Mediant is Between/Corollary 2/Proof 3

Proof
Let:
 * $t := \dfrac a b = \dfrac c d$

Then:
 * $a = t c$

and:
 * $c = t d$

Hence:
 * $\dfrac {a + b}{c + d} = \dfrac {t \paren {c + d} }{c + d} = t$