Prove Chuquet's règle des nombres moyens (rule of average numbers): if given positive numbers \(a, b, c,\) and \(d\) where \(\dfrac{a}{c} < \dfrac{b}{d}\), then \(\dfrac{a}{c} < \dfrac{a + b}{c + d} < \dfrac{b}{d}\).
Le Triparty en la science des nombres, Nicolas Chuquet, 1484