Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/521

  [ 57 ] 2. THIS equation, in different angles, is as the content under the ine comple- ment and the cube of the ine. For the triangle OKF, is as the rectangle of the ine and the ine complement. 3. IT is at a maximum, at an angle whole ine complement is to the radius, as the quare of the greater axis is to the um of the quares of the two axes; which in orbits nearly circular, is about 60 degrees of mean anomaly. 4. IN orbits of different eccentricities, it increaes in the quadruplicate propor- tion of the eccentricity. 5. IT oberves the contrary igns to that for the elliptic equant, called Bul- lialdus's equation ; ubducting from the mean motion in the firt and third qua- drants, and adding in the econd and fourth, if the motion is reckoned from the aphelion. THE ue of thee equations, in find- ing the place of a planet from the upper focus, will appear from the following rules, which are eaily proved from what has been aid. LET t be equal to CA the emi- tranvere, c equal to FC the ditance of the center from the focus, b equal to CD the emi-conjugate, and R an angle ubtended by an arch equal to                                       the