Tetrabiblos and Centiloquy

And when I have considered the two larger parts in which there will be a correspondence of the quantity of the part and the quantity of the whole and the part: these remaining figures will be established through correspondence in this way: so that for the first part, when we assign a length to the two right angles original: "duos rectos angloꝝ" - referring to 180 degrees which is the length of the diameter: from its half and its third it will be. That is, the half will be the square original: "tetragona" - the square aspect of 90 degrees length, and its third will be the hexagonal original: "exagona" - the sextile aspect of 60 degrees length. And with this length doubled, the trine 120 degrees length is established. However, through the correspondence of the whole and the part, it happens thus: when we have made a proportion from the square length to the two other lengths between which it is established, and the proportion of one was one-and-a-half sesquialtera: a 3:2 ratio and the other was one-and-a-third sesquitertia: a 4:3 ratio: when we have assigned the proportion from it to that which was less than it, and whose proportion to it is one-and-a-half, its length will become hexagonal; and when we have assigned the proportion to that which is greater than it, and whose proportion is one-and-a-third, we establish the trine length. Therefore, they have called the trine and hexagonal of these affinities "agreeing," because they are established from signs agreeing in gender: for they are all either masculine or feminine. But those which are formed from the diameter or from the square figure, they have named "disagreeing," because they are always found in the contrariety of signs that otherwise agree in gender.

¶ Chapter 15. On the high and low signs which are called commanding and obeying.

Parts of which the length from any one and the same point of the equinoctial points The points where the celestial equator and ecliptic intersect; the equinoxes is the same, are called high sublimies and low infimę; and they are those whose ascensions and descensions happen in equal times, because they are carried in equal circumferences of the parallel circles to the equinoctial circle. Moreover, those of these parts which are formed in the middle of the summer circle are called high; and those which are in the middle of the winter circle are named low. This is because when the sun proceeds through the middle of the summer circle, it makes the days longer than the nights. But when it illuminates the middle of the winter circle, it demonstrates that the days are shorter than the nights. This refers to "commanding" and "obeying" signs, which have equal daylight hours based on their distance from the equinoxes.

Chapter 16. On signs beholding each other and equated to themselves in strength.

They say likewise that there are certain parts which are equal to other parts in strength, when their length from any one point of the two tropic points The solstices is one and the same: because when the sun has traveled through either of these two points, day will equal day, and night will equal night, and the times of the hours horarū will be the same. They also say that these parts, because of the aforementioned occasions, "behold" each other, and that each one of them rises from the same parts of the horizon oriʒontis in the east, and sets in the same parts in the west.

Chapter 17. On signs contradicting each other and between which no connection is made.

Parts which are called contradicting and foreign are those between which no affinity is contained from the modes of affinities mentioned before. That is, they are neither from the commanding precipientia nor from the obeying obediētib⁹, nor from those beholding each other which are equal to each other in strength; nor are they from those which, placed through any of the four figures, have any affinity to each other. That is, by the diameter...