28.15. a) Construct a segment that is twice as long as the given segment.
b) Construct a segment that is $n$ times as long as the given segment.
28.15. a) Let $AB$ be the given segment. Draw a circle with center $B$ and radius $AB$. By laying off chords $AX, XY$, and $YZ$ equal in length to $AB$ on this circle, we obtain equilateral triangles $ABX, XBY$, and $YBZ$. Therefore, $\angle ABZ=180^{\circ}$ and $AZ=2AB$.

b) The solution to part a) describes how to lay off a segment $BZ$ equal to $AB$ on the line $AB$. By repeating this procedure $n-1$ times, we obtain a segment $AC$, where $AC=nAB$.