Dear Frank (Evans), I don't agree completely on your conclusions :-)
In http://books.google.com it is possible to download the book <John Good - The Art of Shadows, etc. - London 1731> The PDF version downloaded is 7.0 Mb long and has 222 pages. In this book the author always uses the quantity "Planes difference of Longitude" or "Plane's Longitude" to calculate a declining sundial. In the pages 87-88 (of the PDF version) in the "Canon for the calculation" we find the calculation done with the Logarithms . The used formula (p. 88 - the last 5 lines) is Tan(Plane's Long.) = Tan(Decl)/Sin(Lat) This is the formula that gives the difference in Longitude within the place where the sundial is and the place in which the plane of the dial is tangent to the Earth's surface (that I have called Equivalent Point) This quantity is used for finding the angles of the hour lines (pag. 89- hard to read) I have not found where John Good defines or explains what this Plane's Long is : from the text it seems however that this quantity was well known and used, at least in 1731. Therefore I think that the writing <PI Long> must be read <Pl Long> or Plane's Longitude. I leave the search on other ancient texts (for me very difficult for availability and for language) to the English friends :- ) Gianni Ferrari
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