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

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2. THIS equation, in different angles, is as the content under the ſine comple- ment and the cube of the ſine. For the triangle OKF, is as the rectangle of the ſine and the ſine complement. 3. IT is at a maximum, at an angle whole ſine complement is to the radius, as the ſquare of the greater axis is to the ſum of the ſquares of the two axes; which in orbits nearly circular, is about 60 degrees of mean anomaly. 4. IN orbits of different eccentricities, it increaſes in the quadruplicate propor- tion of the eccentricity. 5. IT obſerves the contrary ſigns to that for the elliptic equant, called Bul- lialdus's equation ; ſubducting from the mean motion in the firſt and third qua- drants, and adding in the ſecond and fourth, if the motion is reckoned from the aphelion. THE uſe of theſe equations, in find- ing the place of a planet from the upper focus, will appear from the following rules, which are eaſily proved from what has been ſaid. LET t be equal to CA the ſemi- tranſverſe, c equal to FC the diſtance of the center from the focus, b equal to CD the ſemi-conjugate, and R an angle ſubtended by an arch equal to the