Building on my last post, here is another way to construct a parabola using a collection of straight lines. First, the description, taken from Lockwood’s A Book of Curves (page 7):
Draw any two lines and mark on each a series of points at equal intervals. (The intervals on the second line need not be equal to those on the first.) Call the points on the first line \(A_1, A_2, A_3\), etc.
There are several ways to draw a parabola using straight lines. If you get a chance, you should try one sometime - it is always satisfying to see the outline of a curve slowly emerging from a collection of straight lines.
One method uses a set-square. As described in A Book of Curves by E.H. Lockwood (page 3):
Draw a fixed line \(AY\) and mark a fixed point \(S\). Place a set square \(UQV\) (right-angled at \(Q\)) with the vertex \(Q\) on \(AY\) and the side \(QU\) passing through \(S\) (Fig.