Untitled - JScholarship

THE LAST THREE CENTURIES 235
but Stevin's innovations, though neglected at first, are a
permanent possession. His exponential notation grew in
connection with his notation for decimal fractions. Denoting
the unknown quantity by Q, he places within the circle the
exponent of the power. Thus (i), (2), (3) signify x, a?, a?. He
extends his notation to fractional exponents, ®, 0, @, mean
.T-, x^, x^. He writes 3a.^z^ thus 3(i)M sec(^Mter(^, where
M means multiplication; sec, second; ter, third unknown
quantity. The Q fo'-' ^ "^^ adopted by Girard, Stevin's
great independence of mind is exhibited in his condemnation
of such terms as "sursolid,'' or numbers that are "absurd,"
"irrational," "irregular," "surd," He shows that all numbers
are equally proper expressions of some length, or some
power of the same root. He also rejects all compound expressions,
such as "square-squared," "cube-squared," and
suggests that they be named by their exponents the " fourth,"
"fifth" powers. Stevin's symbol for the unknown failed to
be adopted. But the principle of his exponential notation has
survived. The modern formalism took its sb3pe with Descartes.
In his Geometry, 1637, he uses the last letters of the
alphabet, x in the first place, then the letters y, z to designate
unknown quantities; while the first letters of the alphabet are
made to stand for known quantities. Our exponential notation,
a*, is found in Descartes; however, he does not use general
exponents, like a", nor negative and fractional ones. In
this last respect he did not rise to the ideas of Stevin, In case
of radicals he does not indicate the root by indices, but in
case of cube root, for instance, uses the letter C, thus,
Vo+ii=^.'
Of the early notations for evolution, two have come down
to our time, the German radical sign and Stevin's fractional
1 Cantor, II., 723, 724.