Pappus Of Alexandria
Pappus of Alexandria lived in the fourth century AD to 300 assets, it is one of the most important mathematicians of ancient Greece , known for his work (translated into French under the title "Mathematical Collection").
He was born in Alexandria in Egypt. Although very little about his life are known, the literature we suggest that he was a tutor.
His principal work is known Synagoge (c. 340 AD). It includes at least eight volumes, the rest was lost, the collection covers a wide range of mathematical topics, including geometry , the recreational mathematics , construction of a cube the double of a given cube of polygons and polyhedra.
It was by Pappus we reached the richest sources of Greek mathematics, and we know the titles and content of the major treaties of the Hellenistic period (Little Astronomy, the Treasury's analysis). He introduced the concept of anharmonic ratio.
In geometry , his name is still attached today to Pappus theorem.
Summary |
Pappus and Analysis of Past
Pappus in Book VII of the Mathematical Collection, shows us what the ancients meant by the terms of analysis , and synthesis of porisme: it was a body of methods for solving the ruler and compass problems loci. Pappus cites several treaties (now almost all lost in Latin titles are due to Commandino ) dealing with the "fixed place" ( ):
- , Data, "Data Book" of Euclid
- De locis Plan ("the City plans") from Euclid
- , rations section ("On the report section") of Apollonius of Perga
- De Spatii section ("On the section of area") of Apollonius
- , sections DETERMINATE ("On the Division determined) of Apollonius
- De Tactionibus ("Contacts") of Apollonius
- De Inclinationibus (Slopes) of Apollonius
- , the "Treaty of Lemmas" in three books of Euclid
- De locis Plan ("The places Plans") of Apollonius
- The Conics of Apollonius, in eight books
- Solid places of Aristeas former five books
- The Mdits of Eratosthenes in two books, which dealt with the inclusion of average proportional (see the duplication of the cube and the construction of msolabe ).
The purpose of the analysis of the ancients, such as exhibits Pappus in Book VII of his "Mathematical Collection," was to find a construction with ruler and compass of a given locus, or at least an inventory where such construction was possible. Unfortunately, Pappus only provided summaries of the books he cites, so that the extent and scope of analysis methods has been the subject of many commentaries of the sixteenth to eighteenth century. Based on indications given by Pappus and their personal speculations, a galaxy of famous mathematicians have tried to reconstruct the lost treaties in their original order.
Bibliography
See also the bibliography of Irem (France) and the Complete Dictionary of Scientific Biography .
Works by Pappus
- (Crm) (en) Pappus of Alexandria, Book 7 of The Collection, ed. and trans. the Greek by Alexander Jones, 1986, New York, 2 vols.
- (En) Pappus of Alexandria, The Mathematical Collection, trans. the Greek by Paul Ver Eecke, Paris, 1933, 2 vols. , Repr. 1982.
- (Ar) (en) Abu 'Uthman Sa'id ibn Ya'qub al-Dimishqi (c. 915), The Commentary of Pappus is Book X of Euclid's Elements, ed. and trans. from Arabic by Gustav Junge and William Thomson, Cambridge (Mass.), 1930 ( online ).
- (Crm) (the) Pappi Alexandrini, collects e libris manu quae supersunt scriptis edid latina interpretatione and commentars instruxit Fridericus Hultsch, ed. and trans. the Greek by Friedrich Otto Hultsch , Berlin, 1876-1878, 3 vols. ( online ; Transcript at. ).
Studies Pappus
- Chasles Michel , Brief History of the origin and development of methods in geometry, impr. Hayez, Brussels, 1837
- Paul Eecke worm , The Collection of Alexandria Pappus of Mathematics, Libr. A. Blanchard, Paris 1932 (reprint 1982), "Introduction"
- Henk Bos, Redefining Geometrical exactness, ed. Springer, et al. "Sources and Studies in the Hist. of Math. and Phys. Sc, 2001 ( ISBN 0-387-95090-7 )
- (In) David Eugene Smith , "Pappus's Collection. Reviewed Works: Paul Ver Eecke, Pappus of Alexandria ... ", in Bull. Amer. Math. Soc., Vol. 40, No. 1, 1934, p. 11-12 [ full text (accessed 18/10/2010)]
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