P. HISTORY OF ' AATHEMATICAL - School of Mathematics

384 A HISTORY OF MATHEMATICAL NOTATIONS
z, y, z in a letter (February 6, 1715) to Leibniz. H. Pitot1 applied the
three co-ordinates to the helix in 1724.
SIGNS OF AGGREGATION
342. Introduction.-In a rhetorical or syncopated algebra, the
aggregation of terms could be indicated in words. Hence the need for
symbols of aggregation was not urgent. Not until the fifteenth and
sixteenth centuries did the convenience and need for such signs
definitely present itself. Various devices were invoked: (1) the horizontal
bar, placed below or above the expression affected; (2) the
use of abbreviations of words signifying aggregation, as for instance u
or v for universalis or vniversalis, which, however, did not always indicate
clearly the exact range of terms affected; (3) the use of dots or
commas placed before the expression affected, or at the close of such
an expression, or (still more commonly) placed both before and after;
(4) the use of parentheses (round parentheses or brackets or braces).
Of these devices the parentheses were the slowest to find wide adoption
in all countries, but now they have fairly won their place in
competition with the horizontal bar or vinculum. Parentheses prevailed
for typographical reasons. Other things being equal, there is a
preference for symbols which proceed in orderly fashion as do the
letters in ordinary printing, without the placing of signs in high or low
positions that would break a line into two or more sublines. A vinculum
at once necessitates two terraces of type, the setting of which
calls for more time and greater technical skill. At the present time
H. Pitot, Mdmoires de l'dhie d. scien., ann6e 1724 (Park, 1726). Taken
from H. Wieleitner, Geschichk der Malhemutik, 2. Teil, 2. Halfte (Berlin und Leipzig,
1921), p. 92.
To what extent the letter z has been incorporated in mathematical language
1s illustrated by the French express;?n 81re furl a z, which means "being strong in
mathematics." In the same way, lele d z means "a mathematical head." The
French give an amusing "demonstration" that old men who were tkle d z never
were pressed into military service so as to have been conscripts. For, if they were
conscripts, they would now be e~conscripts. Expressed in symbols we would have
Dividing both sides by z gives
Dividing now by e yielda
82 =ez-conscript.
e
conscript = -.
e
8 =ecomcript.
According to this, the conscript would be la tkte assurh (i.e.,
assured against casualty), which k absurd.
over el or, the head