 Newton's second law? F = m a
Newton was not the first to suggest "Newton's second law".
In 1669 (18 years before Newton), Royal Society member John Wallis wrote,
For body at rest hath a repugnance to motion and body in motion hath a repugnance to rest, though Body as Body
is indifferent to either, and will therefore continue as it is (whether at rest or in motion) till some positive cause alter its
condition. And when such positive cause comes, its acts proportionally to its strength, the lesser the strength with which it
moves, and the heavier the body to be moved, the slower will be the motion.
Also, Thomas Hobbes published his book Leviathan 1651 (36 years before Newton),
That when a thing lies still, unless somewhat else stir it, it will lie still forever, is a truth that no man doubts.
But [the proposition] that when a thing is in motion it will eternally be in motion unless somewhat else stay it,
though the reason be the same (namely that nothing can change itself), is not so easily assented to.
 Newton's law of gravity?
Hooke presented a new gravity/motion theory to the Royal society in 1666 in which he said:
I will explain a system of the world very different from any yet received.
It is founded on the following positions.
 That all the heavenly bodies have not only a gravitation of their parts to their own proper centre,
but that they also mutually attract each other within their spheres of action.
 That all bodies having a simple motion, will continue to move in a straight line,
unless continually deflected from it by some extraneous force, causing them to describe a circle,
an ellipse, or some other curve.
 That this attraction is so much the greater as the bodies are nearer.
In 1672, Hooke tried to prove the Earth moves in an ellipse round the Sun and
in 1679, he proposed an inverse square law for gravity to explain planetary motions
an attractive motion towards the central body ...
my supposition is that the attraction always is in a duplicate proportion to
the distance from the center reciprocal ...
Although Hooke did not give a mathematical proof of his conjectures, he made first claim to the inverse square law for gravity.
This led to a bitter dispute with Newton who then removed most references to Hooke from the Principia.
Their feud lasted decades. In a 1690 lecture to the Royal Society, Hooke said
concerning those properties of gravity which I myself first discovered and showed to this Society and years since,
which of late Mr Newton has done me the favour to print and publish as his own inventions.
 Newton's law of light?
An initial cordial relationship between Hooke and Newton became angry and bitter.
Newton suffered two mental breakdowns and Hooke became cynical and withdrawn.
Hooke claimed Newton's theory of light and color was stolen from ideas he produced 7 years earlier (in 1665).
The Royal Society's Hooke papers and the sole portrait of Hooke painted for the Royal Society were ``lost'' by
Newton when he became President of the Royal Society (they were recently rediscovered).
Newton wanted to burn all of Hooke's papers (he did not succeed).
Ironically, Newton's famous quote (below) appeared in a February 5, 1676 letter
from Newton to the very short Hooke.
If I have seen further, it is by standing on ye shoulders of Giants
 Newton's discovery of Calculus?
Although Newton and Leibniz share the discovery of calculus their relationship
was contentious  with Newton and Leibniz and their respective supporters
alleging plagiarism and undermining each other's credibility.
As President of the Royal Society, Newton appointed an ``impartial'' committee to decide
whether he or Leibniz invented calculus.
He wrote the committee's official published report (although not under his name)
and then wrote a review (again anonymously) which appeared in the Philosophical Transactions of the Royal Society.
Ironically, the introverted Newton died at 80years old a national hero of England
with a state funeral of the highest honors (normally reserved for English statesmen and generals).
whereas the more sociable Leibniz's died at 70years old, almost completely forgotten,
with a funeral attended by only his secretary.
Newton's daunting reputation intimidated British mathematicians.
England did not produce another firstrate mathematician for over a century.
Undaunted and unintimidated by their English neighbors,
the rest of Europe, lead by the Bernoulli family, Leonard Euler, D'Alembert, Lagrange, Laplace, Fourier, and many others,
quickly expanded analytical analysis through differential equations,
the calculus of variations, etc.

