When is a planet in a sign? The strange ideas of Abu Ma’shar.

Recently I’ve been reading Ben Dykes translation of Abu Ma’shar’s Great Introduction to the Science of the Judgements of the Stars (Cazimi Press, 2020). Many of Ma’shar’s ideas have caused me to re-evaluate my own understanding of some basic concepts. His discussion of out-of-sign aspects has me perplexed, and I wonder if in a certain sense Ma’shar doesn’t know what he’s talking about.

Specifically I’m referring to the discussion of out-of-sign aspects on page 451 of Dykes’ translation. Ma’shar gives the example in which the Moon is at the very end of Aquarius and Saturn is at the very beginning of Cancer. In this case, the Moon and Saturn are not considered to be in aspect because Cancer and Aquarius are signs in aversion to one another, and aspects only occur between signs. He also notes that the orb of the body of the Moon will extend into Pisces because the Moon lies at the very end of Aquarius, and thus the ray of Saturn at the very beginning of Pisces will mix with the light of the orb of the Moon, producing a “mixture of their natures” which will be small, and the Moon “will not be reckoned as connecting with” Saturn “until it has changed over to the other sign.”

So far, so good. But Ma’shar states “if the light planet [the Moon in this example] was at the end of the sign [Aquarius in this case], empty of course, with the power of one-half of its body having already gone to the next sign from it, and the rays of some other slow planet [Saturn in this example] are at the beginning of that sign [Pisces in this case] … and they are not looking at each other, then the mixture of their natures will be small and the light one will not be reckoned as connecting with the slow one until it [the slow one] has changed over into the other sign.” [bold mine] To me this sounds like utter nonsense. The comment in bold makes me wonder if Ma’shar’s phrasing could have inspired the later concept of moieties of planets to define when planets were in aspect.

Ma’shar appears to be stating that in this case the Moon is to be considered as inhabiting Aquarius until its entire body has enter Pisces. Thus, even if Saturn’s ray were at 0 Pisces 01′ and the Moon’s body entirely encompassed the ray of Saturn in Pisces, the mere presence of a tiny speck of the Moon’s body in Aquarius would mean the two planets are not connected by aspect. Ma’shar appears to completely disregard the angular diameter of the planets.

Image from https://en.wikipedia.org/wiki/Angular_diameter

Planets are not one-dimensional specs in the sky, but the boundaries between signs can be considered one-dimensional lines. For example, the Sun has an angular diameter of about 32′ of arc. The Moon’s angular diameter varies from about 30′ to 34′ of arc depending on where the moon is in its orbit around the Earth. Saturn has an angular diameter of about 14″ to 20″ of arc.

In Ma’shar’s example, let’s assume that Saturn (that is, the center of Saturn’s body) lies at 00 Cancer 00′ 10″ so that its “trine ray” in Pisces lies at 00 Pisces 00′ 10″. Now if the Moon lies at 29 degrees Aquarius 59′ 59″, Ma’shar would consider to Moon to be in Aquarius even though 99.9% of its body lies in Aquarius, and the body of the Moon completely overlaps the trine ray of Saturn, and he would consider there be be only a “small mixture of their natures.” Only when the outmost edge of the body of the Moon passed into Pisces would Ma’shar consider a trine to exist.

This passage in Ma’shar is patently illogical and displays an ignorance of basic astronomy, which makes one wonder whether the text was somehow corrupted and did not express what Ma’shar orignally intended. Obviously the body of a planet can be in two signs at once, as the planet crosses over the one-dimensional border between signs. Anyone who has watched the sun rise or set is away of the span, measured in minutes on the clock, required for the sun’s entire disk to rise or set with respect to the horizon. The concept of cazimi was extant in Ma’shar’s time, that is, that a planet’s body in direct contact with the body of the sun (within 17′ of the center of the sun, assuming that the sun had an angular diameter of about 34′ of arc) was a special condition because the bodies of both the planet and the sun were overlapping.