ke or issued a pun. Maseres was
the fourth wrangler of 1752, and first Chancellor's medallist (or highest
in classics); his second was Porteus[459] (afterward Bishop of London).
Waring[460] came five years after him: he could not get Maseres through the
second page of his first book on algebra; a negative quantity stood like a
lion in the way. In 1758 he published his _Dissertation on the Use of the
Negative Sign_,[461] 4to. There are some who care little about + and -, who
would give it house-room for the sake of the four words "Printed by Samuel
Richardson."

Maseres speaks as follows: "A single quantity can never be marked with
either of those signs, or considered as either affirmative or negative; for
if any single quantity, as b, is marked either with the sign + or with the
sign - without assigning some other quantity, as a, to which it is to be
added, or from which it is to be subtracted, the mark will have no meaning
or signification: thus if it be said that the square of -5, or the product
of -5 into -5, is equal to +25, such an assertion must either signify no
more than that 5 times 5 is equal to 25 without any regard to the signs, or
it must be mere nonsense and unintelligible jargon. I speak according to
the foregoing definition, by which the affirmativeness or negativeness of
any quantity implies a relation to another quantity of the same kind to
which it {204} is added, or from which it is subtracted; for it may perhaps
be very clear and intelligible to those who have formed to themselves some
other idea of affirmative and negative quantities different from that above
defined."

Nothing can be more correct, or more identically logical: +5 and -5,
standing alone, are jargon if +5 and -5 are to be understood as without
reference to another quantity. But those who have "formed to themselves
some other idea" see meaning enough. The great difficulty of the opponents
of algebra lay in want of power or will to see extension of terms. Maseres
is right when he implies that extension, accompanied by its refusal, makes
jargon. One of my paradoxers was present at a meeting of the Royal Society
(in 1864, I think) and asked permission to make some remarks upon a paper.
He rambled into other things, and, naming me, said that I had written a
book in which two sides of a triangle are pronounced _equal_ to the
third.[462] So they are, in the sense in which the word is used in complete
algebra; in which A + B = C makes A, B,