As shown in the figure, crossing A makes AA' vertical to the river bank and AA'= river width, connecting A'B, crossing GH in E, crossing E makes DE⊥MN in D, and DE is the bridge built. The reason for this is the following：

Build another bridge GF on the river bank to connect af, ga and BG.

∫DE is parallel and equals AA'

A quadrilateral is a parallelogram.

∴DA=EA'

Similarly: AF=A'G

The distance from B to A via DE is: BE+DE+DA=BE+AA'+EA'= segment BA'+AA'

The distance from B through FG to A is BG+GF+FA=BG+AA'+GA'= broken BGA'+AA'

The shortest line segment between two points

∴ paragraph ba'