The ancient Greeks, and Epicurus in particular, wondered about Motion. Nothing was taken as given or for granted. There was a cause for everything, but precisely what the specific cause for a particular phenomenon was not known.
Newton sidesteps the question, as all must, inorder to establish a method of synthesis or praxis that was constructed from known or given things. To this end he metaphysically declared the active principles of all things. His chief active principle was Motive!
Some other principles of action and motion such as celerity and path of motion were also declared. But motive was of a different character to these as cues is to effect. Newton searched long and hard for active principles, but none seemed to be equal to or more fundamental than motive. Heat, light even electrical discharge like sheet lightning all seemed to fundamentally involve motive. And motive was the source of celerity, it was the cause of change in speed, direction and the pressure of corpuscular bodies!.
Corpuscular bodies were not empty. They were bubbles of many properties including celerity, density , elasticity and adhesion. All these properties were effects of motive. But for ,olive to do all this their had to be contra motive. Space or a region had to possesses inherently competing motives, and it was the interaction of motives that allowed the deduction of the observed behaviours of matter..
But what was matter?
Newton from his investigations into Assay and Alchemy recognised one quality of matter and that was density!. Each element of matter is distinguishable by its density. And fire would purify admired compounds to reveal the true elements.. This trial by fire often reduced a compound to its base elements, but not always. Sometimes it compounded base elements into some new unknown material, and density was not always preserved, so it was not possible to confidently declare the new substance as n admixture! What happened to the missing density?
Newton searched hard to find an answer and we do not know if he found one. If he did it would be the basis of the conservation of density in matter, and thus the conservation of matter. Newton was particular in his definition of matter. Nothing that would not pass through fire was allowed to contaminate his measure.. The density of a substance was the Assayers density, and the volume or bulk it occupied was that after it had bern assayed. The quantity of matter was thus as pure and tested a notion as he knew how, and consequently it was only this density that could hold the qualities of celerity etc and which could be affected by motive. All else he set to one side.
Although not a Puritan he seems to have accepted a puritanical notion of matter. Thus any thing which was supposed to be a fluid between corpuscles, being burned away by fire would not be capable of receiving the influence of Motive. Yet metals being thus purified exhibited Magnetic properties, and these he did accept as aspects of motive. In all his experiments he never attempted to measure the motive force of Magnetism. The only recorded attempts to do so is that of Robert Hooke.. Newton took magnetism to be a model of a motive system of forces he called Gravity. Beyond that structure he would not venture. He framed no hypothesis of this particular aspect of Motive.
With this particular mindset in place we can begin to apprehend how it was that Newton took the observations and insights of his fellows to a slightly deeper level of analysis and synthesis. Having sunmixed a causal relationship between speed and distance, and another between acceleration and speed, that is velocity, by means Olof his metaphysical framework in which Motive provides a corpuscle with its celerity,mand celerity provides the corpuscle with its position as an extension proportional to time, newton was bold enough to introduce an Absolute time against which he hoped to compare all motions. In so doing, he utilised the work and ideas of Wallis on the formulation of the Conic section locii.
Newton explained how Fluxions came to him in a dream.mthe dream is as if he was reading The first Stoikeioon of Euclid's Stoikeia., only the definitions were animated!. Each point traces out ( grammethai) a line ( gramme) and each line drags out ( grammethai) a plane surface ( epipedos epiphaneia ) like a rake , and as if an advancing shadow moves across a plane. These dynamic insights were further enhanced by Barrows treatment of Appolonian Conics.
Wallis and Barrow one in Oxford, the other in Cambridge both directed Newtons Studies at different stages of his Acadmic career, and Hooke took it upon himself to confide with all able members of the royal society his present course of study and exploration in order to ensure consistency in publication and demonstration of the gentlemanly deliberations.
Newton rightly acknowledges the influence of all these in directing his study, but none I think can claim to have provided him with his conclusions or his method or praxis..
Thus in a dream, the notion of motive, that is self perpetuating motion from some invisible source of all motions, positions and velocities presents itself. It is not that he could claim that God was behind every motion, but that some active principle was! He was not able to say what it was, but he could plainly see how it caused its effects in ome, proportionately, spaciometric ally, and coherently as if in some mechanical system driven by gears, pulleys and chains and belts. Embedded in all these transmission bodies, by contiguity or collision some active principle impressed itself on and spread between corporea of a corpuscular structure.
Thus,my purifying the substances by fire, he made clear that this motive was not the fluids commonly described in the less rigorous vorticular philosophies of motion. In fact, within the body of a tempered spring Hooke had showed how force was a proportional property of its extension. But it was Newton who did not discount the oscillation of the spring! All school children are routinely taught to steady the spring to get the measurement. Newton was observant of the damped oscillations of the spring prior to its steady state. He knew from Galileo that were it not for the spring, the weight woul accelerate, and he could see that acceleration being counteracted. Thus from Hookes law he saw the dynamic accelerative law he is famous for!
More than that, he could see the inertial reactive frame in which all motion took place. There was no isolated motion, all motion was as a result of a dynamic interactions between a body and it's inertial frame. It is strange, but it took Lagrange to popularise this wholly Newtonian notion. His closest students seemed not to study what he thought or said but rather people's opinions of what he supposedly meant. Only Cotes and De Moivre appear to have taken the trouble to learn his deep praxis.
Motive now provided the acceleration of the weighted object, but also the deceleration of the restraining spring material. This immediately suggest that motive is an equilibrium sustaining and celerity stabilising causal principle. As an active principle it is restorative, balancing, damping. So why acceleration?
This question was to haunt Newton for the rest of his life, and ultimately confused him when he explored motive in a fluid medium.