This work, although beyond my competence in mathematics, is designed for "the common reader." With just — a desideratum I lack — calculus and geometry, Chandra demonstrates certain fundamental scholia of Newton's treatise. But he does more than this. He shows us what Descartes suspected — that the classical geometers and Newton, in a way, new the same things. Descartes was the first to voice his "suspicion" that the classical mathematicians knew the methods of modern, calculus-based numerical analysis, but did not reveal such (Descartes' foundational act, his creation of "analytical geometry," is the point of "closest contact" ( Leo Strauss in a different comparison: Xenophon and Machiavelli) between ancient mathematical science and modern. By casting "Principia" in classical geometry, Newton — in a tradition profoundly indebted to Descartes and, therefore, Spinoza, shows his assent to Descartes' premise. If Newton's "Principia" can be elaborated by Euclid's methods, then, perhaps, Euclid is not so Parmenidean after all. In other words, there is a kinematicism (Parmenides) and a dynamism (Heraclitus) — i.e., Einstein and quantum theory — within classical mathematical science.
I find this in Euclid's ambiguous definition of "point" within his "elements" and within his non-theorem, but postulate, the famous "fifth" — which scholars have labored in vein to derive from his other four axioms.
They have now discovered that it cannot be done, which is why it is a "postulate," rather than an "axiom."
Newton, to say nothing of Euclid, chose all words carefully: Chandra brings this to light for us. This should not cause us to shrug our shoulders and say, "Well, then, it has all been done before, why do anything in science?" It should, rather, challenge us to say, "How can I prove that?"
Maybe you cannot, and I know I cannot: So it has the effect of conserving for us the greatness of our tradition, while asking us to go beyond it by not allowing us the, "We stand on the shoulders of the shoulders of giants, so we see farther than they" platitude. Therefore, above all, the mystery of Newton's cosmology is revealed to us. We have found our way out of the Labyrinth of millenial confusion only to recover the greatness of Our Tradition: Our gratitude to Chandra is infinite! So, perhaps, is the cosmos in which it emerged. Discourse on Method and Meditations on First Philosophy