ma : nb :: mc : nd.
Prop. 5. If
a = mb, and c = md,
then
a − c = m(b − d).
Prop. 6. If
a = mb, c = md,
then are a − nb and c − nd either equal to, or equimultiples of, b and d, viz. a − nb = (m − n)b and c − nd = (m − n)d, where m − n may be unity.
All these propositions relate to equimultiples. Now follow propositions about ratios which are compared as to their magnitude.
§ 52. Prop. 7. If a = b, then a : c :: b : c and c : a :: c : b.