The Mathematical Principles of Natural Philosophy, Book III: Of the System of the World
“Scholium
“If the mean horary motion of the nodes in the quadratures be 16’’ 16’’’ 37iv. 42v. that is, in a whole sidereal year, 39° 38’ 7’’ 50’’’, TH will be to TK in the subduplicate ratio of the number 9,0827646 to the number 10,0827646, that is, as 18,6524761 to 19,6524761. And, therefore, TH is to HK as 18,6524761 to 1; that is, as the motion of the sun in a sidereal year to the mean motion of the node 19° 18’ 1’’.
“But if the mean motion of the moon’s nodes in 20 Julian years is 386° 50’ 15’’, as is collected from the observations made use of in the theory of the moon, the mean motion of the nodes in one sidereal year will be 19° 20’ 31’’ 58’’’. and TH will be to HK as 360° to 19° 20’ 31’’ 58’’’; that is, as 18,61214 to 1: and from hence the mean horary motion of the nodes in the quadratures will come out 16’’ 18’’’ 48iv. And the greatest equation of the nodes in the octants will be 1° 29’ 57’’.”