NavList:

Antoine,

I wish I could take credit for the idea to cut and fold the diagram, but that was Hanno's suggestion in post g30486. I must say, I am amazed by your analysis in post g30505. I was trying to wrap my head around just where the vertices of the pyramid would be located in relation to the Earth. You have confirmed my suspicion. You must be highly adept at thinking in 3D, not having the actual pyramid in hand.

...Which leads me to:

Hanno,

Having constructed the pyramid as described, I instantly understood what Antoine was explaining. I sat staring at it, trying to visualize the Earth in relation to it. As Antoine explained, if the line CP represents the radius of Earth, it becomes immediately obvious that the points O and S cannot be on the Earth's surface. What I am still confused about is how angle OC'S' is equal to the zenith distance of the body. But I suppose reading the book and a little more staring might help with that. ;)

Cheers,

Sean C.

PS

I believe Antoine mentioned "Brent's pyramid" several times. No doubt he was referring to "Breed's pyramid". Perhaps that contributed to some confusion? (Just blame auto-correct, Antoine. ;) )