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ChristianKl comments on How Many LHC Failures Is Too Many? - Less Wrong
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The video is somewhat odd in that he claims Descartes had no problem with experiments, but I recall the philosopher proposing rules which contradicted experiments and hand-waving this by appealing to the impossibility of observing bodies in isolation.
In any case, Hakob does make clear that Descartes used a more Aristotelian method as a rhetorical device to persuade Aristotelians. (In effect, he proved the method of intuitive truth unreliable by producing a contradiction.) I don't believe his work includes any workable method you could use to do science, while Newton's rules for natural philosophy seem like an OK approximation.
The main point is that if you buy the philosophic commitments of Descartes the hypothetico-deductive method is a straightforward conclusion. Newton might have expressed the method more clearly but various people moved in that directions once Descartes successfully argued against the old way.
Possibly, but I wouldn't say the popes started science by being terrible rulers, thereby creating a clearer distinction between religious and secular.
Asking on StackExchange gives a variety of people before Newton: http://hsm.stackexchange.com/questions/5275/was-isacc-newton-the-first-person-to-articulate-the-scientific-method-in-europe/5277#5277
Even there, someone points out that Bacon wasn't big on math. I'll grant you I should give him more credit for a sensible conclusion on heat, and for encouraging experiments.