Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/523

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and in the caſe of the planets, always near the double of that equation.

  THE angle RFA at the upper focus

F being known, the angle RSA at the Sun in the other focus, is found by the common rule of Biſhop Ward ; viz. the tangent of half the angle RSA, is to be to the tangent of half the angle RFA, always in the given proportion of the perihelion diſtance SP to the aphelion di- ſtance SA. How theſe equations are in the ſeveral eccentricities of the Moon's orbit, will appear by the following Table. Eccentr, E. S. 0.040 1.23 09 0.045 1.45 13 0.050 2.09 17 0.055 2.36 23 0.060 3.06 30 0.065 3.38 38 0.070 4.14 47

To add one example; ſuppoſe the ec- centricity 0.060, the mean anomaly 30°. The ſine of the double of the mean ano- maly, that is, the ſine of 60 is to the ra- dius, nearly as 87 to 100; whence, if the equation E = 3'.06", be divided in that

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