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).
[Illustration]
[44] Whalley, in his note upon this chapter, seems to have been
surprised that no mention is made here by Ptolemy of the _conjunction_;
but he overlooked the fact that the chapter treats only of parts of the
zodiac configurated _with each other_; and that it was not possible
for Ptolemy to conceive how any part could be configurated _with
itself_. It is, therefore, by no means wonderful that the conjunction
is not inserted here along with the rest of the aspects; although it
is frequently adverted to in subsequent chapters, and its efficacy
particularly described.
Of these configurations, the trine and the sextile 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 sexes.[45]
[45] From the tenor of this chapter it was formerly doubted whether the
author intended to admit in his theory only zodiacal aspects, and to
reject those which are called mundane; but Placidus has referred to the
4th Chapter of the 8th Book of the Almagest (which will be found in the
Appendix to this translation) to prove that Ptolemy distinctly taught
two kinds of aspect; one in the zodiac and one in the world. Whalley
quotes the opinion of Placidus, which he says is farther confirmed by
the 12th Chapter of the 3rd Book of this very treatise, where it is
stated that the ascendant and the eleventh house are in sextile to each
other; the ascendant and the mid-heaven in quartile; the ascendant and
the ninth house in trine; and the ascendant and the occidental angle
in opposition; all which certainly seems to be applicable to mundane
aspects in particular.