One: The Manuscript.- 1. Introduction.- 2. History of the Manuscript.- 3. Description of the Leibniz Copy.- 4. Date of the Original Descartes Manuscript.- Two: Solid Geometry: The Elements of Solids.- 5. Some Geometric Background.- 6. Translation and Commentary, Part I.- 7. General Comments.- 8. Note on the Euler Papers of 1750 and 1751.- 9. Descartes and Euler.- Three: Number Theory: Polyhedral Numbers.- 10. The Figurate Numbers of the Greeks.- 11. Translation and Commentary, Part II.- 12. General Comments.- Notes.- Index of Persons.

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