Nothing pleases me more than to report on the conscientious natue of Mr Newton. For it is not carelessly or without the consideration of others that he proposes and supposes! Having regard to those who are his colleagues and demonstrated to and for him many principles in experimental forms, he set aabout the task of philosophically combining them in some satisfactory exposition that mimics Euclid, with a just regard to the reputations of himself, his sources and his collaborators. Mr. Newton lived in dangerous times!
Those who have never studies logic, suppose it to be the art of persuasion, but it was never so. It is in fact the tool of offense and defense in argument, employing such stratagems as are necessary to stay the hand and mouth of any opposer and to cause such a one to submit exhaustd by irrefutable arguments. Such a person may remain never convinced or convicted, but rather, simmering, biding his time until such opportunity present itself to demonstrate his opinion and to force submission or the staying of mouths. Thus Logic is adversarial and coercive and not at all to be confused with that contemplation that first dlights, then entraps and then convinces one into acceptance.
It may be, that by rule, a submitting protagonist adopts the views of his defeater, but this is not persuasion but assuasion, and one who is so inclined indeed will change with every victor who overcomes him. But the one who knows his own mind, and settled in it proceeds through life cannot be won by logic. In every case Acceptance is a personal, subjective decision which no one else can make on another's behalf, whether coerced, hypnotised, blagged, or deceived, only the person can do it or undo it.
Many have gone to their deaths with fine convictions, and some have remained alive with cowardly and beggarly ones. The quality of ones life is determined by such, and it is good therefore to pay attention to what one accepts knowingly or unknowingly. Being of open mind , therefore, allows one to discover all things in time and in sequence, whether good or bad, about oneself and ones environments. Being also aware that it is within ones own power only to accept what one wishes, compensates for any other lack of power one may imagine themselves to be in.
Bearing this in mind, it is Mr. Newtons gentler approach which is more likely to lead to, upon understanding, conversion of accepted convictions if there be any at odds with what he discusses. At the same time he himself shows himself open to a similar circumstance with similar outcome.
It is for this very reason that Mr. Newton applies lemma upon lemma, reasonable notion upon other reasonable notion , consolidation upon earlier supposition, more confirming detail upon what is merely apparent , not to convince the reader per se, but to convince himself that he has not gone all the way astray and is inviting others to follow him into error! For, god love him!, it is not error he is after, but that immaterial thing called by some the "Truth". And the truth of the matter being that we can only know what we empirically experience, however odd, or however conflicting it may seem.
Thus when we come into such a dynamic world as it is we needs must make careful distinctions and employ such well appointed tools as we can to make some sense of it. And should magnitudes apparently vanish and also come into being we should not consign that to magic or mystery but should pursue it as best we can. Thus the notions of nascent and evanescent, though imprecise, serve to focus th mind on the comings and goings of magnitudes. But where Mr. Newton surpasses all others is in his notion of quantifyng these comings and goings by the use of the only tools we have, and they are comparisons of magnitudes, especially in the form of quantities.
To this end he introduces the notion of equality, which he applies both to magnitude and Ratios for a purpose which the reader will be advised of as he goes through the exposition. Equality, i have written before on, and in fact it is a more subtle notion of the Euclidean Duality, and used in the similar fashion. However, whereas Euclid suffices to say that any thins be dual with each other if one of the things fits any other of the things, this will not suffice for the dynamic situation. Firstly because though it is inherently a dynamic definition of duality it is not explicitly so. Later Euclid extends this notion by many methods of comparison, and indeed the algorithm of commensurability, but for Newton all these results must be first announced and explored and demonstrated to ensure that he is proceeding safely to his goal, which is a mechanical exposition of the motion of heavenly bodies as empirically observed.
So also must he safely convey the workings of what we now call a vector algebra, after both Hamilton, Grassmann(in particular) and that interloper Gibbs! Sorry to characterize him as such, but i have reason to warn the reader of him.Having established the systems of equality he will rely on, and the combinatorial methods he will also rely on, he has only to exposit the methods of Fluxions, in the which the dynamics of points, lines and surfaces and volumes are closely studied and mathematically demonstrated. For this he required a detailed mathematics, which due to Descartes and De Fermat he and others were schooled in up to the point of great facility with the heuristic methods of Euclid and others. Taking what is clearly laid out in Euclid's works and that of Archimedes, Pappus and Ptolemy , and that of moderns whom he mentions, he renders it all intelligible by rendering it all down into its parts and slowly and carefully synthesising it into a new method of calculus, in which the dynamic plays as important a part as the ideal forms ( which only appear static), and the proper conduct of the mind and the application of the calculus is painstakingly laid out.
As best as one is able to accept and deal with magnitudes arising by velocities and accelerations out of points and instances, and disappearing in the same, Newton has made a stab at how we might safely quantify such things as they acquire their real form and substance in our more certain world. He admits that he has not solved the philosophical problems, but hopes that he has helped in that direction rather than creating an impenetrable obstacle to such progress.
We are indeed in safe hands with Mr. Newton, much more i might add than with Mr Einstein.