We use this device by moving the wheeled pointer so that it marks the same number on the vertical ruler as on the horizontal ruler. The tip of the pointer traces out the conch curve.
Durer gave this diagram in his 1525 book Vnderweysung der Messung ("A Manual of Measurement"). He explained it as follows: "I draw a horizontal line ab and divide it by means of sixteen points equidistant from each other....I then erect a vertical line at point 13 of the horizontal line ab.... This line I also mark with the same numbers, beginning from the bottom. Then I take a ruler and mark the length ab off on it. Placing one end of the ruler on point 1 of the horizontal line ab and letting its edge touch point 1 of the vertical line, I mark the point indicated by the other end of the ruler....I proceed likewise with all the numbers on the horizontal and vertical lines until I reach point 16. Subsequently, I draw the conch line as in the diagram below."
So Durer was interested in the curve on the left, the conch
curve. Should we want to draw a curve like this, Durer
recommends the following device:
We use this device by moving the wheeled pointer so that
it marks the same number on the vertical ruler as on the
horizontal ruler. The tip of the pointer traces out the
conch curve.
Durer did not mention that the curve on the right was a parabola, although he had explained how to construct parabolas earlier in the book. The book has been translated from the German by Walter L. Strauss as "The Painter's Manual" (New York: Abaris Books, Inc., 1977); see particularly pages 105-109.