 [In this new science] each problem will be solved according to its own nature as for example, in arithmetic some questions are resolved by rational numbers, others only by surd [irrational] numbers, and others finally can be imagined but not solved. So also I hope to show for continuous quantities that some problems can be solved by straight lines and circles alone; others only by other curved lines, which, however, result from a single motion and can therefore be drawn with new types of compasses, which are no less exact and geometrical, I think, than the common ones used to draw circles; and finally others that can be solved by curved lines generated by diverse motions not subordinated to one another, which curves are certainly only imaginary such as the rather well-known quadratrix. I cannot imagine anything that could not be solved by such lines at least, though I hope to show which questions can be solved in this or that way and not any other, so that almost nothing will remain to be found in geometry. It is, of course, an infinite task, not for one man only. Incredibly ambitious; but I have seen some light through the dark chaos of the science, by the help of which I think all the thickest darkness can be dispelled (AT X, 156–158; CSMK 2–3; translation from Sasaki 2003, 102).