Part I: From Archimedes to Newton |
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The
links Solutions, Corrections
and Typos are pdf files that can be accessed with Acrobat
Reader |
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1.
The Greeks Measure the Universe |
1.
The Pythagoreans Measure Length
2.
The Measure of Angles
3.
Eratosthenes Measures the Earth
4. Right Triangles
5. Aristarchus Sizes up the Universe
6.
The Sandreckoner
7. Postscript
Exercises
and Solutions
Corrections
and Typos
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Pythagoras
Eratosthenes
Aristarchus
Archimedes
Stellar
Parallax |
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2.
Ptolemy and the Dynamics of the Universe |
1.
A Geometry of the Shadows of the Motion of the Sun
2.
Geometry in the Almagest
3.
The Solar Model
4.
The Modern Perspective
5.
Another Look at the Solar Model
6.
Epicycles
7.
Postscript
Exercises
and Solutions
Corrections
and Typos
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Hipparchus
Ptolemy
Retrograde
Motion with Epicycles |
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3.
Archimedes Measures Area
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1.
The Conic Sections
2.
The Question of Area
3.
Playing with Squares
4.
The Area of the Parabolic Section
5.
The Method
6.
Postscript
Exercises
and Solutions
Corrections
and Typos
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Greek
Texts in Translation
Apollonius
Archimedes
More
about Archimedes
The
Story of Archimedes's Manuscript
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4.
A New Astronomy and a New Geometry |
1.
A New Astronomy
2.
The Studies of Galileo
3.
The Geometry of Descartes
4.
Circles and Trigonometry
5.
The Ellipse
6.
Cavalieri's Principle
7.
Kepler's Analysis of the Orbits
8.
The Method of Successive Approximations
9.
Computing Orbital Information
10.
Postscript
Exercises
and Solutions
Corrections
and Typos
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Copernicus
Brahe
Kepler
Galileo
Descartes
Cavalieri
The
Planets
Planetary
Data
Kepler's
Equation and
the Rudolphine
tables
Computer
Model of Elliptical Orbits
Generated by Kepler's Equations
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5.
The Calculus of Leibniz |
1.
Straight Lines
2.
Tangent Lines to Curves
3.
Areas and Differentials
4.
The Fundamental Theorem of Calculus
5.
Functions
a. The Derivative
b. Antiderivatives
6.
Some Applications
a. Finding Maximum
and Minimum Values
b. Volumes
c. Lengths of Curves
7.
Postscript
Exercises
and Solutions
Corrections
and Typos
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Leibniz
Additional
Sources for Leibniz
Leibniz's
Role in the Developement of Calculus |
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6.
The Calculus of Newton |
1.
Areas under Simple Curves
2.
The Fundamental Theorem (again)
3.
Computing Definite Integrals
4.
Moving Points
5.
The Trajectory of a Projectile
6.
Application to Ballistics?
7.
Postscript
Exercises
and Solutions
Corrections
and Typos
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Newton
Newton's
Role in the Development of Calculus
Title
Page of "Analysis per Quantitatum ..."
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7.
The Principia |
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1.
Equal Areas in Equal Times
2.
Analyzing Centripetal Force
3.
The Inverse Square Law
4.
Test Case: The Orbit of the Moon
5.
The Law of Universal Gravitation
6.
Incredible Consequences
7.
Postscript
Exercises
and Solutions
Corrections
and Typos |
Title
Page of the Principia
Newton's
Work on Orbits and Gravitation
The
"Newton" One Pound Note
Facts
about the Solar System
Planetary
Data
Galileo
Probe
Space Elevator
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