Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/522

       [ 58 ] the radius, viz, 57°. 17'. 44". 48"', or 57, 2957795 degrees. Take an angle T = cc/2tt R ; E = b/2t T; S = 4c/3b T. The angle T be will the greatet e- quation for the triangle OFK ; the an- gle S will be the greatet equation for the egment LMG ; and the angle E will be the greatet equation for the area OKFL. Which greatet equations be- ing found, the equations at any angle of mean anomaly, will be determined by the following rules. LET M be the mean anomaly ; and let &tau; be to T as the ine of the angle 2 M to the radius : In which pro- portion, as alo in the following, there is no need of any great ex- actnes, it being ufficient to take the proportions in round numbers. TAKE e to E as the ine of 2M +/- 2 &tau; to the radius; and s to S as the cube of the ine of M +/- &tau; to the cube of the radius. THEN the angle QFL is equal to M + e + s, in the firt quadrant LN, or M - e + s , in the econd quadrant Nl, or M + e - s in the third quadrant, or M — e — s in the fourth quadrant. NOTE, That the mall equation &tau; is al- ways of the lame ign with the equation e;                                      and