On the breaking of water waves on a sloping beach of arbitrary shape

Greenspan [1] considered water waves of finite amplitude on a beach of constant slope. He proved that: ($\left ( {{G_1}} \right )$) A wave of elevation with nonzero slope at the front propagating shoreward into quiescent water always breaks before the shore.†($\left ( {{G_2}} \right )$) Under the same conditions a wave of depression never breaks.