Leibniz and Cartesian geometry (1673--1676) (Q2825749)

Let us mention the conclusions of the author's paper, as those did appear there (reviewer's translation), in short: Leibniz has developed the following criteria at the end of the year 1676:NEWLINENEWLINE 1) Geometrical curves have to be exact (i.e. not in the way as Descartes treated those);NEWLINENEWLINE 2) In order to accept a geometrical problem as being solved, one has to provide it indeed by geometrical means; the curves used here should be the most easy ones for which the problem is solved;NEWLINENEWLINE 3) In accordance to its division in categories as Euclidean, Apollonian and Archimedian ones, the procedure under 2) means that lines and circles, then the other conics and algebraic curves of higher degrees and at last transcendental curves may be of a geometrical nature.NEWLINENEWLINE [The reviewer found it a difficult task to translate those lines from the German language into English, faithfully representing the intentions of the authors.]NEWLINENEWLINE There is much to learn from this paper; take a look in it.NEWLINENEWLINEFor the entire collection see [Zbl 1321.01006].