# An elementary treatise on geometry : simplified for by Francis J. Grund

By Francis J. Grund

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Additional info for An elementary treatise on geometry : simplified for beginners not versed in algebra. Part I, containing plane geometry, with its application to the solution of problems

Example text

If from a point M, in a triangle ABC, two lines, BM, are drawn to the two extremities of any side, , in that triangle, hy these two what relation does to the side AB in the triangle ? serve with regard to the MB, sum of AC, BC, of AMB, made the two lines, opposite you AM ob- and A31B, and which include the angle sides, the angle ACB, which is And what do hear to the angle lines, AM, AB, the triangle that of the two which include the angle ACB? C D DM C MB A The angle AJSIB, made hy the lines A.

46 included by ekics ii»c AB, BD, in the triangle sequently, tiiese two triungles AC side AD in drawn from it to follows from No. There Tthly. ABD con- ; and the third equal to the third side but one point in the line 3/N, on tacJi the point snch, A, is that a strmglit line, of a given length. This 4. but ene point in the line is the peipendicidar , in of ; 1, Sect. ) pa'pendicultstr, of the side triangle, is (Query h Tltere 6thly. side one in the the other. are equal which a MN, on each line draicn to the MN A an angle of a given forms with the line magnitude.

A /\ Fig. II. Fig. UL GEOMETRY. ABC, If the two triangles, it is ed same manner, and after the side BC (Fig. ) the side AB that ; is ABC. three times as the side ab is, if is one third the side be one third of the side ABC, would The same figures, composed of any number of holds true of all similar, their sides are proportional to are different BC ; or not be similar to each other. There that the side ac must also be one third of the the triangles abc, proportion. half of the is also be half of the side BC If twice as is of the triangle abc, must be in propoT' if (Fig.