P. HISTORY OF ' AATHEMATICAL - School of Mathematics

INDMDUAL WRITERS 185
All terms being multiplied by g, and properly ordered, one obtains
y6+2Z3y3=B6. As this equation is quadratic with a positive affected
term, it has also a cube root. Thus the required reduction is effected.
"Conclusion: If thereforc 23+3B2x = 2Z3, and dB6+Z8- Z3 = 09,
then - B1-D2 is x, as required."
D
The value of x in x3+3B22=2Z3 is -written on page 150 of the
1646 edition thus:
" ~C.I/B plano-plano-plani+ Z solido-solido+ Z solido -
~C.I/B plano-plano-plani+Z solido-solido. -Z solido ."
The combining of vinculum and radical sign shown here indicates
the influence of Descartes upon Van Schooten, the editor of Vieta's
collected works. As regards Vieta's own notations, it is evident that
compactness was not secured by him to the same degree as by earlier
writers. For powers he did not adopt either the Italian symbolism of
Pacioli, Tartaglia, and Cardan or the German symbolism of Rudolff
and Stifel. It must be emphasized that the radical sign, as found in
the 1646 edition of his works, is a modification introduced by Van
Schooten. Vieta himself rejected the radical sign and used, instead,
the letter 1 (latus, "the side of a square") or the word radix. The I
had been introduced by Ka~nus ($322); in the Zeteticorum, etc., of
1593 Vieta wrote 1. 121 for 1/121. In the 1646 edition (p. 400) one
finds 42+42+/2+1/2, which is Van Schooten's revision of the
text of Vieta: Vieta's own symbolism for this expression was, in 1593,l
"Radix binomiae 2
and in 1595:
+Radix binomiae
" R. bin. 2+R. bin. 2+R. bin. 2+R. 2. ,"
a notation employed also by his contemporary Adrian Van Roomen.
178. Vieta distinguished between number and magnitude even in
his notation. In numerical equations the unknown number is no longer
represented by a vowel; the unknown number and its powers are represented,
respectively, by N (numerus), Q (quadratus), C (cubus), and
Variorum de rebus muthem. Responsorum liber VZZZ (Tours, 1593), corollary
to Caput XVIII, p. 120'. This and the next reference are taken from Tropfke,
op. cit., Vol. I1 (1921), p. 152, 153.
2 Ad Problaa p d omnibus mathematicis lolius orbis conslruadum proposuit
Adtianus Romanus, Franeisci Vielae responmm (Paris, 1595), BI. A IT.