How Koch Houses Are Calculated.

How Alcabitius Houses Are Calculated.

I’ve decided to do a series of mini-posts on time-based houses. I’ll start with the Alcabitius house system:

Alcabitius begins with the diurnal semi-arc of the Ascendant. It measures the interval in right ascension from the Ascendant to the Right Ascension of the Midheaven (RAMC), then divides that interval into three equal parts to locate the eleventh and twelfth house cusps. These positions are then projected back onto the ecliptic using spherical trigonometry.

The idea here is that Alcabitius follows the motion of a single zodiacal degree. Every zodiacal degree possesses its own fixed declination and therefore follows its own unique path across the sky as the Earth rotates. The ascending degree rises, culminates, and sets along this single path, producing one continuous semi-arc from the eastern horizon to the meridian. Alcabitius simply divides this one semi-arc into three equal parts before projecting the resulting positions back onto the ecliptic.

Unlike Placidus, Alcabitius never abandons the geometry of the original ascending degree. The entire construction belongs to one degree throughout, making it a remarkably elegant and unified time-based house system.