Both Koch and Alcabitius employ the principle of trisection of the semi-diurnal arcs by a time division. The Koch houses are created by trisecting the MC semi-arcs and Alcabitius houses by dividing the diurnal circle of the ascendant.

please note that in the celestial sphere "time" is always an arc of space, so the distinction between "time division" and "space division" has little meaning.

A semiarc is a diurnal circle. These 2 systems use the diurnal semiarc to divide houses 5 and 6, and the nocturnal semiarc to divide houses 8-9, so from this perspective they are "absurd".

Koch goes further than Alchabitius and to divide the MC semiarc invents a series of quasi-ascendants and cuasi-sidereal times that have no geometrical meaning, they are just calculation tricks, so your friend is correct in saying that Koch houses have no counterpart in the celestial sphere: they are geometrically meaningless or badly defined.

In her 1977 book on Houses Dona-Marie Lorenz describes Koch as a good example of "how an algorithm can be confused with a definition". Unlike all the other house systems, Koch's is only an algorithm with no geometrical counterpart.

Juan

Where did you get the information that Lilly switched from Alcabitius to Regiomontanus?

Its strange I am positive I read this somewhere too. I think it was a piece about Lilly rather than one of his publications. I seem to recall this was in his early studies long before he published any astrology. I will need to have a hunt.