Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/524

  [ 60 ] proportion, it will produce 2'.40" near- ly, for the equation e: the ine of M is, in this cae, equal to 1/2 the radius, the cube is 1/8 of the cube of the radius; whence if the equation S=30" be divi- ded in the ame proportion, it will produce near 4" for the equation s. There- fore the angle RFA, which is M + e + s, will be 3O°.2'.44"; and the half is 15°.l'.22" ; wherefore if the tangent of this angle be diminihed, in the proportion of 1.06, the aphelion ditance, to 94 the perihelion ditance, it will produce the tan- gent of 13°.23'.13" ; the double of which 26°.46'.26", is the true anomaly or angle at the Sun RSA. And conequently, the equation of the center is 3°.13'.34" to be ubducted, at 30 degrees mean anomaly. WHEN the place of a planet is found by this, or any other method; the place may be corrected to any degree of ex- actnes by the common property of the equant, viz. that the rays are recipro- cally in the duplicate proportion of the velocity about the center. For in this cae, if there be a difference between the mean motion belonging to the angle aumed at the upper focus, and the given mean motion, the error of the an- gle aumed is to the difference, as the rectangle of the emi-axes to the rect-                                         angle