Instruction in the Elements of the Art of Astrology

45. TarkIb al-nisbah. When there are four proportional~,
and the sum of the first and second is to the
second as the sum of the third and
COBPOSITION
fourth is to the fourth, the proportion
is said to be by composition. Our
example is a multiple and the fifth thereof, 5:1::15:3
6:)::18:3.
46. Tafgil al-nisbah. men there are four prop
tionals, the excess of the first over the second is
to the second, as the excess of the
DIVISION third over the fourth is to the fourth,
the proportion is said to be by division
or separation. As the first term in our example is
smaller, than the second, 1:5::3:15, proportion by separation
can only occur after inversion, thus; 5:1::15:3
yielding 4:1::12:3.
When there are four proporto
its excess over the
second, as the third is to its excess
CONVERSION over the fourth, the proportion is
said to be by conversion. Our example
after inversion, 5:1::15:3, gives 5:4::15:12.
48. Nisbah al-musawEt al-muntagimah. When the
ratio of Fhe first to the second is =same as that of
the third to the fourth, and that
PROPORTION BY of the second to the fifth the same
ORDINATE EQUALITY as that of the fourth to the sixth,
and so on for any number of proportionate
terms, then the terminal numbers are also in
proportion, as in our example, the first is 1/5 of the
second, and the second 1/4 of the fifth, so the first
is 1/20 of the fifth, as is the third of the sixth.