P. HISTORY OF ' AATHEMATICAL - School of Mathematics

258 A HISTORY OF MATHEMATICAL NOTATIONS
use a slightly different and less suggestive scheme, namely, the capital
letter Z for proportions involving either integers or fractions. Thus,
3 : 8 = 16 : x is given by Recorde in the form PI6. This rather un-
usual notation is found much later in the American Accomptant of
Chauncey Lee (Lansinburgh, 1797, p. 223) who writes,
"Cause
4.5 y:z
Effect"
and finds Q = 90 X 18 s4.5 = 360 dollars.
222. Addition and subtraction of fractions.-Perhaps even more
popular than in the solution of proportion involving fractions was the
use of guiding lines crossing each other in the addition and subtraction
of fractions. Chuquetl represents the addition of f and + by the
following scheme :
" 10 12 l'
-
-x:
-
.15-
The lower horizontal line gives 3 X 5 = 15 ; we have also 2 X 5 = 10,
3X4= 12; hence the sum *#=1,\.
The same line-process is found in Pacioli; Rudolph: Apianus.'
In England, Tonstall and Recorde do not employ this intersecting
line-system, but Edmund Wingate6 avails himself of it, with only
alight variations in the mode of using it. We find it also in Oronce
Fine," Feliciano17 Schreckenfuchs,g H~rtega,~ Baeza,Io the Italian
Nicolas Chuquet, op. cit., Vol. XIII, p. 606; reprint p. (54).
Luca Pacioli, op. cit. (1523), fol. 51, 52, 53.
Whristoph Rudolph, op. cil., under addition and subtraction of fractions.
Petrus Apianus, Kauflmansz Reehnung (Ingolstadt, 1527).
E. Wingate, op. cil. (1704), p. 152.
Orontii Finei Delphinabls, liberalimn Disciplinarum projessoris Regii Prolondhesis:
Opwr varillm (Paris, 1532), fol. 4b.
Francesco Feliciano, Libto de an'thmetiea e geomelria (1550).
8 0. Schreckenfuche, op. cit., "Annot.," fol. 25b.
9 Hortega, op. cil. (1552), fol. 55a, 63b.
lo Numerandi doelrina, authore Lodoico Bdza (Paris, 1556), fol. 38b.