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1. PLANE TRIGONOMETRY treats of the relations and calculations of the sides and angles of plane triangles.

2. The circumference of every circle (as before observed in Geom. Def. 56) is supposed to be divided into 360 equal parts, called Degrees ; also each degree into 60 Minutes, and each minute into 60 Seconds, and so on.

Hence a semicircle contains 180 degrees, and a quadrant 90 degrees.

3. The Measure of an angle (Def. 57, Geom.) is an arc of any

circle contained between the two lines which form that angle, the angular point being the centre; and it is estimated by the number of degrees contained in that arc

Hence, a right angle, being measured by a quadrant, or quarter of the circle, is an angle of 90 degrees; and the sum of the three angles of every triangle, or two right angles, is equal to 180 degrees. Therefore, in a right-angled triangle, taking one of the acute angles from 90 degrees, leaves the other acute angle; and the sum of the two angles, in any triangle, taken from 180 degrees, leaves the third angle; or one angle being taken from 180 degrees, leaves the sum of the other two angles. VOL. II.

B

4. Degrees

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