Meridian (or "East Point"): pretends that all events occur at the Equator.
Campanus : pretends that all skies are as those witnessed at the Equator.
Regiomontanus: loses eight houses as it fails to unite Campanian and semi-arc principles.
Topocentric: fails to reproduce the semi-arc system by using great circles.
Koch: adds five fictitious "birthtimes" for any single event, causing houses to overlap.
Alcabitius: commences with the horizon circle but then replaces it with a Meridian circle.
Porphyry: commences with the oblique sphere but replaces this with a protractor.
Natural Graduation: commences with the oblique sphere but replaces it with calculus.