This is an old request to the list, and I'm not going to answer it, but it
is worth looking at the wonderfully detailed Newton biography,
RS Westfall, Never at Rest, CUP, 1980 & reprinted several times,
pages 707 - 712, on the earlier Section VII of Principia Book II in which
he describes in detail the evolution of Proposition XXXVI, on which the
later propositions depend. Here are the beginning and the end of this
passage:
"Newton immediately dispatched a further batch of the text [to Cotes who,
in 1710, was going through the material for the revised 2nd edition of the
Principia] which included the rest of Book II and Book III as far as
Proposition XXIV. It began with Section VII [Propositions XXXII-XL], the
heart of Newton's theory of the resistance of fluids, the topic, he had
told Gregory, which was giving him the most trouble. No part of the
Principia had been more imperfect. It was an important topic, moreover, for
it provided the heart of his argument against Cartesian natural philosophy.
...
No one would care to deny that [his treatment of Proposition XXXVI] was a
virtuoso performance. Few would care to dignify it with the title of
scientific investigation."
I wish I could write like that, and with that authority!
David Fowler