Download NewtonDefns

Geographic Data Model
• Conceptual Model – a set of concepts that describe
a subject and allow reasoning about it
• Mathematical Model – a conceptual model
expressed in symbols and equations
• Data Model – a conceptual model expressed in a
data structure (e.g. ascii files, Excel tables, …..)
• Geographic Data Model – a conceptual model for
describing and reasoning about the world
expressed in a GIS database
Isaac Newton
The Principia
Mathematical Principles of Natural Philosophy
Originally published in 1686, third edition 1726
Translated by I. Bernard Cohen and Anne Whitman
University of California Press, 1999
Originally published as
“Philosophiae Naturalis Principia Mathematica”
In Latin
Introduction
Isaac Newton
Trinity College, Cambridge
5 May 1686
• The ancients divided mechanics into two parts: the
rational, which proceeds rigorously through
demonstrations, and the practical. Practical mechanics
is the subject that comprises all the manual arts, from
which the subject of mechanics as a whole has adopted
its name.
• But since those who practice the art do not generally
work with a high degree of exactness, the whole
subject of mechanics is distinguished from geometry by
the attribution of exactness to geometry and of
anything less than exactness to mechanics. Yet the
errors do not come from the art but from those who
practice the art.
Introduction (Cont.)
• Geometry postulates the solution of those problems
from mechanics and teaches the use of problems thus
solved. And geometry can boast that with so few
principles derived from other fields it can do so much.
• Since the manual arts are applied especially to making
bodies move, geometry is commonly used in reference
to magnitude and mechanics in reference to motion
• In this sense rational mechanics will be the science,
expressed in exact propositions and demonstrations, of
the motions that result from any forces whatever, and
of the forces that are required for any motions
whatever
Definitions
The quantity of matter is a measure of matter that
arises from density and volume
• “If the density of air is doubled in a space that is also
doubled, there is four times as much air, and there is six
times as much air if the space is tripled”
Quantity of motion is a measure of motion that
arises from the velocity and the quantity of matter
jointly
• “If a body is twice as large as another and has equal
velocity there is twice as much motion, and if it has
twice the velocity there is four times as much motion”
Laws
Law 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 the forces impressed
Law 2
• A change in motion is proportional to the motive force
impressed and takes place along the straight line in
which that force is impressed
Law 3
• To any action there is always an opposite and equal
reaction; in other words, the actions of two bodies
upon each other are always equal and always opposite
in direction