Octagon Framing: Then and Now?

Hi folks,
I'm looking at a small booklet on the rafter/framing square that's a reprint of a 1923 Audel's publication. On page 42 of this booklet is a partial image of the back of an old Eagle square where instead of the usual Essex board measure table there is an octagon rafter table for gazebos, turrets, and the like. The image, unfortunately, includes values for only a handful of the columns. The rows in the table are:
Length of Octagon Hip Rafters per Foot Run Length of Octagon Jacks Spaced One Foot Side Cut of Octagon Hip Rafters Side Cut of Octagon Jack Rafters
Thinking it would be useful to have the complete table, I set out to calculate the table values. Calculating the two length rows was pretty straightforward and my values matched the printed values pretty close. But, the side cut values in the table are baffling me. Let me try to explain.
Assuming that octagon roofs are framed with eight common rafters centred on each side of the octagon and meeting in the centre at 45 degrees to each other, the hip rafters would be centred on the octagon's corners and form an angle with the commons of half that, or 22.5 degrees. A zero pitch roof, therefore, would require a side cut on each side of the hip of 22.5 degrees.
I would expect then that a rise of only 1 inch per foot of run would not change this angle very much at all. The table, however, states that for a 1 inch rise the hip side cut will be found by using edge values of 16. The other edge value being always 12, I calculate a side cut angle of about 53 degrees.
It's unlikely this is a misprint, so I'm thinking either the framing technique was vastly different back when the Eagle octagon rafter square was being used, or I am clueless about how this table was to be used.
If someone could help me either correct my math, or explain how these tables are to be used correctly, I'd really appreciate it.
Thanks for your time,

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