. Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre. Prop. XIV.—Given two lines that would meet if sufficiently pro-longed, to draw the bisectrix of their included angle without findingits vertex. * Solution.—Let AB and CD be the given lines. Through any point P, of AB, draw PRparallel to CD (Bk. III. Prob. 6). Bisect theangle BPR by the line PQ, and draw the linePR perpendicular to PQ; bisect PR in S(Bk. III. Prob. 1), and draw SY parallel toPQ. Because CD is parallel to PR, the anglebetween the given li
. Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre. Prop. XIV.—Given two lines that would meet if sufficiently pro-longed, to draw the bisectrix of their included angle without findingits vertex. * Solution.—Let AB and CD be the given lines. Through any point P, of AB, draw PRparallel to CD (Bk. III. Prob. 6). Bisect theangle BPR by the line PQ, and draw the linePR perpendicular to PQ; bisect PR in S(Bk. III. Prob. 1), and draw SY parallel toPQ. Because CD is parallel to PR, the anglebetween the given lines is equal to the angle RPB, and consequently the required bisectrix is parallel to PQ;hence, PR is perpendicular to that bisectrix. Since S is the middle. 14 KEY.
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Keywords: ., bookcentury1800, bookdecade1870, booksubjectgeometry, bookyear187
