J.M. Ashmand - Ptolemy's Tetrabiblos - Ch. 16 lyrics

CHAPTER XVI 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 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, [paragraph continues] AC, CB, will make the quartile distance AC; and the division into three aliquot parts, AD, DE, EB, will make the s**tile 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 s**tile, AD, the super-proportion DC, equal to the half of the s**tile), and the trine AE (if there be added to the quartile AC the super-proportion CE, equal to the third part of the quartile). Of these configurations, the trine and the s**tile are each called harmonious, because they are constituted between signs of the same kind; being formed between either all feminine or all masculine signs. The opposition and quartile are considered to be discordant, because they are configurations made between signs not of the same kind, but of different natures and s**es