivisibles has been 
employed by mathematicians of eminence, not pretending 
that they have an actual existence, with a view of aiding our 
conceptions, and illustrating difficult subjects relative to the 
quadratures, cubatures, and rectifications of curves, &c. Cay- 
allerius, Terricallus, Wallis, and others, employed such prin- 
ciples in the solution of problems ; but no legitimate deduc- 
tion could be made from them, but by assuming an infinite 
number of terms, which necessarily implies, that each must 
be infinitely little, or infinitely divisible. 
The subject of infinites as defined and understood by Math- 
ematicians, being that, on which the Metaphysique, or ulti- 
mate principles of the higher and more difficult branches of 
the mathematics are based; it is of importance, that all ob- 
jections and cavils, which may be made to the doctrine, 
should be obviated. ‘hose which were started by Berkeley, 
and other ingenious men of the last century, have long since 
been annihilated, in the opinion of the learned, by the mas- 
terly productions of Keil, Robins, and Maslaurin. To their 
writings I beg leave to refer those, who aré desirous of being 
enlightened on this subject. v 
