P. HISTORY OF ' AATHEMATICAL - School of Mathematics

370 A HISTORY OF MATHEMATICAL NOTATIONS
general favor than Rudolff's older and clumsier designation ($5 153,
155).
328. Rudolfs signs outside of Germany.-The clumsy signs of
Christoff Rudolff, in place of which Stifel had introduced in 1544 and
1553 better symbols of his own, found adoption in somewhat modified
form among a few writers of later date. They occur in Aurel's Spanish
Am'thmetica, 1552 (5 165). They are given in Recorde, Whetstone of
Witte (1557) (5 168), who, after introducing the first sign, /., proceeds:
"The seconde signe is annexed with Surde Cubes, to expresse
their rootes. As this .&.I6 whiche signifieth the Cubike roote of .16.
And .&.20. betokeneth the Cubike roote of .20. And so forthe. But
many tymes it hath the Cossike signe with it also: as &.ce 25 the
Cubzke roote of .25. And &.ce.32. the Cubike roote of .32. The
thirde figure doeth represente a zenzizenzike roote. As .d.12. is the
zenzizenzike roote of .12. And d.35. is the zenzizenzike roote of .35.
And likewaies if it haue with it the Cossike signe .aa. As 43~24
the
zenzizenzike roote of .24. and so of other."
The Swiss Ardiiser in 1627 employed Rudolff's signs for square
root and cube root.' J. H. Rahn in 1659 used & for evolution,2
which may be a modified symbol of Rudolff; Rahn's sign is adopted
by Thomas Brancker in his English translation of Rahn in 1668, also
by Edward Hatton3 in 1721, and by John Kirkby in 1725. Ozanams
in 1702 writes 25+ 92 and also 4 5 +,42. Samuel Jeakes in 1696
gives modifications of Rudolff's signs, along with other signs, in an
elaborate explanation of the "characters" of "Surdes"; / means
root, /: or V or V/ universal root, 4 or /a square root, & or
1/'4 cube root, & or /ag squared square root, or dp
sursolide root.
On the Continent, Johann Caramue17 in 1670 used / for square
root and repeated the symbol // for cube root: "//27.
Cubica Numeri 27. hoc est, 3."
est Radix
1 Johann Ardiiser, Geometriae Thhae et Pradicae, XII. Bucher (Ziirich,
1627), fol. 81A.
2 Johann Heinrich F&h, Teulsche Algebra (Ziirich, 1659).
3 Edward Hatton, An Inlire System of Arithmelie (London, 1721), p. 287.
4 John Kirkby, Ariihrnetical Inslilulim (London, 1735), p. 7.
6 J. Ozanam, Nouveam Elemens d'algebre ... par M. Ozanam, 1. Partie (Amsterdam,
1702), p. 82.
6Samuel Jeake, AO~~ZTIKHAOI'~A, ur Arithmetick (London, 1696), p. 293.
Joannis Caramvelis Mathesis Bieeps. Velus, et Nova (Campaniae, 1670),
p. 132.