A most important addition to this list has been made in recent years through an extraordinary piece of good fortune. In 1906 J. L. Heiberg, the most recent editor of the text of Archimedes, discovered a palimpsest of mathematical content in the "Jerusalemic Library" of one Papadopoulos Kerameus at Constantinople. This proved to contain writings of Archimedes copied in a good hand of the tenth century. An attempt had been made (fortunately with only partial success) to wash out the old writing, and then the parchment was used again to write a Euchologion upon. However, on most of the leaves the earlier writing remains more or less legible. The important fact about the MS. is that it contains, besides substantial portions of the treatises previously known, (1) a considerable portion of the work, in two books, _On Floating Bodies_, which was formerly supposed to have been lost in Greek and only to have survived in the translation by Wilhelm of Morbeke, and (2) most precious of all, the greater part of the book called _The Method, treating of Mechanical Problems_ and addressed to Eratosthenes. The important treatise so happily recovered is now included in Heiberg's new (second) edition of the Greek text of Archimedes (Teubner, 1910-15), and some account of it will be given in the next chapter. The order in which the treatises appear in the MSS. was not the order of composition; but from the various prefaces and from internal evidence 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 [Delta] = [root]{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.