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

INTRODUCTION.

23

deeper select 10000000, by means of which number the difference
betwixt all the sines can be better expressed. That is the reason why
I have adopted it for the whole sine, and as the maximum of the geomuetrical progression. In computing tables, even very large numbers
are to be made still larger by placing a period betwixt the original
number, and ciphers added to it. Thus at the commencement of my
computation I have changed 10000000 into 10000000-0000000, lest
the most minute error might, by frequent multiplication, grow into
an enormous one. In numbers so divided, whatever is noted after
the period is a fraction, whose denominator is unity, with as many.ciphers after it as there are figures after the period. Thus, 10000000'4
is equivalent to 10000000-1. So 25-803 is the same as 250. Also
'9999998-0005021 is 9999998, o50- and so on. From the tables so
computed, the fractions placed after the period may be rejected without
any sensible error, for in these very large numbers the error is to be
considered insensible and nugatory where it does not exceed unity.
For when the table is completed, for the numbers 9987643-8213051,
which are equivalent to 998764300s2'3,5 there may be taken 9987643
without any sensible error."
Norton's tract did not reach a second edition, and the subject appears not to have been brought under general notice. About eleven
years after, the substance of Norton's tract was published by Henry
Lyte in 1619, with a dedication to Charles Prince of Wales.1 His
work contains no additions nor improvements on the notation of Stevin.
The notation adopted by Norton is somewhat in form different from
that of Stevin. Instead of circles with small figures placed within
them, Norton employed a parenthesis, with small figures placed
between the upper ends; thus 8(0)9(1)3(2)7(4) means 8-9307.
In the first chapter of his Clavis, published in 1631, Oughtred
explained the principle of decimals, and separated the integers
from the decimals by the mark._, which he called the separatrix,
as in p. 2 he writes 0 15, 0100005, and 3791236, for '56,
~00005, and 379-236 respectively. The theory as given by Oughtred
and his notation were generally adopted by writers on arithmetic for more than thirty years after his time. Both the English
and foreign writers on arithmetic adopted different modes of notation, all of them, however, following more or less the notation of
sexagesimals.
The Arithmeticse Theorea et Praxis of A. Tacquet, published
in 1656, marks the places of decimals with Roman numerals as
exponents, after the manner of Stevinus, who employed figures.
Briggs in the introduction to his Arithmetica Logarithmica employs a line placed under the decimals to distinguish them from
the integral numbers; thus, p. 5, he writes, 343 for 3-43, and 16807
for 16-807. In his posthumous work, "Trigonometria Britannica,"
published by Gellibrand, appears the same method of separating
decimals and integers, as, p. 30, 131595971 denotes 1-31595971.
It may be a matter for surprise that the convenience of Napier's;simple notation for the separation of decimals from integers was so
1 The following is a copy of the title page: "The Art of Tens; or, Decimal
Arithmetike; wherein the art of Arithmetike is taught in a more exact and perfect
method, avoyding the intricacies of fractions. Exercised by Henry Lyte, gentleman,
and by him set forth for his countries good. London, 1619."