Elements of geometry and trigonometry . le, or of an arc, is what re-mains after takinf^ that angle or arc from 180°. Thus A beingany angle or arc, 180°—A is its supplement. In any triangle, either angle is the supplement of the sum ofthe two others, since the three together make 180°. If any arc or angle be added to its supplement, the sum willbe 180°. Hence if an arc or angle be greater than 180°, itssupplement will be negative. Thus, the supplement of 200°is —20°. The supplement of any angle of a triangle, or indeedof the sum of either two angles, is always positive. GENERAL IDEAS RELATING
Elements of geometry and trigonometry . le, or of an arc, is what re-mains after takinf^ that angle or arc from 180°. Thus A beingany angle or arc, 180°—A is its supplement. In any triangle, either angle is the supplement of the sum ofthe two others, since the three together make 180°. If any arc or angle be added to its supplement, the sum willbe 180°. Hence if an arc or angle be greater than 180°, itssupplement will be negative. Thus, the supplement of 200°is —20°. The supplement of any angle of a triangle, or indeedof the sum of either two angles, is always positive. GENERAL IDEAS RELATING TO TRIGONOMETRICAL LINES. V. The sine of an arc isthe perpendicular let fall fromone extremity of the arc, onthe diameter which passesthrough the otiier , MP is the sine of thearc AM, or of the angle ACM. The tanfrent of an arc is aline touching the arc at oneextremity, and limited by theprolongation of the diameterwhich passes through theother extremity. Thus AT isthe tangent of the arc AM,or of the angle PLANE TUlGOxNOMKTRV. 215 The secant of an arc is tlic line drawn froin the centre ofllie circJe through one extremity of th«i arc ami hniiled by thetan;;ent drawn throuf^h tlie other extreniitv. Thus CT is thesecant of the arc AM, or of tlie angle ACM. The versed sine of an arc, is the j)art of the diameter inter-cepted between one extjemity of the arc and tlic foot of thesine. Tims, AP is the versed sine of the arc A^l, or the angleACM. These four lines Ml*, AT, (yT, AP, are dependent upon thearc AM, and are always determined by it and the radius ; thevare tlius designated : Mr=sin AM, or sin ACM,AT=tang AM, or tang ACM,CTmsec AM, or sec ACM,APiirver-sin A^I, or ver-sin Having taken the arc AD equal to a quadrant, from thepoints M and 1) draw the lines M(|, DS, j)erpendicular to theradius CD, the one terminated by tliat radius, the other termi-nated by tiic radius CM produced ; the lines ^IQ, DS, and C8,will, in hke nïanner, be the si
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
