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

26

INTRODUCTION.

relations and the elementary operations of numbers. These symbols
have been designated symbols of operation, to distinguish them from
figures which have been named symbols of number. As to the symbols
themselves, they stand simply as abbreviations of written words, and
only require their assumed meaning to be understood so as to render
intelligible the expressions in which they occur. The operations of
arithmetic can dispense with the use of them; but where several
operations are to be performed, some the reverse of others, it will be
found useful to indicate the operations by means of these symbols.
The mark = was introduced and used by Robert Recorde for the
sign of equality. The first account of its use occurs in his treatise on
Algebra, entitled "The Whetstone of Witte." In the rule of
equation he remarks:-" And to avoide the tediouse repetition of
these woordes, is equalle to, I will set as I doe often in woorke use, a
pair of paralleles, or gemowe lines of one length, thus: =, bicause
noe 2 thynges can be more equalle."
When the symbol = is used in arithmetical reasonings or calculalations, it must be understood as having relation only to pure arithmetical equality. Napier adopted it and defined it in these words:"Betwixt the parts of an equation that are equal to each other, a
double line is interposed, which is the sign of equation." Mr. Babbage, however, in one of his papers on Notation, observes: —" It is a
curious circumstance that the symbol which now represents equality
was first used to denote subtraction, in which sense it was applied by
Albert Girard, and that a word signifying equality was always used
instead until the time of iEarriot."
The signs of relative magnitude, > meaning is greater than, and
< is less than, when placed between any two numbers, were first introduced by Thomas Hlarriot, in his " Artis Analyticse Praxis."
-The sign + is used to signify addition, and was first employed by
Michael Stifel in his "Arithmetica Integra," which was published in
1544. Its origin is uncertain; it has been supposed to be the abbreviated form of the word et, as found in some manuscripts. The mark
+ was used by Stifel for the word plus, and employed strictly as the
arithmetical sign of addition, instead of the words " is added to."
The sign - was also employed by Stifel in the same work as the
sign of subtraction. Some have supposed he adopted it from the fact
that a small line - was commonly used in Latin writings to show the
contraction of a word by the omission of one or more of its letters, as
secuda for secundum, numerum for numerorum, &c., and that he
named the mark minus, and used it instead of the words " taken from,"
or " subtracted from."
The sign x of multiplication was introduced by Oughtred in his
"Clavis Mathematica." It is used to indicate the product of two
numbers when placed between them, and stands for the words " multiplied into." The product of more numbers than two may be expressed in a similar manner.
The sign - placed between two numbers denotes the division of
the former by the latter, and stands for the words " divided by," or
" is divided by." The Hindus placed the divisor under the dividend,
with no line of separation. The line was afterwards introduced by
the Arabians, and has since been universally adopted.