Astronomicon, Book I

tetragons: the side of a tetragon consists not of 4 but of 3 signs, or of 90 degrees, inasmuch as 12 ÷ 4 = 3 and 360 ÷ 4 = 90. To Romans, whose slovenly use of their ordinal numbers had already in Manilius' lifetime thrown the new Julian calendar out of gear, because the pontifices did not know what Caesar and Sosigenes meant by quarto quoque anno [every fourth year], these lessons from the dame-school were not superfluous; but Greek readers receive similar monitions from the so-called Porphyry, isag. pp. 186 sq. "One must see whether the figures are perfect in terms of degrees and not merely zodiacally; the trigon aspect occurs through 120 degrees, the tetragon through 90 degrees, the hexagon through 60 degrees, and the diameter through 180 degrees. For often they are configured by signs, but not by degrees." The inordinate length of Manilius' exposition is perhaps after all less due to a low estimate of his readers' knowledge of ciphering than to the pleasure he takes in exercising that eminent aptitude for doing sums in verse which is the brightest facet of his genius.

352-357

The trine aspect, says Manilius, has much more force than the quadrate. This statement, which he repeats by implication in verses 673-680, is confirmed by no astrologer within my knowledge, and by some it is apparently contradicted.

Thus Firmicus II 23 says indeed (4) "the trigon... is joined... with the horoscope... in the greatest... association," but also says (5) "the quadrate also is joined with the horoscope... in a most valid association of radiation"; Censorinus de die nat. 8 9 is equally impartial, "the two visions, the tetragōnoi and trigōnoi, are highly effective," and so is the author of Cens. frag. 3 8 (schol. German. Breys. pp. 199 and 223) "stars look at one another from the fifth sign, which is called trigonon, and they have the greatest agreement; likewise from the fourth, which is called tetragonon..., and they provide a maximum effect in either case." The difference usually made between the trigon and the tetragon is a difference not of force but of quality; the former is harmonious or good and the latter discordant or evil: Firm. II 22 4 and 6, Paul. Alex. E and schol. D 4, Sext. emp. 40, Ptol. tetr. p. 9u., Porph. isag. p. 186, Hermipp. I 19, C.C.A.G. VIII ii p. 74 17-9.

358-384

Two hexagons inscribed in the circle connect the alternate signs as follows.

1. Aries Gemini Leo Libra Sagittarius Aquarius.
2. Taurus Cancer Virgo Scorpius Capricornus Pisces.

Thus one hexagon consists of the masculine and the other of the feminine signs.