Authors writing about history of physics describe that before the writing of the Principia several scholars were aware that if the orbits of the planets would be circular (which they knew wasn't the case) then Kepler's third law was consistent with an inverse square law for gravity. These scholars included figures such as Christopher Wren, John Hooke, and Edmond Halley.
It seems to me that this implies that during that time the relation F=ma was already generally accepted as valid. Since without F=ma you cannot even evaluate the case of circular motion. However, I cannot find descriptions of how that came to be.
I wonder: was F=ma blindly assumed? It seems so. Of course, since F=ma is in fact correct assuming it was justified, but I find it odd that I cannot find any history of how F=ma came to be established.
To my knowledge the earliest attempts at experimental investigation of the relation between acceleration and force was by Galilei. To my recollection historians describe that Galilei had small balls rolling down inclines. A small vessel with a smaal hole near the bottom released a slow stream of water. Galilei (according to the description) would use several different lengths of inclines. He would allow the water to start flowing on release, and stop the flowing when the ball reached the end of the incline. the weight difference between start and end would then be a proportional measure of the time it took the ball to roll down the incline.
This experiment may have actually been performed by Galilei, or possibly it was only a description of something that one could do (similar to the description of simultaneous dropping of two different weights from a high tower that was described as possible demonstration, with later authors erroneously describing that as something that Galilei had actually done.)
I tried looking up information about the views of Pierre Gassendi, who, as I understand it, is recognized as the first to formulate the modern notion of what today is referred to as 'Newton's first law'. But I didn't find description of Gassendi proposing F=ma
Speaking in general:
If you do not assume F=ma then it seems to me you cannot make any progress when it comes to formulating a theory of mechanics. And of course when you want to do science you must believe that you are in a position where progress is possible.
Once newtonian mechanics became established the law F=ma became knows as Newton's second law, and I suppose the vast majority of authors simply assume that Newton was to first to formulate it.
I argue that cannot be, as earlier established work is dependent on the presupposition of F=ma.