Part I: From Archimedes to Newton
The links Solutions, Corrections and Typos are pdf files that can be accessed with Acrobat Reader
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






Stellar Parallax

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




Retrograde Motion with Epicycles

3. Archimedes Measures Area 

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


Greek Texts in Translation



More about Archimedes

The Story of Archimedes's Manuscript

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








The Planets

Planetary Data

Kepler's Equation and
Rudolphine tables

Computer Model of Elliptical Orbits
Generated by Kepler's Equations



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



Additional Sources for Leibniz

Leibniz's Role in the Developement of Calculus

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



Newton's Role in the Development of Calculus

Title Page of "Analysis per Quantitatum ..."

7. The Principia

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