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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.

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