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Hakob Barseghyan teaches in his History and Philosophy of Science course that Descartes started it. The hypothetico-deductive method (what's commonly called the scientific method) is a result of the philosophic commitments of Descartes thought.
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.
Given that Newton was a person who cared about the religious that would be a bad example. He spent a lot of time with biblical chronology.
You claimed that science wouldn't have been invented at the time without Newton. It's historically no accident that Leibniz discovered calculus independently from Newton. The interest in numerical reasoning was already there.
To get back to the claim, following the scientific method and explicitly writing it down are two different activities. It takes time to move from the implicit to the explicit.
But Newton didn't propose a religious method for science, which is my point. Did you think I meant that the popes turned Dante atheist? What they did was give him a desire for a secular ruler and an "almost messianic sense of the imperial role".
That sort of thinking may have given rise to Descartes' science fiction, so to speak - secular aspirations which go beyond even a New Order of the Ages. So there are a few possible prerequisites for a scientific method. As for someone else writing one down, maybe; what we observe is that the best early formulation came from a brilliant freak.
Why do you think that Newtons proposal of his method of science had something to do with desire for a secular ruler?
Why do you think Newton's focus on new observations/experiments came from Cartesian ontology, when Newton doesn't wholly buy that ontology?
I'm saying the popes inadvertently created a separate concept of secular aspirations - often opposed to religious authorities, though not to God if he turns out to exist. This "imperial role" business is arguably a rival form of the idea, though Newton did in fact work for the Crown.
My main source is lecture series towards which I linked above. The Newtonian worldview is presented as the lecture that follows after the one I linked.
At the time the Crown was the head of the church in England.
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.