P. HISTORY OF ' AATHEMATICAL - School of Mathematics

MULTIPLICATION 259
translation of Fine's works,' Gemma Frisius? Ey~aguirre? Clavius14
the French translation of Tartaglia,6 Follinus,6 Girard,' Hainlin,a
Cara~nuel,~ Jeake,lo Corachan,ll Chalosse,12 De Moya,ls and in slightly
modified form in Crusoe.'4
223. Division of fractions.-Less frequent than in the preceding
processes is the use of lines in the multiplication or division of fractions,
which called for only one of the two steps taken in solving a
proportion involving fractions. Pietro Borgi (1488)15 divides Q by $
!x3 . " In dividing 3 by ), Pacioli16 writes
6
thus:
- -
and obtains # or 13.
Petrus Apianus (1527) uses the X in division. Juan de Hortega
(1552)" divides 8 by #, according to the following scheme:
Opere di Orontw Fineo del Dejinaio. ... Trdotte da Cosimo Bartoli (Venice,
1587), fol. 31.
Arilhmelicae Praclicae methodvs facilia, per Gemmam Frium ... iam recb
ab ipao authore emendata ... (Paris, 1569), fol. 20.
a Sebastian Fernandez Eygaguirre, Libro de Arilhmeticu (Brussels, 1608), p. 38.
Chr. Clavius, Opera omnia, Tom. I (1611), Euclid, p. 383.
L7Arilhmetique de Nicolaa Tarlaglia Brescian, trduit ... par Gvillavmo
Goaselin de Caen (Paris, 1613), p. 37.
Algebra eive fiber de debs Ocwltis, ... Hermannvs Follinvs (Cologne, 1622),
p. 40.
Albert Girard, Invention Nowelb en LIAlgebre (Amterdam, 1629).
8 Joban. Jacob Hainlin, Synopsis ~ ~ i(Tiibingen, c a 1653), p. 32.
0 Joannia Caramvelia Mathais Biceps Vetus el Nova (Companiae, 1670), p. 20.
lo Samuel Jeake, op. cit., p. 51.
ll Juan Bautista Corachan, Arilhmtica demonstrada (Barcelona, 1719), p. 87.
* L'Arilhmtique pa^ lee fractd ... par M. Chalosse (Paris, 1747), p. 8.
* J. P. de Moya, op. cit. (1784), p. 103.
l4 George E. Crueoe, Y Mathematical ("Why Mathematics?") (Pittsburgh,
Pa., 1921), p. 21.
Pietm Borgi, Arithmeticu (Venice, 1488), fol. 33B.
18L. Pacioli, op. cit. (1523), fol. 54a.
l7 Juan de Hortega, op. cit. (1552), fol. 66a.