Elementary arithmetic, with brief notices of its history... by Robert Potts.

13
measure of the angle; for the angle increases or decreases as the
arc which subtends it at the center increases or decreases.
If in a circle two diameters be drawn at right angles to each
other, the circumference is divided into four equal parts, called
quadrants, and each of these quadrants subtends a right angle at
the centre of the circle. If any one of the quadrants be divided
into ninety equal arcs, and straight lines be drawn from the centre
of the circle to all the divisions of the quadrant, it will be seen that
each of the ninety arcs subtends ninety equal angles at the centre of
the circle. The angle which is the ninetieth part of a right angle is
called a degree, and the ninetieth part of the quadrantal arc is also
called a degree of the quadrant.
The angular degree and the circular degree must not be confounded,
as the former is the ninetieth part of a right angle, and the latter is
the small arc which subtends that small angle at the centre of the
circle. Each degree is divided into sixty equal parts called minutes,
and each minute into sixty equal parts called seconds, and so on:
according to the following table:
60 seconds are equal to 1 minute.
60 minutes,, 1 degree.
90 degrees,, 1 quadrant, or a right angle.
4 quadrants,, 1 circumference of a circle, or 4 right angles.
It may also be observed, that the radius being equal to the chord of
the arc which subtends an angle of sixty degrees, it is not improbable
this fact may have suggested the sexagesimal division of the degree,
the minute, the second, &c. It may also be noted, that the whole circumference of a circle can be divided into six equal arcs, each arc
subtended by a chord equal to the radius, and each of these arcs
will subtend an angle of sixty degrees at the centre of the circle.
There is another division' of the circumference of the circle, which
indicates the points of the mariner's compass. This division is rather
inaccurately named "points of the compass," which expression more
fitly denotes the directions to which the needle points than the angular
space between two successive divisions. The cardinal points of the
compass are the east, west, north, and south. The east is reckoned
from the centre (on which the needle moves) towards the right, the
west towards the left of the horizontal diameter, the north towards
the upper part, and the south towards the lower part of the other
diameter at right angles to the former.
The whole circumference is divided into 32 equal arcs, of which
each quadrant contains 8, and the length of each is 11~ 15'.
1 This division is easily made. Describe a square, join the bisections of tho
opposite sides, draw the diagonals, and inscribe a circle in the square. The circum.
ference of the circle is divided into 8 equal arcs, next dividing each of these arcs into
4 equal arcs, the 32 points are found, and can be marked beginning at E, W,
N, or S.