If four magnitudes be proportional, they will also be proportional alternately.
Proof
Let a:b=c:d. Test a:c against b:d with equimultiples
ma, mc, nb, nd: by V.4 the original proportion lifts to ma:mb=nc:nd, and by V.15 to ma:nc=mb:nd. The sign of ma−nc matches the sign of mb−nd for all m, n, which by V.5 is
the alternated proportion a:c=b:d.