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

INTRODUCTION.

25

way than by altering the place of this decimal separator, yet I cannot
see any reason to suppose that he gave a meaning to the quantity
with its separator inserted. I apprehend that if asked what his
1231456 was, he would have answered:-It gives 123-4o6o-, not it
is 123-Ao6o. It is a wire-drawn distinction; but what mathematician is there who does not know the great difference which so
slight a change of idea has often led to? The person who first
distinctly saw that the answer - 7 always implies that the problem
requires seven things of the kind diametrically opposed to those
which were assumed in the reasoning, made a great step in
algebra. But some other stepped over his head, who first
proposed to let- 7 stand for seven such diametrically opposite things."
William Oughtred, Etonensis (as he always styled himself), was
born and educated at Eton College, whence in 1592 he was elected
a scholar to King's College, Cambridge, and afterwards to a Fellowship. He devoted his attention chiefly to the mathematical sciences,
and both by his example and his writings contributed to promote and
extend the knowledge of them. His principal work was the " Clavis
Mathematica," published in 1631. It passed through several editions,
and was in repute for a considerable period; and it appears to have
been the chief elementary work used in the Universities of Oxford
and Cambridge. An English translation of the Key, "new forged
and filed," was published in 1647, and dedicated by the author to
Sir Richard Onslow and Arthur Onslow, Esq. In 1682 was published
"Oughtredus Explicatus sive Commentarius in ejus Clavem Mathematicam, ad Juvenes Academicos, authore Gilberto Clark." This
commentary it appears had been written by the author twenty years
before, when he was a member of Sidney Sussex College, Cambridge.
Another translation into English was afterwards made from the best
edition, with notes, and published in 1694. Oughtred published several
other works on the mathematics; and after his death, a selection
from his papers was published in 1676 at Oxford, under the title of
"Opuscula Mathematica hactenus inedita." Lilly, the astrologer,
in his life styles William Oughtred the most famous mathematician
then in Europe. After he had accepted the rectory of Aldbury, near
Guildford, he continued his studies to the end of his life.
The late Dr. Peacock, Dean of Ely, remarks of him:-" In those
days the members of these Royal Foundations had not yet begun to
consider the pursuits of literature and science incompatible with
each other. His works enjoyed a well-deserved reputation in his
day, and he is spoken of in his old age with singular reverence by
Wallis. He died in 1660, in his eighty-seventh year, from excess of
joy on hearing of the restoration of the monarchy."
There are other names deserving of mention, both of Italy,
France, Spain, Holland, and Germany, as well as of our own country,
who have subsequently introduced improvements and promoted the
extension of the knowledge of the Science of Number. The labour
of performing calculations with large numbers has been considerably
lessened by the extension of the denary scale to decimal fractions,
and still more by the invention of Logarithms; the former extending the powers of the notation, and the latter perfecting the
methods of computation of the Indian arithmetic.
In addition to the symbols assumed for the expression of numbers,
other symbols have, from time to time, been devised to express the