Reading Five Pages Deeply

Swerdlow on Ptolemy’s solar model, checked assertion by assertion

Gerd Graßhoff

Humboldt-Universität zu Berlin · Deutsches Museum, München

2026-11-10

Five pages, 45 assertions

Swerdlow, The Renaissance of Astronomy (2026), pp. 19–23: Ptolemy’s solar model.

confirmed 35
discrepancies 9
beyond arithmetic 1

Every assertion has an address, a formal counterpart, and a result that is recomputed.

The argument of page 19

The parallelogram and the apsides

The page’s one sentence of argument gives the first case. The other two are left to the reader.

Eccentricity and apogee

Ptolemy’s reported values follow from his rounded arcs of mean motion, not from the day counts of the seasons.

Two misprints

A dropped inequality sign in the rule for the equation of centre; 16;37° for 16;47° in the advance of al-Battānī’s apogee.

What the reading adds

  • A record that runs: every assertion with its address
  • Roundings of Ptolemy and al-Battānī made visible
  • Nothing changes what the pages say about the history of astronomy
  • All of it changes how far a reader can trust them without checking

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