[Portrait of Clavius]
Disputation on Planetary Systems from Chapter 4 of
Christoph Clavius,
In Sphaeram Ioannis de Sacro Bosco Commentarius.
Venice, 1596. Edited by James M. Lattis.
(Emended by the editor with corrections from later editions)

Some Clavius background

(Links to some related Web sites are at bottom of this page.)
Biographical sketch of Clavius

Very selective bibliography on Clavius


The primary text

Brief notes on the text

This is Clavius's Disputation on the cosmological systems that competed with each other in the late sixteenth century. Clavius's Commentary on the Sphere of Sacrobosco was published many times in many places across Europe for over forty years and employed as an introductory text book at many schools. Thus, it must have been known to a significant fraction of persons educated from about 1570 to around 1615. Occupying most of Chapter 4, this Disputation is a remarkable and important summary of the diversity of cosmological thought in the late sixteenth century. Few texts are better qualified to bear witness to the context in which the literate public would have received the cosmological debates of that era.

The text was transcribed directly from the original printed version of 1596. Obvious typographical errors have been corrected, and a few corrections have been taken from the final edition of 1611. Page breaks are indicated by a page reference enclosed in pointy brackets. Italics are used as in the original, i.e. generally to indicate quotations. E.g. the text begins with a quotation from Sacrobosco's Sphere, on which Clavius, like many other medieval and early modern astronomy educators, wrote his commentary. Italics also indicate titles. The original contains marginal notes, which here appear enclosed by hyphens.

Images, scanned from the 1596 edition, appear in roughly the same place with respect to the text as in the printed book.

The Latin text

  1. Opening and apologia
  2. Plan of the argument
  3. What eccentrics and epicycles are
  4. Nature of planetary motion
  5. Plurality of planetary motions and orbs
  6. Concentric orbs
  7. Ptolemaic orbs
  8. Observations supporting eccentrics I: Variations in apparent magnitude
  9. Criticisms of the preceding
  10. Fracastoro's explanation
  11. Observations supporting eccentrics II: Variations in proper motion
  12. Observations supporting eccentrics III: Variability of eclipses
  13. Observations supporting eccentrics IIII: Diurnal parallax
  14. Observations supporting epicycles I: Variations in apparent magnitude at apogee
  15. Observations supporting epicycles II: Variations in proper motion at apogee
  16. Observations supporting epicycles III: Variability of lunar eclipses
  17. Observations supporting epicycles IIII: Variability of lunar parallax
  18. Other arguments 1: Dynamics of celestial spheres
  19. Other arguments 2: Rejection of the alternatives, fluid heavens and concentric spheres
  20. Other arguments 3: Proper methodology in natural philosophy
  21. Response of the adversaries
  22. Confutation of the response of the adversaries: Proper syllogisms
  23. How this pertains to Copernicus
  24. Arguments against eccentrics and epicycles
  25. Fracastoro's arguments
  26. Solutions of the arguments
  27. Solution of Fracastoro's arguments

Related Links

Loyola University's Jesuits and the Science

MacTutor History of Mathematics archive

Clark University's History of Mathematics Page

Home page of Jim Lattis

James M. Lattis----lattis@sal.wisc.edu