Rhodes, Diana L. (Author)
Apollonius of Perga was one of the greatest mathematicians of the ancient world. He is most famous for his work on the curves obtained from the intersection of a plane and a cone, written in eight books: Conics. This is an English translation of the fourth book of that work, which examines the intersections and tangencies of these curves. Ungari and Fried's recently published book on Apollonius' Conics criticized the use of anachronistic mathematical concepts and techniques in the interpretation and analysis of ancient texts. Mindful of that, the drawings herein illustrating each proposition were created using only the meeting point formulas and constructions found in, or directly obtainable from, the works of Apollonius himself or Euclid's Elements. The first chapter provides a brief context for Apollonius and his work, as well as an introduction to the methods used in the translation and the computer- generated drawings. The second chapter outlines the key elements of the ancient mathematical foundations upon which Conics was written. The combination of ancient mathematical formulas and constructs with modern computer mathematical software led to a deeper analysis of the work itself; this analysis is detailed in the third chapter. The few constructions which were not immediately supplied by ancient texts are also presented here. Since Conics IV is a mathematical text, it builds on an already established logical framework. This framework is no longer well-known to the modern world. Therefore the setting-out and diagrams of earlier propositions required to support the given proofs are supplied in an appendix. In addition, the appendix contains an English translation of the alternate proofs given by Eutocius. A small list of defined terms and a short glossary of Greek words are also supplied.
...MoreDescription Cited in Diss. Abstr. Int. B 68/05 (2007). Pub. no. AAT 3261918.
Book
Apollonius of Perga, ;
Rāshid, Rushdī;
(2008-2010)
Apollonius de Perge, Coniques: texte grec et arabe
(/isis/citation/CBB001022022/)
Book
Apollonius, ;
Rashed, Roshdi;
(2009)
Apollonius de Perge, Coniques: texte grec et arabe
(/isis/citation/CBB001450694/)
Article
Sidoli, Nathan;
(2004)
On the Use of the Term diastēma in Ancient Greek Constructions
(/isis/citation/CBB000410835/)
Article
Rashed, Roshdi;
(2007)
Lire les anciens textes mathématiques: le cinquième livre des Coniques d'Apollonius
(/isis/citation/CBB000933157/)
Book
Fried, Michael N.;
Unguru, Sabetai;
(2001)
Apollonius of Perga's Conica: Text, Context, Subtext
(/isis/citation/CBB000340186/)
Article
Nathan Sidoli;
(2018)
The Concept of Given in Greek Mathematics
(/isis/citation/CBB871621734/)
Article
Fried, Michael;
(2003)
The Use of Analogy in Book VII of Apollonius' Conica
(/isis/citation/CBB000740736/)
Thesis
McKinney, Colin Bryan Powell;
(2010)
Conjugate Diameters: Apollonius of Perga and Eutocius of Ascalon
(/isis/citation/CBB001560832/)
Chapter
Rashed, Roshdi;
(2008)
Le concept de tangente dans les Coniques d'Apollonius
(/isis/citation/CBB000950184/)
Book
Jaap Mansfeld;
(1998)
Prolegomena Mathematica: From Apollonius of Perga to the Late Neoplatonism with an Appendix on Pappus and the History of Platonism
(/isis/citation/CBB015172971/)
Book
Apollonius of Perga, ;
Rashed, Roshdi;
Bellosta, Hélène;
(2010)
La section des droites selon de rapports
(/isis/citation/CBB001220540/)
Book
Fried, Michael N.;
(2011)
Edmond Halley's Reconstruction of the Lost Book of Apollonius's Conics: Translation and Commentary
(/isis/citation/CBB001024500/)
Article
Krol, Z.;
(2006)
Ancient Geometry and Plato's Philosophy on the Base of Pappus' “Comment on the Xth Book of Elements of Euclid”
(/isis/citation/CBB000931646/)
Article
Acerbi, Fabio;
(2010)
Two Approaches to Foundations in Greek Mathematics: Apollonius and Geminus
(/isis/citation/CBB001034633/)
Article
Unguru, Sabetai;
Fried, Michael N.;
(2007)
Apollonius, Davidoff, Rorty, and Zeuthen: From A to Z, or, What Else is There?
(/isis/citation/CBB000701065/)
Book
Apollonius, ;
(2002)
Apollonius's Conics Book IV
(/isis/citation/CBB000203100/)
Article
Nikolantonakis, Konstantinos;
(2007)
The Treatise “On the Section of a Cylinder” of Serenus of Antinoeia and the Apollonian Tradition
(/isis/citation/CBB000933151/)
Article
Glasner, Ruth;
(2001)
Zeno of Elea's Argument from Bisection: Newly Discovered Evidence in a Hebrew Translation of Averroes
(/isis/citation/CBB000411043/)
Article
Ortiz García, Paloma;
(2006)
La traducción de textos matemáticos griegos al españo
(/isis/citation/CBB001023872/)
Article
Takahashi, Ken'ichi;
(2001)
A Manuscript of Euclid's De speculis: A Latin Text of MS 98.22 of the Archivo y Biblioteca Capitulares de la Catedral, Toledo
(/isis/citation/CBB000102365/)
Be the first to comment!