Now since, by Art. '33, 1 500 and — $ 500 neutralize each
other, we have remaining the isolated negative quantity
— $ 200 as the algebraic representative of the required prop-
erty. In Arithmetic, we should say that he owed or was in
debt $200; in Algebra, we make also the equivalent state-
ment that his property amounts to — $ 200.
In this way wfe can conceive the possibility of the indepen-
dent existence of negative quantities ; and as, in Arithmetic,
losses ma}'^ be added, subtracted, multiplied, etc., precisely as
though they were gains, so, in Algebra, negative quantities



DEFINITIONS AND NOTATION. 13

may be added, subtracted, multiplied, etc., precisely as though
they were positive.
The distinction of positive and negative quantities is applied
in a great many cases in the language of every-day life and in
the mathematical sciences. Thus, in the thermometer, we
speak of a temperature above zero as -f, and one below as — ;
for instance, + 25° means 25° above zero, and — 10° means
10° below zero. In navigation, north latitude is considered
-f-, and south latitude — ; longitude west of Greenwich is con-
sidered H-, and longitude east of Greenwich — ; for example,
a place in latitude — 30°, longitude -|- &5°, would be in latitude
30° south of the equator, and in longitude 95° west of Green-
wich. And, in general, when we 'have to consider quantities
the exact reverse of each other in quality or condition, we
may regard quantities of either quality or condition as posi-
tive, and those of the opposite quality or condition as negative.
