INF 
By the custom of London, an infant un- 
married, and above the age of fourteen, 
if under twenty- one, may b>nd himself ap- 
prentice to a freeman of London, by in- 
denture, with proper covenants, which co- 
venants, by the custom of London, will be 
as binding as if of age. 
If an infant draw a bill of exchange, yet 
he shall not be liable on the custom of mer- 
chants, but he may plead infancy in the 
same manner as he may to any other con- 
tract. 
An action on an account stated, will not 
lie against an infant, though it be for neces- 
saries. 
INFANTRY, in military affairs, denotes 
the whole body of foot-soldiers. 
INFINITE, that which has neither be- 
ginning nor end : in which sense God alone 
is infinite. See God. 
Infinite, or Infinitely great line in 
geometry, denotes only an indefinite or 
indeterminate line, to which no certain 
bounds, or limits, are prescribed. 
Infinite quantities. The very idea of 
magnitudes infinitely great, or such as ex- 
ceed any assignable quantities, does in- 
clude a negation of limits : yet if we nearly 
examine this notion, we shall find that such 
magnitudes are not equal among them- 
selves, but that there are really besides in- 
finite length and infinite area, three several 
sorts of infinite solidity; all of which are 
quantitates sui generis , and that those of 
each species are in given proportions. 
Infinite length, or a line infinitely long, 
is to be considered either as beginning at 
a point, and so infinitely extended one 
way, or else' both ways from the same 
point; in which case the one, which is a 
beginning infinity, is the one half of the 
whole, which is the sum of the beginning 
and ceasing infinity; or, as may be said, 
of infinity a parte ante and a parte post, 
which is analogous to eternity in time and 
duration, in which there is always as much 
to follow as is past, from any point or mo- 
ment of time: nor doth the addition or 
subduction of finite length, or space of 
time, alter the case either in infinity or 
eternity, since both the one or the other 
cannot be any part of the whole. As to 
infinite surface, or area, any right line, in- 
finitely extended both ways on an infinite 
plane, does divide that infinite plane into 
equal parts, the one to the right, and the 
other to the left of the said line; but if 
from any point, in such a plane, two right 
lines be infinitely extended, so as to make 
INF 
an angle, the infinite area, intercepted be- 
tween those infinite right lines, is to the 
whole infinite plane as the arch of a circle, 
on the point of concourse of those lines as 
a centre, intercepted between the said lines, 
is to the circumference of the circle ; or, as 
the degrees of the angle to the three hun- 
dred and sixty degrees of a circle : for ex- 
ample, right lines meeting at a right angle 
do include, on an infinite plane, a quarter 
part of the whole infinite area of such a 
plane. 
But if two parallel infinite lines be sup- 
posed drawn on such an infinite plane, the 
area intercepted between them will be 
likewise infinite ; but at the same time will 
be infinitely less than that space, which is 
intercepted between two infinite lines that 
are inclined, though with never so small 
an angle; for that, in the one case, the 
given finite distance of the parallel lines 
diminishes the infinity in one degree of 
dimension; whereas, in a sector there is 
infinity in both dimensions : and conse- 
quently the quantities are the one infinitely 
greater than the other, and there is no pro- 
portion between them. 
From the same consideration arise the 
three several species of infinite space or 
solidity ; for a parallelopiped, or a cylinder, 
infinitely long, is greater than any finite 
magnitude, how great soever; and all such 
solids, supposed to be formed on given 
bases, are as those bases in proportion to 
one another. But if two of these three 
dimensions are wanting, as in the space in- 
tercepted between two parallel planes in- 
finitely extended, and at a finite distance, 
or with infinite length and breadth, with 
a finite thickness, all such solids shall be as 
the given finite distances one to another ; 
but these quantities, though infinitely great- 
er than the other, are yet infinitely less 
than any of those, wherein all the three 
dimensions are infinite. Such are the spaces 
intercepted between two inclined planes 
infinitely extended ; the space intercepted 
by the surface of a cone, or the sides of a 
pyramid, likewise infinitely continued, &c. 
of all which notwithstanding, the proportions 
one to another, and to the to otbv, or vast 
abyss of infinite space (wherein is the locus 
of all things that are or can be ; or to the 
solid of infinite length, breadth and thick- 
ness takes all manner of ways) are easily 
assignable ; for the space between two 
planes is to the whole as the angle of those 
planes to the three hundred and sixty de- 
grees of the circle. As for cones and 
