Syllogism and mathesis. Hegel and Husserl on the method of philosophy

In the essay, I address the issue of whether in Hegel's and Husserl's conception of philosophy there is a room for the modern conception of mathesis. I start from Lachterman's observation that mathesis is not an axiomatic or formalized system from which an infinity of statements can be derived, but it is rather a set of useful prescriptions for the motion of mind. From this perspective I claim that Hegel appropriates this conviction by refusing, however, to identify his logical set of prescriptions with mathesis, while Husserl leaves a room for it, thank to his criticism of the "technization" of science, even though he really never realizes it.