P. HISTORY OF ' AATHEMATICAL - School of Mathematics

336 A HISTORY OF MATHEMATICAL NOTATIONS
to in $5 101, 111, 112, 124. The multiplicative principle in marking
powers is elucidated in $5 101, 111, 116, 135, 142.
Before proceeding further, it seems desirable to direct attention
to certain Arabic words used in algebra and their translations into
Latin. There arose a curious discrepancy in the choice of the principal
unknown quantity; should it be what we call x, or should it be x2?
al-Khow8rizmf and the older Arabs looked upon x2 as the principal
unknown, and called it mdl ("assets," "sum of money").' This viewpoint
may have come to them from India. Accordingly, x (the Arabic
jidr, 'lplant-root," 'ibasis,l' "lowest part") must be the square root of
ma1 and is found from the equation to which the problem gives rise.
By squaring x the sum of money could be ascertained.
Al-Khowhrizmi also had a general term for the unknown, shai
("thing"); it was interpreted broadly and could stand for either ma1
or jidr (xZ or x). Later, John of Seville, Gerard of Cremona, Leonardo
of Pisa, translated the Arabic jidr into the Latin radix, our x; the
Arabic shai into res. John of Seville says in his arithmeti~:~ "Quaeritur
ergo, quae res cum. X. radicibus suis idem decies accepta radice
sua efficiat 39." ("It is asked, therefore, what thing together with 10
of its roots or what is the same, ten times the root obtained from it,
yields 39.") This statement yields the equation x2+10x=39. Later
shai was also translated as causa, a word which Leonardo of Pisa
used occasionally for the designation of a second unknown quantity.
The Latin res was translated into the Italian word cosa, and from
that evolved the German word coss and the English adjective "cossic."
We have seen that the abbreviations of the words cosa and cubus,
via., co. and cu., came to be used as algebraic symbols. The words
numerus, dragma, denarius, which were often used in connection with
a given absolute number, experienced contractions sometimes em-
ployed as symbols. Plato of Tivoli13,in his translation from the Hebrew
of the Liber embadorum of 1145, used a new term, latus ("side"),
for the first, power of the unknown, x, and the name embadum ("content")
for the second power, xZ. The term latus was found mainly
in early Latin writers drawing from Greek sources and was used later
by Ramus (§ 322), Vieta (5 327), and others.
291. Double significance of "R" and "1."-There came to exiet
considerable confusion on the meaning of terms and symbols, not only
J. Rusks, Silzungsberichte Heidelbezgw Akad., Phil.-hist. Klasse (1917),
Vol. 11, p. 61 f.; J. Tropfke, op. cil., Vol. I1 (2d ed., 1921), p. 106.
"hnpfke, op. cil., Vol. I1 (2d ed., 1921), p. 107.
a M. Curtze, BibZwlh mathematicu (3d ser.), Vol. I (1900), p. 322, n. 1.