P. HISTORY OF ' AATHEMATICAL - School of Mathematics

ROOTS 367
Cose-uel Algobre-. It contains the passage: "Quum 8 assimiletur
radici de radice punctus deleatur de radice, 8 in se ducatur et rema.net
adhuc inter se aequalia"; that is, "When x2=/2, erase the point
before the x and multiply x2 by itself, then things equal to each other
are obtained." In another place one finds the statement, per punctum
intellige radicem-"by a point understand a root." But no dot is
actually used in the manuscript for the designation of a root.
The third manuscript is at the University of Gottingen, Codex
Gotting. Philos. 30. It is a letter written in Latin by Initius Algebras,'
probably before 1524. An elaboration of this manuscript was made
in German by Andreas Ale~ander.~ In it the radical sign is a heavy
point with a stroke of the pen up and bending to the right, thus /.
It is followed by a symbol indicating the index of the root; /a indicates
square root; /c" cube root; /cc" the ninth root, etc. More-
over, /c~8+/22~ stands for /8+/z, where cs (i.e., cmnmunis)
signifies the root of the binomial which is designated as one quantity,
by lines, vertical and horizontal. Such lines are found earlier in
Chuquet (5 130). The 8, indicating the square root of the binomial,
is placed as a subscript after the binomial. Calling these two lines a
lL gnomon," M. Curtze adds the following:
"This gnomon has here the signification, that what it embraces is
not a length, but a power. Thus, the simple 8 is a length or simple
number, while is a square consisting of eight areal units whose
linear unit is /8)8. In the same way pCe would be a cube, made up of
8 cubical units, of which /ce18 is its side, etc. A double point, with the
tail attached to the last, signifies always the root of the root. For
example, ./ce88 would mean the cube root of the cube root of 88. It
L
is identical with /cc%8, but is used only when the radicand is a
so-called median [Mediale] in the Euclidean sen~e."~
326. The fourth manuscript is an algebra or Coss completed by
Adam Riese4 in 1524; it was not printed until 1892. Riese was familiar
with the small Latin algebra in the Dresden collection, cited above;
1 Znitizls Algebras: Algebrae Arabis Arithmetici viri clarrisimi fiber ad Ylem
geometram magistrum suum. This mas published by M. Curtze in Abhandlungen
zur Geschichte der mathemdischen Wissenschaften, Heft XI11 (1902), p. 435-611.
Matters of notation are explained by Curtze in his introduction, p. 443-48.
G. Enestrom, Biblwtheca malhemalica (3d ser.), Vol. I11 (1902), p. 355-60.
a M. Curtre, op. cit., p. 444.
B. Berlet, Adam Riese, sein Leben, seine Rechenbiicher und seine Art nr
rechnen; die Coss von Adam Riese (Leipzig-Frankfurt a/M., 1892).