The proofs of only four propositions have survived.

Two of these are the 19th: ``To divide a given triangle into two equal parts by a line which passes through a point situated in the interior of the triangle,'' and the 29th: ``To draw in a given circle two parallel lines cutting off a certain fraction from the circle.'' in his presentation.

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Pappus believed such results to be important in astronomy and included Euclid's Pappus further states that ``Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics.'' The contents of Euclid's treatise is therefore regarded to have been quite similar to the first three or four books of Apollonius's work.I know it's not publishable or anything, but it's still one of my favorite papers because it was so difficult to do.(I wrote it on a computer with about 12K of free RAM and only a cassette tape drive for storage!In this case, hopefully the meaning will be clear from the context.References to footnotes (actually, I guess ``sidenotes'' since they are contained in a column to the right of the text in graphical browsers) appear in square-brackets, like this: .Justine Waddell was most recently seen as Julia Bertram opposite Jonny Lee Miller and Harold Pinter in Patricia Rozema's highly acclaimed Miramax feature, Mansfield Park.She also played Countess Nordstrom in Bernard Rose's feature version of Anna Karenina, with Sophie Marceau and James Fox, and won the Broadcasting Press Guild Award as Best Actress for her starring role in the mini-series, Wives and Daughters, directed by Nicholas Renton.) In fact, the whole History of Science course was quite an experience.Students wishing to use this paper for their own reports on Euclid should know how to avoid plagiarism and how to cite online sources.(Sasha) '', 1997 (Almeida Theatre), (Ralph Fiennes) (Bill Paterson); (Countess Nordston) ' ' (Anna Karenina) 1997 ; (Tess) ' '' (Tess of the d'Urbervilles) 1998; (Julia Bertram) '- (Mansf ield Park) 1999; , , (Nina) '', 'Ian Charleson award'.'Prism Award' ' ' (Natalie Wood) ' ' (The Mystery of Natalie Wood), 2004 .However, it is likely that this has been appropriated from a similar story told about Menaechmus (fl. These divisions may be into figures -- a triangle into a triangle and a quadrilateral, say.The figures so divided include triangles, parallelograms, trapezia, quadrilaterals, circles, and figures bounded by an arc of a circle and two straight lines which form a given angle.It contributed greatly to the ``geometrization'' of mathematics and set the standard for rigor and logical structure for mathematical works.Euclid enjoys a reputation as a fair, forthright, and kind individual.