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1. Mechanism for describing an algebraic curve
This question has been central to kinematics for several centuries, and its origins can be traced back to Watt, with the drawing of a straight line. It's important to understand the theoretical and practical implications. There's a big difference between generating a curve and reproducing one.
Let's illustrate this with the circle:
by tracing the edge of a coin with a pencil, we draw a circle that is the reproduction of an existing circle;
with one instrument, the compass, we can generate any circle of given radius, i.e. of given equation.
For the right, the answer is much more difficult:
the common drawing of the line with the ruler is the reproduction of an existing line;
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Mechanism for describing an algebraic curve
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