Transcript Cosgrove and Rohrbacker: Newton`s Principia

Newton’s
Philisophæ Naturalis Principia
Mathematica
Newton’s Life – Early Years
 Born 1642 in Woolsthorpe,
Lincolnshire
 1661 – left home to attend
Trinity College, Cambridge
 Discovered contemporary
scientists and a love for
learning
 1665 – Received his
bachelor’s degree
Newton’s Life – Annus Mirabilis
 Newton returned home for the plague years of
1665 – 1667
 Extremely prolific time for him
 Invented the calculus, experimented in light and
chemistry, laid the foundations for mechanics and
gravitation
Newton’s Life – Writing the Principia
 1667 – Returned to
Cambridge
 1669 – Promoted to Lucasian
professor, and turned his
focus to his research
 Prompted by friend and
astronomer Edmund Halley,
expanded his research in
mechanics and gravitation
 1687 – Publication of
Philisophæ Naturalis
Principia Mathematica
Newton’s Life - Recognition
 Principia almost immediately recognized as a work of
genius
 “Nature, and Nature’s Laws lay hid in Night.
God said, Let Newton be! And All was Light.”
 Recognition by the Royal Society of London – appointed
President of the Royal Society in 1703
 1705 – knighted by Queen Anne, the first scientist to
receive this honor
Newton’s Life - Conflict
 Although a genius, Newton was also emotionally and
mentally unstable
 Longstanding argument with Robert Hooke
 Widespread controversy and feud with Leibniz over the
invention of the calculus
Newton’s Life – Beyond Science
 Had many other interests, including alchemy, the
Hermetic tradition, and theology
 Considered a theologian in his time, but his beliefs were
controversial
 1693 – Newton finished with scientific exploration
 Eventually became Master of the Mint and a social figure
in London
 Died March 20, 1727, from gallstones
Newton’s Methodology
 Primary goal: uncovering the truth
 Ultimate empiricist
 Set the standard for experimental approach
Rules of Reasoning
 Set forth in Book III of the Principia
 RULE I:
“We are to admit no more causes of
natural things than such as are both true and
sufficient to explain their appearances”
 RULE II: “Therefore to the same and natural effects
we must, as far as possible, assign the same causes”
Rules of Reasoning (cont’d)
 RULE III: “ The qualities of bodies, which admit neither
intensification nor remission of degrees, and which are
found to belong to all bodies within the reach of our
experiments, are to be esteemed the universal qualities of
all bodies whatsoever”
 RULE IV: “In experimental philosophy we are to look
upon propositions inferred by general induction from
phenomena as accurately or very nearly true,
notwithstanding any contrary hypotheses that may be
imagined, till such time as other phenomena occur, by
which they may either be made more accurate, or liable
to exceptions.”
Hypotheses non fingo
 “Hypotheses non fingo” - “I do not frame
hypotheses”
 “Whatever is not deduced from the phenomena is to
be called an hypothesis; and hypotheses, whether
metaphysical or physical, whether of occult qualities
or of mechanical, have no place in experimental
philosophy”
 Advocated a scientific method based strictly on
observation and induction, not prior assumptions
Hypotheses non fingo (cont’d)
 Mathematical  Physical  Philosophical

Mathematical = Observation

Physical = induction from mathematics

Philsophical = search for the cause
Outline of Newton’s Principia
 Begins with basic definitions (ex. mass, force, momentum)
 His three laws of motion and corollaries follow these definitions.
 Book I, The Motion of Bodies, contains his mathematical proofs,
which are based in geometry, but introduced concepts of calculus.
 Newton called this math “fluxions”
 Section II of Book I discusses motion of a body around a fixed force
center.
 Section III discusses motion of bodies in conic sections.
Outline of Newton’s Principia
 Newton uses Book III, The
System of the World, to
show how his theorems
apply to natural
phenomena.
 Astronomical data supports
Kepler’s three laws of
planetary motion.
 His Rules of Reasoning in
Philosophy are contained
in Book III.
Newton’s Definitions
 Mass:
 “The quantity of matter is the measure of the same, arising
from its density and bulk conjunctly.”
 Momentum:
 “The quantity of motion is the measure of the same, arising
from the velocity and quantity of matter conjunctly.”
Newton’s Definitions
 Inertia:
 “The Innate Force of Matter, is a power of resisting, by
which every body, as much as in it lies, endeavors to
persevere in its present state, whether it be of rest or of
moving uniformly forward in a right line.”
 Impressed force:
 “An impressed force is an action exerted upon a body, in
order to change its state, either of rest, or of moving
uniformly forward in a right line.”
 Centripetal force:
 “A centripetal force is that by which bodies are drawn or
impelled, or any way tend, towards a point as to a centre.”
Newton’s First Law
 “Every body continues in its state of rest, or of
uniform motion in a right line, unless it is compelled
to change that state by forces impressed upon it.”
 Also referred to as “law of inertia”
 Differs from the concept of impetus, as inertia
applies to bodies both at rest and in motion, and a
body with inertia moves in a straight line path.
Newton’s Second Law
 “The change of motion is proportional to the




motive force impressed; and is made in the
direction of the right line in which that force acts.”
In short: FΔt = Δp or Fα Δ p
While F = ma famously comes from this law, this
equation is never actually stated this way in
Principia.
Leonhard Euler is the first to recognize this
equation as the basis for mechanics.
Can only be applied to inertial reference frames.
Newton’s Third Law
 “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.”
 Newton’s explanation of
this law: two equal
hemispheres in contact
with each other at rest in
empty space.
Newton’s Corollaries
 Corollary I:

“A body by two forces conjoined will describe the diagonal of a
parallelogram, in the same time that it would describe the sides by
those forces apart.”
 Corollary II:

“And hence is explained the composition of any one direct force
AD, our of any two oblique forces AB and BD; and, on the contrary
the resolution of any one direct force AD in two oblique forces AB
and BD: which composition and resolution are abundantly
confirmed in Mechanics.”
 First two corollaries essentially describing vector
components of forces
Parallelogram Law of Forces
This vector notation did not exist in Newton’s time, so he
made use of parallelograms.
Newton’s Corollaries (cont’d)
 Remaining four corollaries were primarily concerned
with action-reaction forces.
 Example: Corollary III explains that net forces acting
on a body are the sum of the forces on that body.
 Although Newton termed these ideas as corollaries,
they do not follow naturally from his previous
definitions and laws.
Questions?