Elements of geometry and trigonometry . 2.). INIoreover, the side AO is com-mon to the two triangles AOD, AOF ; and the angles adjacentto the equal side are ecjual : hence the triangles themselves areequal (Book 1. Prop. VI.) ; and DO is equal to OF. In the samemanner it may be shown that the two triangles BOD, BOE,are equal ; therefore OD is equal to OE ; therefore the threeperpendiculars OD, OE, OF, are all equal. Now, if from the poin-t O as a centre, with the radius OD,a circle be described, this circle will evidently be inscribed inthe triangle ABC ; for the side AB, being perpendicular t
Elements of geometry and trigonometry . 2.). INIoreover, the side AO is com-mon to the two triangles AOD, AOF ; and the angles adjacentto the equal side are ecjual : hence the triangles themselves areequal (Book 1. Prop. VI.) ; and DO is equal to OF. In the samemanner it may be shown that the two triangles BOD, BOE,are equal ; therefore OD is equal to OE ; therefore the threeperpendiculars OD, OE, OF, are all equal. Now, if from the poin-t O as a centre, with the radius OD,a circle be described, this circle will evidently be inscribed inthe triangle ABC ; for the side AB, being perpendicular to theradius at its extremity, is a tangent ; and the same thing is trueof the sides BC, AC. Scholium. The three lines which bisect the angles of a tri-angle meet in the same point. PROBLEM XVI. On a given straight line to describe a segment that shall containa given angle ; that is to say, a segment such, that all the an-gles inscribed in it, shall be equal to the given angle. Let AB be the given straight line, and C the given
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
