Archimedes, The Method, with Heath’s introductory note on Democritus and the cone (1912)
Source: Internet Archive
methodofarchimed00arch; local OCR text.txt, the complete archive_djvu.txt, retrieved 2026-09-08. Metadata: T. L. Heath, The Method of Archimedes, recently discovered by Heiberg: a supplement to the Works of Archimedes 1897 (Cambridge: Cambridge University Press, 1912). The Greek text was published by Heiberg in Hermes 42 (1907). Public domain: Heath died in 1940 and the book predates 1929. Extraction: archive.org OCR; Greek quotations are partly garbled, English prose is clean. Rights: public domain.
Source digest
Archimedes’ preface to Eratosthenes states that Democritus first asserted, without proof, that cone and pyramid are one third of cylinder and prism, and that Eudoxus proved it. Heath’s introductory note (pp. 8–11) quotes Plutarch’s cone dilemma in full and reads the phrase “made up of equal circles” as evidence that Democritus already treated a solid as a sum of parallel laminae, the idea the mechanical method then uses by balancing sections. For this project, this joins the Plutarch passage of H04 to the earliest ancient use of sections as a method of discovery, and it is the ancient counterpart of Cavalieri’s “all the lines”.
Passage anchors
- Archive lines 383–420: the Democritus discussion and the Plutarch quotation with the reference De Comm. Not. adv. Stoicos xxxix. 3.
- The translation of the preface to Eratosthenes, later in the file: the statement about Democritus and Eudoxus.
- Proposition 1 onward: the balancing of sections.
Coverage and limits
Reading level passage for the introductory note and the
preface; metadata for the propositions.