OTHER FORMS FOR PROPORTIONS
If four numbers, for example, a, b, c, and d,form a proportion, such as
they also form a proportion according to otherarrangements.
The four selected numbers are in proportionby INVERSION in the form
The inversion relationship is proved as follows, by first multiplying both members of theoriginal proportion by :
Note that the product of the means and the product of the extremes still yield the same equality as in the original proportion.
The inversion relationship may be illustratedby the following numerical example:
The four selected numbers (a, b, c, and d)are in proportion by ALTERNATION in the following form:
To prove the alternation relationship, first
multiply both sides of the original proportion
by b/ c, as follows:
The following numerical example illustrates alternation: