Ptolemy's Tetrabiblos · Ptolemy
MUTUAL CONFIGURATIONS OF THE SIGNS
There are certain familiarities or connections between different parts of the zodiac; and the chief of these is that which exists between such parts as are configurated with each other. This mutual configuration attaches to all parts diametrically distant from each other, containing between them two right angles, or six signs, or a hundred and eighty degrees: it also exists in all parts at the triangular distance from each other, containing between them one right angle and a third, or four signs, or a hundred and twenty degrees; also, in all parts at the quadrate distance from each other, containing between them exactly one right angle, or three signs, or ninety degrees; and, also, in all parts at the hexagonal distance from each other, containing between them two-thirds of a right angle, or two signs, or sixty degrees.[44] These several distances are taken for the following reasons: the distance by diameter, however, is in itself sufficiently clear, and requires no further explanation; but, as to the rest, after the diametrical points have been connected by a straight line, AB; the space of the two right angles, contained on the diameter, is then to be divided into aliquot parts of the two greatest denominations; that is to say, into halves, AFC, CFB, and into thirds, AFD, DFE, EFB: there will then be provided for the third part (AD) a super-proportion (DC), equal to its own half; and for the half (AC) a super-proportion (CE), equal to its own third part; so that the division into two aliquot parts, AC, CB, will make the quartile distance AC; and the division into three aliquot parts, AD, DE, EB, will make the sextile distance AD, and the trinal distance AE. The respective super-proportions (on either side of the intermediate quartile AC, formed by the one right angle AFC), will also again make the quartile AC (if there be added to the sextile, AD, the super-proportion DC, equal to the half of the sextile), and the trine AE (if there be added to the quartile AC the super-proportion CE, equal to the third part of the quartile).
Any two signs configurated with each other at an equal distance from the same, or from either equinoctial point, are termed commanding and obeying, because the ascensional and descensional times of the one are equal to those of the other, and both describe equal parallels. The signs in the summer semicircle are commanding; those in the winter semicircle, obeying: for, when the Sun is present in the former, he makes the day longer than the night; and, when in the latter, he produces the contrary effect.
Text from Project Gutenberg, public domain in the United States.