P. HISTORY OF ' AATHEMATICAL - School of Mathematics

110 A HISTORY OF MATHEMATICAL NOTATIONS
point constitute so many faults: the point should not enter a numerical
expression other than as a contracted sign of multiplication."!
476. The logarithms of fractions less than one gave rise to a
diversity of notation which has prevailed down to the present time.
Richard Norwood" in 1631 (writing "s" when he means "log sine")
gives "s, D 6 7 deg. 2 3' 9,9 6 5 2 4 8 0," where D is an angle of
the triangle A D B. Here we have the characteristic increased by ]0
and separated from the mantissa by a comma. Similarly, in John
Ward,s "the Sine of the Angle C 49°-30' 9,8810455."
The writing of the negative sign over the characteristic, to indicate
that the characteristic is negative, is found in Oughtred's Clavis
mathematicae (except the 1631 edition which does not consider
logarithms). We quote from the 1652 edition (p. 122): "Ut numeri
436, Log: est 2,6394865 at numeri 4 3 6 0 0, est 4, 6 3 9 4 8 6 5.
et numeri 4~, Log: est 0,6394865. Denique numeri 010 0 4 30.
Log: est 3, 6394865." Observe that the characteristic is separated
from the mantissa by a comma, and that a different sign is
used for decimal fractions. In his Circles of Proportion (London,
1632), page 4, Oughtred gives log 2 as "0. 3 0 1 03."
Ozanam' in 1692 gives the logarithm of i as 1'_0. 1 2 4 9 3 8 8,"
the fractional part being here negative and the minus sign placed in
front of the logarithm. Likewise, Benito Bails- gives "log. -h\r =
-1, 04 1 393."
477. Oughtred's practice of placing the minus sign of a negative
characteristic above the characteristic has found favor among British
authors of recent time, such as H. S. Hall and S. R. Knight," E. M.
Langley," C. G. Knott," and F. Castle." Langley directs computors
"to reject the superfluous 10." The notation "2, 7 9 5 8 0 0" if;
found also in the Report of the British Association (1896), page 7.5.
However, it has been far from universal even in England. A. de
I Desire Andre, Des' Notations matMmatiques (Paris, 1909), p. 20.
2 Richard Norwood, Triqonometrie (London, 1631), Book I, p. 20.
a Posthumous Works 0/ John Ward (London, 1730), p. 74.
4J. Ozanam, Cours de mathematiques, Vol. II (new ed.; Paris, 1692), p. 61i.
I Primcipios de matematica de la real academia de San Fernando par Don Benito
Bails (2d. ed.), Vol. I (Madrid, 1788), p. 191.
'H. S. Hall and S. R. Knight, Elementary Algebra, ed. F. L. Sevenoak (New
York, 1895), p. 339.
T Edward M. Langley, A Treatise on Computation (London, 1895), p. 111,123.
8 C. G. Knott, Logarithmical Tables (Edinburgh, 1914).
I Frank Castle, Practical Mathematics/or Beginners (London, 19(5), p. 127.