Thank you, Fred (Sawyer) and Chris (Lusby Taylor) for delivering the drawing.
Now I can follow the train of thougth of William Emerson and I can even formulate a simpler proof of his theorem. It suffices to prove that in an equatorial sundial the two line segments on the parallel line, on both sides of the hour line that is 6 hours away from the chosen hour line, are equal. (And that's easy) Then you can conclude that it is the case in any pole-style sundial, applying two general propositions: 1. Any pole-style sundial is always the projection of an equatorial sundial and each line segment in the sundial is the projection of a line segment of the equatorial sundial 2. The projection of a line segment devided into two equal parts has always the form of a line segment divided into two equal parts. Best wishes. Willy LEENDERS Hasselt in Flanders (Belgium) Visit my website on the sundials in the province of Limburg in Flanders (Belgium) and on worthwhile facts about sundials www.wijzerweb.be Op 9-apr-2010, om 11:53 heeft Chris Lusby Taylor het volgende geschreven: > Hi Willy, > No, but I bet it looks like this. > > Best wishes > Chris > ----- Original Message ----- > From: Willy Leenders > To: Sundial sundiallist > Sent: Thursday, April 08, 2010 7:22 PM > Subject: Drawing that belongs to the theorem of Emerson > > This is the address where you can find "Dialing or the art of drawing dials" > (1770) by William Emerson: > http://books.google.be/books?id=-bk2AAAAMAAJ&pg=PA177&dq=%22william+emerson%22+art+dialing&ei=Iya7S9yoLYSqywTRh_k5&cd=8#v=onepage&q&f=false > > On page 42 (page 220 of the scanned pages) you can find proposition XXIV: "In > any dial whatever, if a line be drawn parallel to any hourline, to intersect > the other hour lines, and note the sixth hour line from this. Then any two > hour lines on each side this sixth, which are equidistant in hours, will also > be equidistant along this parallel line." (known as the Theorem of William > Emerson). > > The drawing (fig. 11) used in the proof of the theorem is not scanned. > Can someone send me that picture? > > > Willy LEENDERS > Hasselt in Flanders (Belgium) > [email protected] > > Visit my website on the sundials in the province of Limburg in Flanders > (Belgium) and on worthwhile facts about sundials > www.wijzerweb.be > > > > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > <EmersonDiag11.gif>
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