P. HISTORY OF ' AATHEMATICAL - School of Mathematics

128 A HISTORY OF MATHEMATICAL NOTATIONS
nated by a symbol consisting of c and a flourish (probably intended for
co). Then follows the equation 900 iii lcoz= lm@. (our 900 -z= 23).
One sees here a mixture of two notations for z and d: the notation
co and cu made familiar by Luca Pacioli, and Bombelli's exponential
notation, with the 1 and 3, placed above the line, each.exponent resting
in a cup. It is possible that the part of the algebra here photographed
may go back as far as about 1550. The cross-writing in the
photograph begins: "in libro vecchio a carte 82: quella di far di 10
due parti: dice messer Nicolo che l'ona e R 43 p 5 iii R18: et l'altra
il resto sino a 10, cioe 5 iii R 43 P. 18." This Nicolo is supposed to
be Nicolo Tartaglia who died in 1557. The phrasing "Messer Nicolo"
implies, so Bortolotti argues, that Nicolo was a living contemporary.
If these contentions are valid, then the manuscript in question waa
written in 1557 or earlier.'
FIG. 52.-From the manuscript of the Algebra of Bombelli in the Comunale
Library of l301ognn. (Courtesy of Professor E. Bortolotti, of Bologna.)
The novel notations of Bombelli and of Ghaligai before him did
not find imitators in Italy. Thus, in 1581 there appeared at Brescia
the arithmetic and mensuration of Antonio Maria Visconti,2 which
follows the common notation of Pacioli, Gardan, and Tartaglia in
designating powers of the unknown.
GERMAN : IOHANN WIDMAN
(1489, 1526)
146. Widman's Behennde vnnd 11.ubsche Rechnfig aufl allen Kauffmanschafften
is the earliest printed arithmetic which contains the
signs plus (+) and minus ( - ) (see $5 201, 202).
1 Since the foregoing was written, E. Bortolotti has published an article, on
mathematics at Bologna in the sixteenth century, in the Periodic0 di Matematiche
(4th ser., Vol. V, 1925), p. 147-84, which contains much detailed information, and
fifteen facsimile reproductions of manuscripts exhibiting the notations then in use
atBologna, particularly theuseof sdssh (-) and the sign (=) to exprew equality.
gntonii Mariae Viciwmitia Civis Placentini praetica numermm & mnsurarum
(Brixiae, 1581).