Plane trigonometry with practical applications, by Leonard E. Dickson.

CHAPTER VIII
TRIGONOMETRIC FUNCTIONS OF ANY ANGLE
79. Rectangular coordinates. The reader became familiar in
Chapter VI with the idea of locating a point on the earth's surface by means of its latitude and longitude, the former being its
distance north or south of the equator, and the latter being the
arc on the equator which is intercepted between its meridian and
a fixed meridian, as that through Greenwich. Similarly, in defining the two rectangular coordinates of a point P in a plane, we
employ (Fig. 58) a horizontal line X'X (which plays the rl6e of
the equator) and a vertical line
Y'Y (which plays the role of the P
meridian of Greenwich).
If to the distance of a point P X
from X'X we prefix the sign + or,X.. X
-, according as P is above or p,,
below X'X, we obtain a positive
or negative number y which is
called the ordinate of P (and plays
the role of latitude, north or south). Likewise, if to the distance
of P from Y'Y we prefix the sign + or -, according as P is to
the right or left of Y'Y, we obtain a positive or negative number
x which is called the abscissa of P (and plays the role of longitude,
east or west).
The abscissa x and ordinate y are together called the (rectangular) coordinates of P. The point P is designated by (x, y).
In Fig. 58. the coordinates of P are x = + 3, y = + 2, whence P is (3,2);
those of P' are x = -3, y = + 2, whence P' is (- 3, 2). Similarly, P" is
(- 3, - 2), and P"' is (3, - 2).
As a further illustration of the signs of coordinates, we recall from Art. 63
that it is convenient in surveying to mark north latitudes +, south latitudes -, east departures +, and west departures -.
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