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Isaac Newton–The Principia

Page history last edited by Alyson Collins 13 years, 8 months ago



In the year 1665/6 Newton began devoloping infinitesimal calculus, but it was not until the famed visit of Edmund Halley in 1684 that he began the work that contained his "World System" - the Philosophiae naturalis prinicipia mathematica. By this time, there were many ideas which Newton could base his all-encompassing work on. In 1642, Gassendi published the idea that bodies travel in a straight line unless acted upon by an outside force. This view was repeated by Descartes in his Philosophy of Nature of 1644. Along with Huygens, Descartes published many other ideas on the rules of motion, collisions, and gravity.

     As the title of Newton's work suggests, it is in essence a mathematical work, written like the framework of classical Euclidean geometry. The first two books concern abstract, theoretical principles that govern bodies. All the arguments are developed and then proven using deduction from definitions and axioms that Newton had previously set forth.

     Newton does not shy away from mentioning God in his work. One of the editions includes a statement (in the General Scholium) about God's ominpresence in the world (Dear). Perhaps, Newton postulated, it was only by God's will that objects obey the law of gravity.

     The main criticisms of Newton's Principia were based on the argument that mathematical descriptions are not the same as physical explanations. Philosophers such as Descartes and Huygens desired a cause for the gravitational force which Newton failed to provide. The lack of such statements of "innate ideas" or any investigations of causes was perhaps related to the eventual victory of Newtonianism in the famed Leibniz - Newton clash. For example, the Principia was easily given a theological packaging in the Boyle Lectures series.



Newton's Life


    Isaac Newton was born on December 25, 1642 in Lincolnshire, England to a farming couple, after the death of his father. From early in life, he displayed an interest  in invention and mechanics. He started with different varieties of sundials and later moved to making models of mills and machinery, whose mechanics he understood at a remarkably young age. At age seventeen, he was expected to manage the family farm, but Newton wanted to pursue his intellectual interests further; he was allowed to go to Trinity College in Cambridge in 1661. In 1665, a plague shut down the university and Newton went home, where he spent his time digesting what he'd learned about mechanics, optics, and natural philosophy.

    When he returned to Cambridge, at age twenty-six, he was named Lucasian Professor of Mathematics. In 1679, he began his work on what would become his theory of universal gravitation. The following years would see Newton gaining several important titles: Master of the Mint in 1699, President of the Royal Society in 1703, and a knighting by Queen Anne in 1703, making him Sir Isaac Newton. He died in London in 1727 and was entombed at Westminster Abbey.



Mathematical Principles of Natural Philosophy - 1687


Principia Book I

In the first book of the Principia, Newton came to the conclusion that both time and space were absolute. Absolute time, to Newton, meant that time flows uniformly in one direction. By absolute space, Newton was referring to a fixed primary reference frame which everything moves with respect to that frame. Newton showed this absolute reference frame by posing the bucket experiment. A bucket filled with water is suspended by a rope. The rope is wound up; the bucket spins when released. At first the water remains still, but eventually comes to rotate with the bucket. According to the bucket's reference frame, the water is still, but yet it climbs the sides of the bucket. It is clear from this that the water must be rotating with respect to something. Newton called for the introduction of this fixed primary reference frame to solve the dilemma. These arguments are continued into book two, which deals with fluid dynamics. 


   Book I primarily deals with mathematical concepts and Newton is careful not to make any assumptions or assertions that his system is equal to our actual world. He utilizes a complex modification of classical geometry, which, as Densmore explains, better expressed the relationship between God and the universe, was capable of presenting irrational numbers, and always possessed a clear reference frame (xvi-xv).  Moreover, Newton deals primarily with ratios, as they are applicable to a variety of situations.

     Book I is structured in such a way that Newton begins by first presenting mathematical definitions for the items he will use later in the book such as quantity of matter and inertia. Some other definitions that Newton defines are quantity of motion, inherent force, impressed force, and action. Newton then sets down his three laws using these previously defined terms. The remainder of the book explores some of the finer details of these laws and concentrates on the mathematical principles Newton is forming in order to help describe the physical world. In the Scholium at the end of Book I, Newton discusses absolute space and time and his laws of motion. He also proves Kepler's equal area, equal time law in regards to circular motion (centripetal force).


Principia Book II

     In book two, Newton lays down his own analysis of movements through fluids, or essentially fluid dynamics.  He derives the speed of sound from his initial laws and principles and discusses Descartes' idea of vortices in order to refute them. This is just one of Newton's attacks on Descartes' physics, which Newton did not agree with.



Principia Book III

Only in Book III does Newton make a transition from the abstract to real world examples. He takes the concepts from Book I and applies them to real life. First, he establishes his own guidelines for philosophical thought in four simple principles to guide consideration of these proposals. Book III was intended to be the more "pop sci" version of Newton's ideas. He wanted to make them accessible to a more general audience, those without rigorous mathematical training. He laid out these rules of pursuing science to make sure his readers understood how science proceeds. The general idea of the rules is to keep things simple and not needlessley mulitply causes and properties. Then he transitions into his argument by laying out observable phenomena to explain in his propositions, which follow. 

In this book he develops the idea of universal gravitation, proposing that all bodies are attracted to one another by force at a distance, contradicting the motion by contact views of most mechanical philosophers. He takes the system developed in the first two books and applies it to the cosmos, creating a seemingly universal system. This system united the physics on earth (terrestrial physics) and the physics of the heavens(celestial physics), which had previously been separate realms in natural philosophy. This characteristic, called Newtonian Synthesis, is one of the most impressive and well known features of the Principia. 


General Scholium

Written after the first edition of Principia was published, the General Scholium presents a sort of "final word" on Newton's sentiments and purposes in the work. It is also in this section that Newton makes the famous claim "I frame no hypotheses." This phrase is generally misinterpreted to mean that all of Newton's work was ironclad and airtight. The phrase actually refers to Newton's theory of gravity, and to understand it one must understand Newton's definition of "hypothesis." To Newton, a hypothesis was anything that could not be explained through experiment. Gravity, an occult property, possessed this characteristic. Newton did not postulate its existence because that would not have been experimentally verifiable, and he would not allow that in his mathematically based argument of the universe. He instead conceded that he believed that gravity existed, but was unable to find its underlying cause. The General Scholium is also where Newton discussed God and how he belived that God was the first cause of everything, omnipresent, omnipotent, and omniscient.


Four Important Consequences of the Principia


1) 1st comprehensive theory about tides: caused by the mutal gravitational attraction between the moon and sun


2) complexity of the moon's motion explained by the 3 body idea: you have to take into consideration that the moon's motion is effected by the simultaneous and mutal attraction between the sun, moon and earth


3) comets: Previously comets had been thought of as random events in the celestial realm, but Newton argued that comets are subject to the same grvitational laws as the planets (i.e. they are regular events).  Edmund Halley used this idea to predict the famous Halley's comet.


4) non-spherical earth: Newton showed by experimentation (pendulums) how the earth was squashed at the poles due to gravitational pull


Stark Contrast between the Principia and Opticks


1) Opticks more accesible: Newton wrote the Principia in Latin, but he wrote Opticks in English


2) The Principia was theoretical, Opticks experimental





 Primary Sources

"For whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses... have no place in experimental philosophy.  In this philosophy, propositions are deduced from the phenomena, and are rendered general by induction. ... And it is enough that gravity really exists, and acts according to the laws set forth by us, and is sufficient [to explain] all the motions of the heavenly bodies and of our sea."

-Newton, "General Scholium" 



Key Terms and Definitions


Newtonian Synthesis- Method by which Newton builds up an axiomatic system by deduction, and then reveals its universal applications. 

Inherant Force-Force contained within a body that keeps it in motion or resists being moved

Impressed Force-the Force acting upon a body


Relevant Links

An illustration of Newton's Bucket Experiment


Comments (10)

Marek said

at 8:22 pm on Nov 28, 2008

Hopefully this is enough to start with. Sorry it appeared so late.

Mark Philippi said

at 11:24 pm on Nov 29, 2008

Place the bucket experiment where you will, I just wanted to get it out there but didn't know where to put it.

Grant Berry said

at 3:01 pm on Nov 30, 2008

I moved some stuff around, added info on the third book, and put up a definition for Newtonian synthesis. Some of the answers from the study guide are in there too.

jgm829@... said

at 5:58 pm on Dec 1, 2008

I added some information on Newton's life.

Nicole Hagstrom said

at 12:06 am on Dec 2, 2008

I added a bit on Book I and the General Scholium. I moved the hypothesis section to the GS as well with minor changes to make it agree with the first sentence. If I'm incorrect in its placement, feel free to move it back.

liz mastroianni said

at 10:15 am on Dec 2, 2008

didn't change anything major just fixed some grammar, pretty good start tho

Kristy Carey said

at 12:20 pm on Dec 2, 2008

I edited, added bits here and there, linked to some previous pages and added the link to the Bucket illustration. It's useful, because I found that hard to picture in my head.

Alyson Collins said

at 12:50 pm on Dec 2, 2008

This was a good summary! I was almost afraid to add anything lest I mess it up. I did add a few things though.

Amanda Beattie said

at 1:15 pm on Dec 2, 2008

Made minor changes throughout, added Inherent and Impressed Force.

Alyson Collins said

at 1:55 pm on Dec 3, 2008

I added the stuff to this note pagefrom this last lecture that Dr. Ramberg added about the Principia and Opticks because I thought it made more sense to go here.

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