Elements of geometry and trigonometry . e AG, BG, areequal. But if the chord AG is e(|ual to the chord GB, the arcAG will be equal to the arc GB (Prop. IV.) ; hence, the radiusCG, at right angles to the chord AB, divides the arc subtendedby that chord into two equal parts at the point G. Scholium. The centre C, the middle j)oint D, of the chordAB, and the middle point G, of the arc subtended by thischord, are three points of the same line perpendicular to thechord. But two points are sufficient to determine the positionof a straight line ; hence every straijiht line which passes throughtwo of
Elements of geometry and trigonometry . e AG, BG, areequal. But if the chord AG is e(|ual to the chord GB, the arcAG will be equal to the arc GB (Prop. IV.) ; hence, the radiusCG, at right angles to the chord AB, divides the arc subtendedby that chord into two equal parts at the point G. Scholium. The centre C, the middle j)oint D, of the chordAB, and the middle point G, of the arc subtended by thischord, are three points of the same line perpendicular to thechord. But two points are sufficient to determine the positionof a straight line ; hence every straijiht line which passes throughtwo of th. points just mentioned, will necessarily pass throughthe third, and be perpendicular to the chonl. It follows, likewise, that the. jtri-jtendicular raised from themiddle of a chord pusses through the centre of the circle, andthrough the middle of the arc subtended by that chord. For, this perpendicular is the same as the one let fall fromthe centre on the same chord, since both of them pass throughthe centre and middle of the
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
