. Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre. 32 Draw the bisectrix CP of the angle DCB, and at P draw a tangentPT to the quadrant, meeting CB pro-duced at T. Draw the bisectrix TO, of theangle CTP, and from the point O, inwhich it meets CP, draw OR and OQperpendicular to CB and CD; withO as a centre, and OR as a radius,describe a circle. Because TO is the bisectrix of the angle RTP, OR = OP(Prop. IV, Key); because CP is the bisectrix of the angle BCD,OR = OQ: hence, the circle OR passes thro
. Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre. 32 Draw the bisectrix CP of the angle DCB, and at P draw a tangentPT to the quadrant, meeting CB pro-duced at T. Draw the bisectrix TO, of theangle CTP, and from the point O, inwhich it meets CP, draw OR and OQperpendicular to CB and CD; withO as a centre, and OR as a radius,describe a circle. Because TO is the bisectrix of the angle RTP, OR = OP(Prop. IV, Key); because CP is the bisectrix of the angle BCD,OR = OQ: hence, the circle OR passes through P and Q. Thiscircle is tangent to CT because CT is perpendicular to OR at R, andfor a like reason it is also tangent to CD at Q; the circle OR is tan-gent to the arc DPB, because CO = CP — OP: hence, the circleOR is the required circle. Prop. XLVL—Through a given point P, within a given angleABC, draio a circle that shall be tangent to both sides of that angle. Solution.—Let P be the given point and ABC the given angle. Draw the bisectrix BO, of thegiven angle, and also the line BP;from any point Q, of BO, draw QRperpendicular to AB, a
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectgeometry, bookyear187
