A ratio compares two quantities of the same kind; a proportion states that two ratios are equal.
1Ratios
a : b = a/b; multiplying both terms by the same number leaves it unchanged
Dividing T in the ratio a : b gives aT/(a + b) and bT/(a + b)
If A : B = a : b and B : C = c : d, then A : C = ac : bd
2Proportions
a : b :: c : d ⇔ ad = bc
Fourth proportional to a, b, c = bc/a
Third proportional to a, b = b²/a; mean proportional = √(ab)