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

22

INTRODIUCTION.

smalnes of this book, and considering your worthynes to whom it is
dedicated, may perchance esteeme this our conceyte absurd. But if
the proportion be considered, the small quantity thereof compared to
humane imbecility, and the great utility unto high and ingenious
intendiments, it will be found to have made comparison of the
extreame tearmes, which permit not any conversion of proportion.
But what of that? Is this an admirable invention? No, certainly;
for it is so meane as that it scant deserveth the name of an invention. For as the countryman by chance sometime findeth a great
treasure, without any use of skill or cunning, so hath it happened
herein. Therefore if any will thinke, that I vaunt my selfe of my
knowledge, because of the explication of these utilities, out of doubt,
he showeth himselfe to have neyther judgement, understanding, nor
knowledge to discerne simple things from ingenious inventions, but
he (rather) seemeth envious of the common benefite; yet, howsoever,
it were not fit to omit the benefit hereof, for the convenience of sucl
calumny." This most important invention of Simon Stevin appears
not to have been appreciated by his contemporaries, but some time
elapsed before its excellence was perceived and its use discovered.
The notation he employed, being analogous to the notation of sexagesimals then in use, was a needless and cumbrous addition, and this
probably did not favour its general adoption. And it may be observed
that this notation appears to have kept from his view, that the ratio
of the descending scale from the unit's place towards the right was
the inverse of the ascending scale from the unit's place towards the
left, and that the perfection of his scheme only required some mark
for separating the integers from the decimals.
This important improvement was effected by John Napier, the
inventor of logarithms. Instead of employing the notation of Stevinus,
he simply separates the integers from the decimals by placing a point
between them without making any remark on his own simplification
of the notation. He afterwards writes the result of his example by
placing one, two, three, &c., accents at the right of the first, second,
third, &c., places of decimals. In page 21 of his "Rabdologia," which
he published in 1617, he gives the following account in an "Admonitio
pro Decimali Arithmetica":-" But should those fractions whose
denominators are various be found disagreeable on account of the
difficulty of working with them, and should that other kind, whose
denominators are always tenth, or hundredth, or thousandth, &c.,.
parts (which that most learned mathematician Simon Stevin, in his
' Decimal Arithmetic' notes and names in this manner, (1) firsts, (2)
seconds, (3) thirds), be preferred on account of their effecting the
same practical facility as integers, then the vulgar division being completed and concluded with a period or a comma, you can annex to the!
dividend or remainder one cipher for tenths, two for hundredths, three
for thousandths, or more at pleasure; and with these proceed to operate
as in the above example [861094 divided by 432] where I have added
three ciphers; the quotient being 1993,273, signifies 1993 integers
and 273 thousandth parts, or o-?b3- or as Stevinus has it, 1993,
21 711 3111." In the example referred to, the decimals are separated
by a comma from the integers, but in the following passage (p. 6)
takl en from his " Logarithmorum Canonis Constructio," published in
1619, the decimals are separated by a period from the integers.
"The less accurate calculators take 100000 as the largest sine, the