Circular Measures
Circular or Angular Measures are used in surveying, navigation, astronomy, geography, reckoning latitude and longitude, and computing differences in time.
A Circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within, called the center.
The Circumference is the bounding line of a circle.
The Radius of a circle is a straight line drawn from the circumference to the center.
The Diameter is a straight line drawn through the center, with the ends terminating in the circumference.
An Arc of a circle is any portion of the circumference.
An Angle is the difference in direction between two straight lines which meet.
If two diameters divide a circle into four equal parts, these diameters make right angles with each other.
An angle less than a right angle is an acute angle.
The circumference of a circle may be divided into 360 equal parts, called degrees. If the circle is large, the degree is large, and if the circle is small, the degree is small, but the degree is always 1⁄360 part of the circumference, whatever the size of the circle.
An angle at the center of a circle is measured by the arc which bounds it.
If the angle is a right angle, it is measured by 1⁄4 of 360 degrees, or 90 degrees; hence, any angle of 90 degrees is a right angle.
An acute angle is always less than 90 degrees.
An obtuse angle is always more than 90 degrees.
Table of Circular Measure
| 60 | seconds (′′) | = | 1 minute (′) |
| 60 | minutes | = | 1 degree (°) |
| 360 | degrees | = | 1 circumference (cir.) |
| Circum- ference | Degrees | Minutes | Seconds | |||
| 1 | = | 360 | = | 21,600 | = | 1,296,000 |
A quadrant is 1⁄4 of a circumference, or 90°; a sextant is 1⁄6 of a circumference, or 60°.
The length of a degree of longitude on the earth’s surface at the Equator is 69.16 miles.
In astronomical calculation 30° are called a sign, and there are therefore 12 signs in a circle.