A treatise on surveying ; in which the theory and practice are fully explained (1860)
Alsop, Samuel · Philadelphia, E. C. & J. Biddle & co. · leaf 78
RICAL SOLUTION OF TRIANGLES. 75 Demonstration.—Let ABC (Fig. 50) Fig. 50. be a triangle, of which AB is greaterthan AC. Make AD = AC. Join DC,and bisect it by AEF. Draw EH paral-lel and equal to CB. Join HB, and pro-duce it to meet AEF in F. Then, sinceEH is equal and parallel to CB, BH is jjVequal… … On EH Now,2AK = 2AG4-2GK=AC+AD+2DG + 2GK=AC + AB-f-BC;or AK == J (AC -f AB + BC), and AI = AK—KI = J (AC + AB-f BC) — BC. But, (Rule 2, Art. 137,) As AD : AEand AB : AF whence (23.6) AB . AD: AE . AF : r : cos. DAE (cos. J BAC),: r : cos. \ BAC;: r»: cos.3 \ BAC. But (36.3, Cor.) AE . AF = AK. AI =…
Surveying
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