Archimedes

generally we are able to establish the following as being approximately the chronological sequence:—

1. On Plane Equilibriums , I. 2. Quadrature of a Parabola. 3. On Plane Equilibriums , II. 4. The Method. 5. On the Sphere and Cylinder , I, II. 6. On Spirals. 7. On Conoids and Spheroids. 8. On Floating Bodies , I, II. 9. Measurement of a Circle. 10. The Sandreckoner.

In addition to the above we have a collection of geometrical propositions which has reached us through the Arabic with the title “Liber assumptorum Archimedis”. They were not written by Archimedes in their present form, but were probably collected by some later Greek writer for the purpose of illustrating some ancient work. It is, however, quite likely that some of the propositions, which are remarkably elegant,

were of Archimedean origin, notably those concerning the geometrical figures made with three and four semicircles respectively and called (from their shape) (1) the shoemaker’s knife and (2) the Salinon or salt-cellar, and another theorem which bears on the trisection of an angle.

An interesting fact which we now know from Arabian sources is that the formula for the area of any triangle in terms of its sides which we write in the form

Δ = √{s (s − a) (s − b) (s − c) },

and which was supposed to be Heron’s because Heron gives the geometrical proof of it, was really due to Archimedes.

Archimedes is further credited with the authorship of the famous Cattle-Problem enunciated in a Greek epigram edited by Lessing in 1773. According to its heading the problem was communicated by Archimedes to the mathematicians at Alexandria in a letter to Eratosthenes; and a