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Property 1:

Product of Means = Product of Extremes Consider 50 / 40 = 5 / 4 in which 40 and 5 are means and 50 and 4 are extremes in proportion. so 40 × 5 = 50 × 4Property 2: If a / x = x / b then x2 = a.b Here x is mean proportion of a and b.Property 3: Duplicate ratio of a:b is a2: b2 and sub duplicate ratio of a:b is ?a : ?bProperty 4: Triplicate ratio of a:b is a3:b3 and sub-triplicate ratio of a:b is 3?a : 3?b.Property 5 (Alternando Rule): If a:b = c:d then a :c = b :dProperty 6(Componendo Dividendo Rule): a/b = c/d then (a+b / a-b) = (c+d / c-d)Property 7: If a/b = c/d = e/f then a/b = c/d = e/f= (a+b+e / c+d+f)These are the seven properties of proportions.