The Mechanism of Action of the Non Geometrical Method Placidus

This presentation provides a precise geometric and computational analysis of the Placidian method of celestial partitioning. We demonstrate that the Placidian method is predicated upon the exhaustiveness of its search for oblique ascensional times (a complete, point-by-point measure of the seasonal time interval for every degree of the intermediate celestial arcs). This contrasts sharply with the Alcabitius and Koch methods, which rely upon the trisection of the seasonal time of, alone, the Ascendant (Alcabitius) and Midheaven (Koch), creating a segmented, non-continuous or incomplete measurement (i.e. a different form of linearity or uniformity from Campanus and Regiomontanus). 

Our exposition establishes that the Placidian method is unique in deriving the angular size of each quadrant division from the trisection of the discrete ascensional time of the specific cuspal degree itself. This principle reveals that every degree holds a fixed relative/variable temporal value at a given latitude. The Placidus system is thus shown to be the sole system that is naturally compatible with the concept of unequal seasonal hours. The resultant angular divisions are relative and non-uniform, accurately reflecting the geometry of the oblique sphere, as opposed to the absolute, arithmetically divided segments produced by the other methods.