Elementary arithmetic, with brief notices of its history... by Robert Potts.

1

CONCRETE NUMBERS.
ART. 1. Quantity or magnitude comprehends whatever is capable
of increase or decrease. The word is applied to all things in which
a real distinction of units can be conceived to exist, and to those in
which no such distinction naturally exists.
Discontziuous quantity includes all such things which consist of
parts separate from each other, as a multitude of objects of any kind,
and the number is known by ascertaining of how many objects tile
multitude consists.
Continuous quantity is that wherein there is no distinction of parts,
or where the parts are all contiguous, or can be supposed to adhere together, as the line, the surface, the volume of space, of which any
arbitrary portion of each may be assumed as the unit, and the exact
number of units in any magnitude can be known by the number of
times this assumed portion is contained in it. Hence it follows that
all kinds of continuous quantity can be denoted by numbers.
MONEY.
2. The standard unit of English money is the pound sterling,
which is divided into other smaller units, called shillings, pence, and
farthings, according to the following table of money of account:4 farthings are equal to 1 penny.
12 pence,, 1 shilling.
20 shillings,, 1 pound.
The letters ~, s, d, q, are the initial letters of the Latin words
libra, solidus, denarius, quadrans, and were formerly used to denote
the names of pounds, shillings, pence, and farthings. The letters
~ s. d. are still employed for that purpose, but the q. is now seldom
used, the fractions a, -, 3 being employed to denote 1, 2, 3 farthings
respectively. Since the four units of English money are the pound,
the shilling, the penny, and the farthing, and that 20 shillings make
one pound, 12 pence one shilling, and 4 farthings one penny; it
follows that any number of pounds can be expressed in shillings, by
multiplying the number of pounds by 20; shillings can be expressed
in pence, by multiplying the number by 12; and pence in farthings, by
multiplying the number by 4.
And conversely. Any number of farthings can be changed to
pence by dividing the number of farthings by 4, pence to shillings by