In this engaging piece of detective work, Nicholas Kollerstrom has combined historical research with computer analysis to investigate long-unanswered questions about Newton's lunar theory of 1702 (whose complete text is included). The lunar theory turns out to have been the basis for numerous eighteenth century tables, and was used in China well into the twentieth century. It was taken (heavily disguised) into the Principia of 1713, with one important correction. In this form, it was remarkably accurate, about as good as the observations on which it was based, and was used by Halley (in a procedure explained here for the first time) to compute lunar positions with an accuracy of under one arcminute---good enough to have won the longitude prize.
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