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

24

INTRODUCTION.

imperfectly appreciated at the time, that it was not generally adopted
until after the middle of the seventeenth century.
Professor De Morgan in his "Arithmetical Books" (p. xxiii.)
questions the fact of Napier having first applied the comma or periodto separate integers from decimals. He remarks: " The inventor of
the single decimal distinction, be it point or line, as in 123*456 or
1231456, is the person who first made this distinction a permanent.
language, not using it merely as a rest in a process, to be useful in
pointing out, afterwards how another process is to come on, or
language is to be applied, but making it his final and permanent,
indication as well of the way of pointing out where the integers end
and the fractions begin, as of the manner in which that distinction
modifies operations. Now, first, I submit that Napier did not do this;
secondly, that if he did do it, Richard Witt did it before him."
It is true that Richard Witt in 1613 published a work entitled
"Arithmetical Questions touching the buying or exchange of annuities, &o., briefly resolved by means of certain breviats."l These are
tables of compound interest cak llated yearly, half-yearly, and
quarterly, and a small vertical line is employed as a separation of
the integers from the decimals. The tables are expressly said to consist of numerators with unity and ciphers annexed for denominators.
On the table of the amounts of ~1 at compound interest at
10 per cent. per annum for one year to thirty years, he remarks," These 30 termes, viz., the 30 numbers [11, 121, 1331, &c.] in the
table, are numerators of improper fractions. The denominators of
which fractions are also a progression: the first term thereof (that is,
the first denominator) being 10, the second ten times the first, which
is 100, and the third ten times the second, which is 1000, and so on
increasing to 30 terms. So it appeareth, that if the numbers (or
numerators) in the tables be taken with their denominators they will
stand thus, {l, which is 1-o-; 21 which is 1; 1-3, which is
lo I 0 1 00, to, i, UU
^',,-; and so forth, till all the thirty termes have their denominators placed under them."
In p. 15 he writes the fraction 1744o94 2 thus, 1714494022, and
employs no other notation in his work. He used the period to
separate pounds, shillings, and pence, as 61. 13sh. 4d. or 6.13. 4d.
It does not appear that Witt employed his separatrix as Napier
had used the comma and period, in the full sense of its modern employment. This is clear from the examples in Napier's " Logarithmorum Canonis Constructio," which had been composed long before
Witt's book was published.
Mir. De Morgan ingenuously adds, " But I can hardly admit him
(Witt) to have arrived at the notation of the decimal point. For,
though his tables are most distinctly stated to contain only numerators, the denominators of which are always unity followed by ciphers,.
and though he has arrived at a complete and permanent command
of the decimal separator (which with him is a vertical line) in every
operation, as is proved by many scores of instances, and though ho
never thinks of multiplying or dividing by a power of 10 in any other
1 In Jeake's Arithmetic, p. 427, " Practice is so called from the frequent use anlI
general practice thereof, and is a compendium or breviat of the brief rules and
most expeditious method of resolving the proportions resolvable by the rule of
three." The word breviat is applied by Witt to his tables of interest.