Around March of 1636, at the age of forty, Descartes moved to Leiden to work out the publishing of the Discourse.
Alternately, it might be the case that like Spinoza (in Ethics Part IV, definitions three and four), Descartes uses the expression "possible existence" to describe actually-existing creatures, and in a way that is consistent with a denial of non-actual reality.
This is precisely the approach that Descartes takes as he treats the Pappus Problem in Book One. Figure 7: The Four-Line Pappus Problem in Book One (G, 27) In Book One, Descartes applies his geometrical analysis to the four-line case of the Pappus problem.
More wrote four letters in all, but only received replies to the first two before Descartes's death in 1650.
The same point is made later in Book Two, where Descartes emphasizes that "no matter how we conceive a curve to be described, provided it be one of those which I have called geometric," it will always be possible to find an equation determining all of the curve's points (G, 56).
As a testament to the significance of Cordemoy's study of language, one scholar has written that Cordemoy "picked up one of Descartes' arguments based on the lack of true speech among animals and developed it fully; so fully, in fact, that after Cordemoy the point was given very little attention, as if subsequent authors considered this the last word on the subject" (Rosenfield 1968, 40).
It is treated in Book One, as Descartes explains his geometrical analysis, and then again in Book Two, where Descartes offers the synthesis, i.e., the geometrical demonstration, of his solution to the Pappus Problem in n-lines, a demonstration which relies on the famous distinction between "geometric" and "mechanical" curves that begins this part of the work.
On the one hand, Descartes offers a geometrical interpretation of root extraction and thus treats five arithmetical operations (as opposed to the four operations of addition, subtraction, multiplication, and division that were treated in his early work).
Part One develops Descartes' metaphysics.
This phrase is also one that Descartes himself uses at Principles II, art.
