Many of the curves discussed in the preceding chapters were drawn from a base–line or a base–circle, and sometimes other curves such as the parabola or hyperbola were used. The strophoid, for example, was drawn first by using a straight line and a point (the first and second methods); then by using a parabola (the envelope method); and finally by using a circle and its diameter (the ‘cissoid’ method). It has also been seen that any curve has its evolute, and its pedal or negative pedal with respect to a given point. Curves have been obtained too by rolling circles along lines or other circles, and by sliding set squares against fixed points or along fixed lines.

These and other methods of obtaining new curves will now be considered. The reader will often be able to recall the use already made of a method and will then be able to use it to draw new curves. There is no end to the number and variety of plane curves: many are well known and and have been studied in detail; others are known, while their geometrical properties remain undiscovered; and there are many more which have yet to be drawn for the first time.