Abhandlungen zur Geschichte der Mathematik.

34 Florian Cajori:
his remarks to common logarithms, while the latter devotes only six lines
to the whole subject of logarithms. A fuller treatment is given by E. STONE.5)
He speaks of NAPIERA' and of natural logarithms without confusing the
two, though, to be sure, he nowhere distinctly contrasts the two systems.
SAVERIEN6) briefly describes NAPIER's logarithms. "NEPER appelle 0 le sinus
entier, de sorte que les logarithmes vont en decroissant, pendant que les
sinus vont en croissant, & qu'ils deviennent par-la negatifs, c'est-a-dire
mloins que rien, pendant que les tangentes deviennent plus grandes que
le ra'ion, c'est-a-dire qu'elles vont au dessus de 45 degres. Ainsi ces logarithmes sont tous differens de ceux dont nous nous servons aujourd'hui." But
the author contradicts himself, for on the very same page he says that
the "logarithmes de NEPER... ont une forme differente de ceux de BRIGGE
dont on fait communement usage. Cependant un de ces logarithmes est a
un logarithme correspondant de BRIGGE, comme 2.3025850929947) est a
1000000000000". The author does not explain how it is possible for
NAPIER'S logarithms to increase as the sine decreases, and at the same
time to be derivable from BRIGGs's in the manner specified. The confusion
appears to have arisen from the desire to associate NAPIER'S name with
logarithms, at a time when logarithms of the kind published by him were
becoming obsolete and his books on logarithms were very scarce, while
tables of natural logarithms were not usually accessible.
The confusion marked in the writings of HALLEY and SAVERIEN spread
among French writers. MONTUCLA, the great mathematical historian of the
eighteenth century, made the same mistake;8) BossUT helped to perpetuate
the error.9) In England CHARLES HUTTON, who in 1785 published the
first edition of his MLatclheaticca Tables (which includes an elaborate and
in many respects excellent history of logarithms) describes NAPIER's logarithms correctly,10) but subsequently (p. 85) he speaks of "the right-angled
hyperbola, the side of whose square inscribed at the vertex is 1, gives
5) Op. cit., artiele "Logarithms".
6) Monsieur SAVERIEN, Dictionnaire Universel de Mathematique et de Physique,
Paris, 1753, Tome second, artiele "Logarithme". In CANTOR'S Gesch. d. M2lath.,
III., p. 490, the date of this dietionary is erroneously given as 1752.
7) The decimal point in this number is evidently a misprint. It should
have been omitted. SAVERIEN'S inaccuracy as a writer is illustrated by his statement that NAPIER took the sinus totus equal to zero. As a matter of fact, NAPIER
took the logarithmi of the sinus totus equal to zero.
8) MONTUCLA, Histoire des mathe'natiques, Tome II., Paris, 1758, p. 21.
9) CHARLES BossUT, Essai sur l'histoire generale des math6m~aticques, Paris,
1802, Tome I., pp. 268 —271.
10) HUTTON, op. cit., 5t. ed., pp. 25-27, 42-49.