P. HISTORY OF ' AATHEMATICAL - School of Mathematics

SYMBOLISTS AND RHETORICIANS 427
guage." In England, William Oughtred used over one hundred and
fifty mathematical symbols, many of his own invention. In geometry
Oughtred showed an even greater tendency to introduce extensive
symbolisms than did HBrigone. Oughtred translated the tenth book
of Euclid's Elements into language largely ideographic, using for the
purpose about forty new symbo1s.l Some of his readers complained of
the excessive brevity and compactness of the exposition, but Oughtred
never relented. He found in John Wallis an enthusiastic disciple. At
the time of Wallis, representatives of the two schools of mathematical
exposition came into open conflict. In treating the "Conic Sections"2
no one before Wallis had employed such an amount of symbolism.
The philosopher Thomas Hobbes protests emphatically: "And for
. . . . your Conic Sections, it is so covered over with the scab of sym-
bols, that I had not the patience to examine whether it be well or ill
dem~nstrated."~ Again Hobbes says: "Symbols are poor unhandsome,
though necessary scaffolds of demonstration"; he explains
further: LLSymbols, though they shorten the writing, yet they do not
make the reader understand it sooner than if it were written in words.
For the conception of the lines and figures . . . . must proceed from
words either spoken or thought upon. So that there is a double labour
of the mind, one to reduce your symbols to words, which are also
symbols, another to attend to the ideas which they sigqify. Besides,
if you but consider how none of the ancients ever used any of them in
their published demonstrations of geometry, nor in their books of
arithmetic . . . . you will not, I think, for the future be so much in
love with them. . . . Whether there is really a double translation,
such as Hobbes claims, and also a double labor of interpretation, is a
matter to be determined by experience.
386. Meanwhile the Algebra of Rahn appeared in 1659 in Zurich
and was translated by Brancker into English and published with additions
by John Pell, at London, in 1668. The work contained some
new symbols and also Pell's division of the page into three columns.
He marked the successive steps in the solution so that all steps in the
process are made evident through the aid of symbols, hardly a word
1 Printed in Oughtred's Clavis mathemdicae (3d ed., 1648, and in the editions
of 1652, 1667, 1693). See our $8 183, 184, 185.
a John Wallis, Operum mathemaliwm, Pars altera (Oxford), De secthibus
conicis (1655).
"ir William Molesworth, The English Works of Thomas Hobbea, Vol. VII
(London, 1845), p. 316.
Ibid., p. 248. 6 IM., p. 329.