462. On a straight line, there are three points $G, D, F$, with $D$ lying midway between the other two; using only a ruler, draw a line through an arbitrary point $H$ parallel to the given line.

## Binet's Problem.
462. Draw the lines $G H$ and $F H$ (Fig. 107). Take an arbitrary point $A$ on $G H$ and draw the lines $A D, A F$. Through the point $C$ of intersection of the lines $F H$ and $A D$, and through $G$, draw the line $G C l$, intersecting $A F$ at point I. The line $H I$ is the required parallel.

Binet, Jean Philippe (1786-1856), French astronomer, professor at the École Polytechnique. His works are mainly in the fields of analysis, theory of equations, probability theory, and mechanics.