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Instruments and Field Book
LANE TRIGONOMETRY teaches the relations and calculations of the sides and angles of plane triangles.
The angles of triangles are measured by the number of degrees, containcd in the arc cut off by the legs of the angle, and whose centre is the angular point. A right angle is therefore an angle of go degrees ; and the sum of the three angles of every triangle, or two right angles, is equal to 180° Wherefore, in a right-angled triangle, one acute angle being subtracted from 90°, the remainder will be the other ; and the sum of any two angles of a triangle, being taken from 180°, will leave the third angle.
Degrees are marked at the top of the figure with a • small , minutes with', seconds with ", and so on. Thus, 57° 30' 12", that is, 57 degrees, 30 minutes and 12 seconds.
The complement of an arc is the difference between that arc and a quadrant. So BC=40° is the complement of AB=50°.
The VOL. II.
The supplement of an arc is what it wants of a semicis cie. So BCD=130° is the supplement of AB= 50°.
The sine of an arc is the line, drawn from one end of the arc perpendicularly upon the diameter, drawn through the other end of the arc. So BE is the sine of AB or of BCD.
The versed sine of an arc is the part of the diameter Øca iween the sine and the beginning of the arc. So AE is the versed sine of AB, and DE the versed sine of BCD.
The tangent of an arc is the line, drawn perpendicularly from one end of the diameter passing through one end of the arc, and terminated by the line, drawn from the centre through the other end of the arc. So AG or DK is the tangent of AB, or of BCD.
The secant of an arc is the line, drawn from the centre through the end of the arc, and terminated by the tangent. So FG or FK is the secant of AB, or of BCD.
The cosine, cotangent, or cosecant, of an arc is the sine, tangent, or secant of the complement of that arc. So BH,