OR THE QUADRIPARTITE MATHEMATICAL TREATISE
18. Of the Triangles.
The familiarity by triangles is as follows. Inasmuch as the triangular and equilateral form is most harmonious with itself, the zodiac also is bounded by three circles, the equinoctial and the two tropics, and its twelve parts are divided into four equilateral triangles. The first of these, which passes through Aries, Leo, and Sagittarius, is composed of three masculine signs and includes the houses of the sun, oc Mars, and of Jupiter. This triangle was assigned to the sun and Jupiter, since Mars is not of the solar sect. The sun assumes first governance of it by day and Jupiter by night. Also, Aries is close to the equinoctial circle, Leo to the summer solstice and Sagittarius to the winter solstice. This triangle is preeminently northern because of Jupiter's share in its government, since Jupiter is fecund and windy, similarly to the winds from the north. However, because of the house of Mars it suffers an admixture of the south-west wind and is constituted Borrolibycon, because Mars causes such winds and also because of the sect of the moon and the feminine quality of the occident.
The second triangle, which is the One drawn through Taurus, Virgo, and Capricorn, is composed of three feminine signs, and consequently was assigned to the moon and Venus; the moon governs it by night and Venus by day. Taurus lies toward the summer tropic, Virgo toward the equinox, and Capricorn toward the winter tropic. This triangle is made preeminently southern because of the dominance of Venus, since this star through the heat and moisture of its power produces similar winds; but as it receives an admixture of Apeliotes because the house of Saturn, Capricornus, is included within it, it is constituted Notapeliotes in contrast to the filet triangle, since Saturn produces winds of this kind and is related to the cast through sharing in the sect of the sun.
The third triangle is the One drawn through Gemini, Libra, and Aquarius, composed of three masculine signs, and having no relation to Mars but rather to Saturn and Mercury because of their houses. It was assigned in turn to these, with Saturn governing during the day on account of his sect and Mercury by night. The sign of Gemini lies toward the summer tropic, Libra toward the equinox, and Aquarius toward the winter tropic. This triangle also is primarily of eastern constitution, because of Saturn, but by admixture north-eastern, because the sect of Jupiter has familiarity with Saturn, inasmuch as it is diurnal.
The fourth triangle, which is the one drawn through Cancer, Scorpio, and Pisces, was left to the only remaining planet, Mars, which is related to it through his house, Scorpio; and along with him, on account of the sect and the femininity of the signs, the moon by night and Venus by day are co-rulers. Cancer is near the summer circle, Scorpio lies close to the winter one, and Pisces to the equinox. This triangle is constituted preeminently western, because it is dominated by Mars and the moon; but by admixture it becomes south-western through the domination of Venus.