Here is what Morris Kline says about Frans van Schooten:
The first task was to explain Descartes's idea. A Latin translation of
La Geometrie by Frans van Schooten (1615-60), first published in 1649
and reprinted several times, not only made the book available in the
language all scholars could read but contained a commentary which
expanded Descartes's compact presentation. In the edition of
1659-61, van Schooten actually gave the algebraic form of a
transformation of coordinates from one base line (x-axis) to another.
He was so impressed with the power of Descartes's method that he
claimed the Greek geometers had used it to derive their results.
Having the algebraic work, the Greeks, according to van Schooten,
saw how to obtain the results synthetically--he showed how this could
be done--& then published their synthetic methods, which are less
perspicuous than the algebraic, to amaze the world. Van Schooten may
have been misled by the word "analysis," which to the Greeks meant
analyzing a problem, and the term "analytic geometry," which
specifically described Descartes's use of algebra as a method.
(Mathematical Thought from Ancient to Modern Times, pages 318-319)
I have a former student, who knows Latin well, and who has some free time.
Shall I suggest to her that she should (could, might) translate the
van Schooten commentary? Where can she obtain a text? I think that Green
Lion Press will publish it. It should contain the Descartes text, too, in
both French and English.
Best wishes,
Sam Kutler