By dividendo, if a:b=x:ya:b = x:ya:b=x:y, then —
Dividendo subtracts the denominator from the numerator on each side: from ab=xy\frac{a}{b} = \frac{x}{y}ba=yx we get a−bb=x−yy\frac{a-b}{b} = \frac{x-y}{y}ba−b=yx−y, i.e. a−b:b=x−y:ya-b : b = x-y : ya−b:b=x−y:y. Subtracting 111 from both equal fractions keeps them equal.