a celia 
fete 
ae 
— Divisibility of Matier. , 101 
be made up of sueh (adivieible portions, a surface of lines,and 
asolid ofsurfaces a circle,therefore, filled with the waeigperie 
of other lesser circles cutting a diameter, shows 
than the assumption itself, which is, that points: sn 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, i is directly contrary to the very defi- 
nitions of geometi Points, lines, and surfaces are 
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 su 
that to be infinite, such a condition would not give to them 
any other property than that included in the Seaition, viz: 
an infinite number of boundaries of'no magnitu m the 
same definitions, it results, thatevenan ge number ofp 
pheries of lesser concentric. pss would not coreee 
up the area ofa given circle. The supposition Pe the author 
is, therefore, mathematically sueobsutbos and impossible. — 
I know full well, that the notion of indivisibles has been 
employed by mathematicians of | eminence, not et etending 
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, em loyed such prin- 
ciples i 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 eee. divisible. 
)j as defined and understood by Math: 
ematicians, being that on which the Metaphysigue, 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 are desirous of being 
gs on this subject. 2 
