CLAS 1108 · Greek Science — Heaven, Earth, and the Lever

Led by Archimedes Simulacrum, with Aristarchus of Samos Simulacrum, Hipparchus Simulacrum, and Eratosthenes Simulacrum

1. Module 8 ○ Open

   Greek Science — Heaven, Earth, and the Lever

   Led by Archimedes Simulacrum, with Aristarchus of Samos Simulacrum, Hipparchus Simulacrum, and Eratosthenes Simulacrum

   The question

   The Greek scientific achievement of the third and second centuries BCE — Archimedes Simulacrum on mechanics and mathematics, Aristarchus of Samos on heliocentric cosmology, Hipparchus Simulacrum on astronomy and trigonometry, Eratosthenes Simulacrum on the size of the Earth and on geography, Euclid on the foundations of geometry, Hero of Alexandria on applied mechanics — was the first sustained empirical-mathematical investigation of the natural world in the European tradition, and the level it reached would not be matched in mathematical depth until the seventeenth century. What did Greek science actually accomplish, and what were its limits?

   Outcome

   The student has read at least one primary text from each of the four (Heath translations of Archimedes Simulacrum; the *Sand-Reckoner* passage on Aristarchus; the relevant Hipparchus Simulacrum fragments; the Cleomedes passage on Eratosthenes Simulacrum' Earth-circumference calculation), can characterise the Greek scientific method and its accomplishments, and can produce a 700-word analytical response on a specific accomplishment.

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   Practice scenarios

   Eratosthenes Simulacrum Measures the Earth

   Eratosthenes Simulacrum walks you through his calculation of the Earth's circumference. Read the surviving description in Cleomedes' *On the Heavens* (any modern translation; the relevant passage is brief — about a page) and a modern reconstruction of the calculation (any reputable source on ancient science — Lloyd, Cuomo, or Russo will do). Then write a 700-word analytical essay: what was the method; what observations did Eratosthenes Simulacrum need; what assumptions did the calculation depend on (Earth is spherical; the Sun is far enough that its rays at any one moment are effectively parallel; Syene and Alexandria are on the same meridian); how good was the result; and what does the calculation tell us about Greek scientific method that an account of, say, Archimedes Simulacrum' mechanics or Hipparchus Simulacrum' astronomy would not?

   Your goals

   • Read the Cleomedes passage and a modern reconstruction before drafting.
   • Reproduce the calculation in your own words, identifying the observations and the assumptions explicitly.
   • Address the question of accuracy — the result depends on the Greek stadion length (which is itself uncertain — the calculation was *good enough* but the precision claim has to be qualified).
   • Place the calculation in the broader Greek scientific tradition.
   • 700 words ± 100, scholarly register.

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