Oh alright, here's the derivation by plane trig at the dial:
.
.First, of course this is what gives the natural and easily-explained
derivation for a Horizontal-Dial's hour-lines, and so I'll show that first:
.
I'll designate lines by the letter-names of their two endpoints.
.
When I state a
When I listed trig, in my previous message, I was referring to the fact
that there's a 3rd derivation-approach that applies plane trig at the dial
itself (but of course not just on the horizontal-plane).
With any one of those 3 derivation-approaches, it would be necessary to
explain either some
Frank--
.
As you described, a Horizontal-Dials' (or any Flat-Dial's)
declination-lines can be constructed, by 3-dimensional analytic geometry,
as the intersection of a cone with a plane.
.
Here's another way:
.
1. For a particular day, and at an hour shown on the dial, calclate the
Sun's altitude.
