Task. Let $AB$ be a given line segment and $n$ a positive integer $> 1$ . Divide $AB$ to $n$ equal parts.

Solution. Draw a half-line $p$ beginning from $A$ but not parallel to $AB$ . From $p$ separate $n$ consecutive equally long segments $AA_1$ , $A_1A_2$ , $A_2A_3$ , ..., $A_{n-1}A_n$ . Draw the line $A_nB$ and denote by $B_1$ , $B_2$ , ..., $B_{n-1}$ the points of $AB$ such that $$A_1B_1\;\parallel\;A_2B_2\;\parallel\;\ldots\;\parallel\;A_{n-1}B_{n-1}\;\parallel\;A_nB$$ (see compass and straightedge construction of parallel line). These points divide the line segment $AB$ in $n$ equal segments.

Proof. For clarity, we prove the theorem only in the case $n = 3$ .