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Slide 1

Claudius Ptolemy

Saving the Heavens

Slide 2

Euclid’s Elements quickly became the standard text for teaching mathematics at the Museum at Alexandria.

Philosophical questions about the world could now be attacked with exact mathematical reasoning.

Slide 3

276 - 194 BCE

Born in Cyrene, in North Africa (now in Lybia).

Studied at Plato’s Academy.

Appointed Librarian at the Museum in Alexandria.

Slide 4

Eratosthenes was prolific. He worked in many fields. He was a:

Poet

Historian

Mathematician

Astronomer

Geographer

He was nicknamed “Beta.”

Not the best at anything, but the second best at many things.

Slide 5

He coined the word “geography” and drew one of the first maps of the world (above).

Slide 6

Eratosthenes made very clever use of a few scant observations, plus a theorem from Euclid to decide one of the great unanswered questions about the world.

Slide 7

Eratosthenes had heard that in the town of Syene (now Aswan) in the south of Egypt, at noon on the summer solstice (June 21 for us) the sun was directly overhead.

I.e. A perfectly upright pole (a gnomon) cast no shadow.

Or, one could look directly down in a well and see one’s reflection.

Slide 8

His data, 2

Based on reports from on a heavily travelled trade route, Eratosthenes calculated that Alexandria was 5000 stadia north of Syene.

Syene

5000 stadia

Slide 9

His data, 3

Eratosthenes then measured the angle formed by the sun’s rays and the upright pole (gnomon) at noon at the solstice in Alexandria. (Noon marked by when the shadow is shortest.)

The angle was 7°12’.

Slide 10

Proposition I.29 from Euclid

A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles.

- Euclid’s Elements at work
- Eratosthenes of Cyrene
- “Beta”
- Eratosthenes’ Map
- Using Euclid
- His data
- Calculating the size of the Earth
- Eratosthenes’ working assumptions
- A slight correction
- Stadium lengths
- Comparative figures
- An astounding achievement
- Hipparchus of Rhodes
- The Table of Chords
- Precession of the equinoxes
- The Problem of the Planets, again
- Claudius Ptolemy
- Ptolemy’s Geography
- The Almagest
- Euclid-like assumptions
- Plato versus Aristotle
- Ptolemy’s Universe
- The Ptolemaic system
- Epicycles and Deferents
- Accounting for Retrograde Motion
- Saving the Appearances
- How did it fit the facts?
- Third Solution: The Equant Point
- Ptolemy’s system worked

- Gravitation
- Direct heat utilization of geothermal energy
- Newton’s law of universal gravitation
- Motion
- Newton’s laws of motion
- Newton’s third law of motion
- Sound

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