Hi Anselmo, I think the essential difference between these two dials is that, for Vitruvius' spider dial, time is indicated by the shadow of the TIP of a vertical gnomon; Oughtred's Double Horizontal, on the other hand, uses the shadow of the vertical style EDGE. The curvilinear grids of hour angle vs. Sun's declination or altitude look superficially similar, but are to a different geometrical projections.
Best regards, John Davis 51d 05m N: 1d 08m E -