Page talk:Newton's Principia (1846).djvu/442

PROPOSITION XXXIII. PROBLEM XIV.

From the construction described in Proposition 33, the true motion of the nodes may be found approximately. However, by a happy accident, the construction can be used to obtain the true motion exactly.

Let the supplementary angle DCE, or DCF be taken, instead of the angle BCE, or BCF, equal to the double distance of the sun from the place of the node, as found by the mean motion. Angle DAG is produced by drawing AE or AF cutting the perpendicular DG in G. Using this angle DAG, added to or subtracted from the mean motion of the nodes as indicated in the proposition, we shall have their true motion without any error,

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