Proportion :

An equality of two or more ratios is called proportion . Four quantities a,b,c,d are said to be in proportion if
a:b = c:d or a:b :: c:d
⇒ = ⇔ ad = bc

Note 1 : First and last terms are called the extremes,(a and b) while the two middles terms b and c are called the means.

Note 2 : Four quantities (a,b,c and d) are in proportional if the product of extremes is equal to the product of the means .
= ⇔ ad = bc
ad (product of extermes), bc (product of means)

Note 3 : Three quantities a,b,c (of same kind) will be in continuous proportion if = ⇒ b² = ac ⇒ b = √ac

Properties of proportion (of four Quantities)

(i) = ⇔ = (is known Altenendo)

(ii) = ⇔ = (is known Invertendo).

(iii) = ⇔ = (is known Componendo).

(iv) = ⇔ = (is known Dividendo)

(v) = ⇔ = (is known Componendo Dividendo)

(vi) = ⇔ (is known Addendo)

(vii) = ⇔ (is known Subtranendo)