The calculus for engineers and physicists : integration and differentiation, with applications to technical problems and classified reference tables of integrals and methods of integration . K The two partial I and h gradients of (Aa + Bh + Cc) are taken;thus 116 THE CALCULUS FOR ENGINEERS. da I a cos a dl (Z2 + /i2)4 dbdl X-l - COS j3 dcdl L-l_e cosy dadh h ha sin a dbdh R-hb -sin/3 dndh _hc siny. Fl8. 29. Therefore equating both partial gradients to zero, we obtain thesimultaneous equations . A cosa-B cos^-i- C cosy=0 )A sin a - B sin /? + C sin y = 0 / ? EUmiaating the terms in B by cross-m
The calculus for engineers and physicists : integration and differentiation, with applications to technical problems and classified reference tables of integrals and methods of integration . K The two partial I and h gradients of (Aa + Bh + Cc) are taken;thus 116 THE CALCULUS FOR ENGINEERS. da I a cos a dl (Z2 + /i2)4 dbdl X-l - COS j3 dcdl L-l_e cosy dadh h ha sin a dbdh R-hb -sin/3 dndh _hc siny. Fl8. 29. Therefore equating both partial gradients to zero, we obtain thesimultaneous equations . A cosa-B cos^-i- C cosy=0 )A sin a - B sin /? + C sin y = 0 / ? EUmiaating the terms in B by cross-multiplication, and againsimilarly eliminating the terms in C, there are obtained the tworatios A_sin(y-j8)^sin(180° + ;8-y) C ~ sin (;8 - a) ~ sin (180° + a - ;^)and A_sm(y-j3)_sin(180° + j8-y) B sin (y - a) sin (y - a) By reference to the figure it will be seen that the three anglesentering into these ratios, namely, (180° + /8-y), (180°+ a-/8). INTEGKATION OF DIFFERENTIAL EQUATIONS. 117 and (y - a), are the three angles between b and c, a and b, e and the sides of a triangle are proportional to the siaes of theopposite angles, it follows immediately that these three anglesA A A bo, ab, and ea, to which the three branches are to be adjusted, arethe exterior angles of a triangle whose sides are made equal (toany convenient scale) to A, C, and B. By constructing thistriangle t
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