Memoirs of John Napier of Merchiston

INVENTION OF LOGARITHMS. 451
Simon Stevinus of Bruges, who published La Practique D' Arithmetique about the year
1582. He afterwards put forth other works upon arithmetic and algebra, along with a
translation of some books of Diophantus, in all of which he evinced the highest genius
for his subject. Algebraic notation received from his hands another of those impulses
by which it has so gradually reached its present perfection ; and arithmetic is indebted
to him as the first who expressly promulgated the doctrine of Decimal fractions. It was
most probably about this period that our own philosopher commenced his endeavours to
create a decided revolution in the science of numbers. A contemporary of Napier's was
the great Vieta, whose name reflects such lustre upon France. His algebraic work first ap-
peared in 1600, but by this time Napier's studies had ripened into the Logarithms, which
were at least in progress. The most accurate chronology of the time of our own phi-
losopher's preparatory labours, therefore, so far as I have been able to ascertain, seems
to be between the publications of Stevinus of Germany, and Vieta of France. The
French philosopher generalized the language of algebraby employing letters to denote known
as well as unknown quantities ; and he extended the theory of equations. It is not likely
that Napier ever saw his treatises, which were only first collected into one volume by
Schooten in 1646. All the other great works that occur in the history of numerical
science, are subsequent to the death of Napier. Countries the most distinguished in Eu-
rope for philosophers, had produced in that recondite path the few we have so briefly
noticed ; and although their names are illustrious and their labours profound, not one of
them struck a blow sufficient to extricate the best wing of the mathematics, which, at the
close of the sixteenth century, still remained with its arithmetic undeveloped, and its
algebra little beyond the rude and infant state in which it was brought from the East.
The name of Recorde is barely sufficient to give England a place in that history at all;
and as for Scotland, until Napier arose, it was only famed for mists that science could
not penetrate, and for the Douglas wars, whose baronial leaders knew little of the denary
system beyond their ten fingers.
It is curious to think how much science had attempted in physical research, and how
deeply numbers had been pondered, before it was perceived that the all-powerful sim-
plicity of Arabic notation was as valuable and as manageable in an infinitely descending
as in an infinitely ascending progression. It was only necessary to reverse the notation,
and the power of the scale was doubled. How obvious and simple does that expe-
dient now appear, " Mais ces moi/ens simples sont le fruit des ide.es profondes et lumineuses*
The decimal fractional division itself was long conceived before that notation was esta-
blished from which it derives all its value and beauty as a part of the Arabic system.
Yet the history of this important chapter of numbers is carelessly recorded where we
might have expected accuracy. " Regiomontanus," says a successor of Henry Briggs
in the Savilian chair, " introduced that simple, but most valuable, modification of the
decimal notation, which consists in fixing the unit's place at any figure, and not neces-
* Bailly.