Newton made groundbreaking discoveries in mathematics, optics, and mechanics and formulated the laws of motion and universal gravitation. He developed calculus independently of Leibniz, though priority disputes arose later. Newton's Principia mathematically described and proved the motion of orbiting bodies, revolutionizing astronomy and physics. His work was foundational in establishing modern science based on experimentation and mathematics rather than metaphysics.

2. Alexander Pope
Nature and Nature's
laws
lay hid in night
God said, Let Newton
be!
and all was light.

3. Westminster Abbey
Here is buried Isaac Newton, Knight, who by a
strength of mind almost divine, and mathematical
principles peculiarly his own, explored the course and
figures of the planets, the paths of comets, the tides
of the sea, the dissimilarities in rays of light, and,
what no other scholar has previously imagined, the
properties of the colours thus produced. Diligent,
sagacious and faithful, in his expositions of nature,
antiquity and the holy Scriptures, he vindicated by his
philosophy the majesty of God mighty and good, and
expressed the simplicity of the Gospel in his
manners. Mortals rejoice that there has existed such
and so great an ornament of the human race!

4. William Wordsworth
And from my pillow, looking forth
by light
Of moon or favouring stars, I could
behold
The antechapel where the statue
stood
Of Newton with his prism and silent
face,
The marble index of a mind for ever
Voyaging through the strange seas
of Thought, alone.

11. I. B. Cohen
“The Newtonian revolution
was not only the apex of the
Scientific Revolution, it
remains one of the most
profound revolutions in the
history of human thought.”
(Cohen, 1985, p. 175)

12. Mathematics
Theory of Limits
Binomial expansion
Geometry of conic sections
The calculus (“method of fluxions & fluents”)
The application of mathematics to physics and
astronomy

13. Conic Sections

15. Physics
Optics and the theory of light and colors
Design of scientific instruments
Codification of dynamics
Invention of the concepts of mass, momentum,
force, and gravity
Discovery of the Law of Universal Gravitation
Discovery of the Gravitational Theory of Tides

17. 1661 – Enters Trinity College, Cambridge @ age of 19
1664 – Begins self-directed study of mathematics; Discovers general
binomial expansion; Begins work on “quadtratures” (integration)
1665 – Receives BA; Leaves Cambridge due to plague;
1666/67 – Works on fluxions, optics & color, and motion; Returns to
Cambridge
1669 – Becomes Fellow of Cambridge and Lucasian professor of
mathematics
1672 – Elected Fellow of the Royal Society; Publishes “On Colour”;
Effectively retires from natural philosophy due to negative
comments by Robert Hooke and others; Writes “excessive, furious”
replies to Hooke’s criticism.

19. Alchemy & Theology
1670 - 1684
John Maynard Keynes: “Newton was not the first of the
age of reason: he was the last of the magicians.”
Wrote well over a million words on alchemy., four
million on theollogy
Rejected mechanical philosophy’s inert particles in
motion for “active principles” (which would become the
forces of attraction and repulsion between particles).
Attempted to define “true Christian” beliefs and
determine the end of time.

22. Heresy
Rejection of triune God as a corruption
Arianism
Christ was a lesser intermediary between God
and man
Demons as delusions of the human mind
Satan as expression of human desires and lusts.
Mortality of Soul

23. Road to Principia
1679 – Hooke introduces Newton to the
concept of “centripetal force” and Newton
proposes the inverse square law.
1684 – Newton begins Principia;
1687 – Publishes Principia after threatening to
pull Book III because of Hooke.

24. Centripetal Force
Hooke noted that the operation of a
force directed toward the center,
continually pulling an object from its
tangential path, is necessary for circular
motion.
Newton termed this “centripetal force”
and refused to acknowledge Hooke.
This contribution by Hooke would
finally lead to a successful celestial
dynamics and “was a deciding factor in
setting Newton on the path that would
lead him to the Principia” (Cohen).

25. Inverse Square Law
Hooke claimed to
have given this to
Newton. He hadn’t
as he himself
believed that

26. Ismael Bullialdus
“As for the power by which the Sun seizes
or holds the planets, and which, being
corporeal, functions in the manner of hands,
it is emitted in straight lines throughout the
whole extent of the world, and like the
species of the Sun, it turns with the body of
the Sun; now, seeing that it is corporeal, it
becomes weaker and attenuated at a greater
distance or interval, and the ratio of its
decrease in strength is the same as in the
case of light, namely, the duplicate
proportion, but inversely, of the distances
that is, 1/d².”
Astronomia philolaica, 1645

27. Definitions
Axioms, or The Laws of
Motion
Three Laws with
Corollaries
Book I – Motion without
resistance
Book II – Motion with
resistance; pendulums;
wave motion;
Book III – The System of
the World

28. Definitions
Mass: “The quantity of matter is that which arises conjointly from its
density and magnitude.”
Momentum: “The quantity of motion is a measure of motion that
arises from the velocity and the quantity of matter jointly.”
Inertia: “Inherent force of matter is the power if resisting by which
every body perseveres in its state either of resting or of moving.”
“Impressed force is the action exerted on a body to change its state
either of resting or of moving uniformly straight forward.”
“Centripetal force is the force by which bodies are drawn from all
sides, are impelled, or in any way tend, toward some point as to a
center.”

30. Laws of Motion
1. Every body perseveres in its state of being at rest or
of moving uniformly straight forward, except insofar as
it is compelled to change its state by forces impressed.
2. A change of momentum is proportional to the impulse
impressed on the body, and happens along the straight
line on which that impulse is impressed.
3. To every action there is always opposed an equal
reaction: or the mutual actions of two bodies upon
each other are always equal, and directed to contrary
parts.

33. Rene Descartes proposed that giant
vortices of microparticles carry
planets around a central sun.
Newton disagreed: “Hence it is clear
that planets are not carried along by
corporeal vortices … [the]
hypothesis of vortices can in no way
be reconciled with astronomical
phenomena and serves less to clarify
the celestial motions than to obscure
them. But how these motions are
performed in free spaces without
vortices can be understood from
Book I and will now be shown in
Book III on the system of the
world” (Principia, II, Scholium)

34. The System of the World
- Rules for the Study of
Natural Philosophy
- Phenomena
- Propositions
- General Scholium

35. Rules for the Study of
Natural Philosophy
1. No more causes of natural things should be admitted than are both
true and sufficient to explain their phenomena.
2. Therefore, the causes assigned to natural effects of the same kind
must be, so far as possible, the same.
3. Those qualities of bodies that cannot be [increased] or [decreased]
and that belong to all bodies on which experiments can be made
should be taken as qualities of all bodies universally.
4. In experimental philosophy, propositions gathered from phenomena
should be considered either exactly or very nearly true
notwithstanding any contrary hypotheses, until yet other
phenomena make such propositions either more exact or liable to
exceptions.

36. System of the World
Universal gravitation & action at a distance
explains
- Orbit of the moon
- Motion of the moons of Jupiter
- Any planetary motion and that of comets
- Tidal motion
and allows derivation of Kepler’s Laws

37. The
moon
falls
around
the
earth

38. Every object in the universe attracts every
other object with a force directed along the
line of centers for the two objects that is
proportional to the product of their masses and
inversely proportional to the square of the
separation between the two objects.

40. “Thus far I have explained the phenomena of the heavens and our sea by
the force of gravity, but I have not yet assigned a cause to gravity … I have
not as yet been able to deduce from phenomena the reason for these
properties of gravity, and I do not feign hypotheses [“hypotheses non
fingo”]. For whatever is not deduced from the phenomena must be called
a hypothesis; and hypotheses, whether metaphysical or physical, or based
on occult qualities, or mechanical, have no place in experimental
philosophy. In this experimental philosophy, propositions are deduced from
the phenomena and are made general by induction. The impenetrability,
mobility, and impetus of bodies, and the laws of motion and the law of
gravity have been found by this method. And it is enough that gravity really
exists and acts according to the laws that we have set forth and is
sufficient to explain all the motions of the heavenly bodies and of our sea.”
General Scholium to Principia

41. Implications
Mechanism
Pathway
Fact

42. 1687 – Opposes entry of
Catholics to the university
1690’s – Publishes primarily on
theology & prophesy
1696 – Leave Cambridge to
become Warden of the Royal Mint
1703 – Becomes President of the
Royal Society
1704 – Publishes Opticks
1712 1727 – Newton dies

43. The Calculus Dispute
1666/67 – Newton invents “the method of fluxions and
fluents”
1675 – Gottfried Leibniz privately uses his “differential
method”
1677 – Leibniz uses his method in a letter to Newton
1684 - Leibniz publishes his method
1693 – Newton first publishes an account of his method
1699 – de Dullier accuses Leibniz of plagiarizing Newton

44. The Calculus Dispute
1704 – A review implies Newton’s debt to Leibniz
1711 – Dispute erupts / Leibniz asks the RSL to adjudicate.
1713 – The publication of the RSL’s report vindicates
Newton
1716 – Death of Leibniz
1727 – Death of Newton
1736 - Posthumous publication of Newton’s Method of
Fluxions.

46. Letter to Hooke, 1676
“What Descartes did was
a good step.You have
added much several ways
… If I have seen a little
further it is by standing on
the shoulders of Giants.”

51. Immanuel Kant
“It is absurd for human
beings ... to hope that
perhaps some day another
Newton might arise who
would explain to us, in
terms of natural laws
unordered by any
intention, how even a mere
blade of grass is produced.”
Critique of Judgment, 1790