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Biography

Elements

Fragments

Other works

• Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
• On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a first-century AD work by Heron of Alexandria.
• Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J O'Connor and E F Robertson who name Theon of Alexandria as a more likely author.O'Connor, John J.; Robertson, Edmund F., "Theon of Alexandria"
• Phaenomena, a treatise on spherical astronomy, survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC.

• Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: "Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal." In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.

Lost works

• Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. It is likely that the first four books of Apollonius's work come directly from Euclid. According to Pappus, "Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics." The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid's work was already lost.
• Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial.
• Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning.
• Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces.
• Several works on mechanics are attributed to Euclid by Arabic sources. On the Heavy and the Light contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. On the Balance treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on mechanics written by Euclid.

Legacy

See also

• Axiomatic method
• Euclid's orchard
• Euclidean algorithm
• Euclidean geometry
• Euclidean relation
• Extended Euclidean algorithm
• List of topics named after Euclid

References

Works cited

• Artmann, Benno (1999). Euclid: The Creation of Mathematics. New York: Springer. {{ISBN|0-387-98423-2}}.
• BOOK, Ball, W.W. Rouse, W. W. Rouse Ball, A Short Account of the History of Mathematics, 1908, 4th, 1960, Dover Publications

• BOOK, Carl B., Boyer, Carl Benjamin Boyer, A History of Mathematics, 2nd, John Wiley & Sons, Inc., 1991, 978-0-471-54397-8,weblink
• WEB,weblink

• BOOK, T. L. Heath, Heath, Thomas (ed.), 1956, 1908, The Thirteen Books of Euclid's Elements, 1, Dover Publications, 978-0-486-60088-8,weblink
• BOOK, Heath, Thomas L., 1908,weblink Euclid and the Traditions About Him, Euclid, Elements

• Heath, Thomas L. (1981). A History of Greek Mathematics, 2 Vols. New York: Dover Publications. {{ISBN|0-486-24073-8|0-486-24074-6}}.
• Kline, Morris (1980). Mathematics: The Loss of Certainty. Oxford: Oxford University Press. {{ISBN|0-19-502754-X}}.
• {{MacTutor Biography|id=Euclid|title=Euclid of Alexandria}}
• {{MacTutor Biography|id=Euclid|title=Theon of Alexandria}}
• Proclus, A commentary on the First Book of Euclid's Elements, translated by Glenn Raymond Morrow, Princeton University Press, 1992. {{ISBN|978-0-691-02090-7}}.
• BOOK, Dirk J., Struik, Dirk Jan Struik, A Concise History of Mathematics, 1967, Dover Publications, 978-0-486-60255-4,
• WEB, Euclid,weblink

Further reading

• BOOK, DeLacy, Estelle Allen, Euclid and Geometry, 1963, Franklin Watts, New York,
• BOOK, Knorr, Wilbur Richard, The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry, 1975, D. Reidel, Dordrecht, Holland, 978-90-277-0509-9,
• BOOK, Mueller, Ian, Philosophy of Mathematics and Deductive Structure in Euclid's Elements, 1981, MIT Press, Cambridge, MA, 978-0-262-13163-6,
• BOOK, Reid, Constance, A Long Way from Euclid, 1963, Crowell, New York,
• BOOK, Szabó, Árpád, The Beginnings of Greek Mathematics, 1978, D. Reidel, Dordrecht, Holland, 978-90-277-0819-9, A.M. Ungar, trans,

External links

• {{Gutenberg author | id=Euclid | name=Euclid}}
• {{Internet Archive author}}
• {{Librivox author |id=2304}}
• Euclid's Elements, All thirteen books, with interactive diagrams using Java. Clark University
• Euclid's Elements, with the original Greek and an English translation on facing pages (includes PDF version for printing). University of Texas.
• Euclid's Elements, books I–VI, in English pdf, in a Project Gutenberg Victorian textbook edition with diagrams.
• Euclid's Elements, All thirteen books, in several languages as Spanish, Catalan, English, German, Portuguese, Arabic, Italian, Russian and Chinese.
• Elementa Geometriae 1482, Venice. From Rare Book Room.
• Elementa 888 AD, Byzantine. From Rare Book Room.
• Texts on Ancient Mathematics and Mathematical Astronomy PDF scans (Note: many are very large files). Includes editions and translations of Euclid's Elements, Data, and Optica, Proclus's Commentary on Euclid, and other historical sources.