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I understand how to construct South-facing vertical an horizontal sundials and the geometry behind their construction by projecting an equatorial sundial into a plane, but I can't quite get how to do that for a declined plane.

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You might find the following useful; scroll down to "Vertical Declining Sundial".

http://www.walkingshadow.info/Publications/Scratch.pdf

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    $\begingroup$ Welcome. Please provide context for links to give the reader some idea what's there. $\endgroup$ – Mike G Jan 3 '20 at 16:09
  • $\begingroup$ The problem with link-only answers is that if the link breaks the answer becomes useless to future readers. It's hard to recreate that entire section here, (slides 16-22) but if you can add at least a quick summary that will make this a better Stack Exchange answer. I looked at it and it's over my head, otherwise I'd just add it myself. Thanks! $\endgroup$ – uhoh Jan 4 '20 at 6:29
  • $\begingroup$ The link broke :( $\endgroup$ – Phineas Nicolson Feb 6 '20 at 1:39

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