History of Greek Mathematics: from Aristarchus to Diophantus: from Aristarchus to Diophantus V

Home , Apollonian circles, Geometric mean theorem, Hinge theorem

FREE HISTORY OF GREEK MATHEMATICS: FROM ARISTARCHUS TO DIOPHANTUS: FROM ARISTARCHUS TO DIOPHANTUS V. 2 PDF

Dimensions x x 27mm g. Publisher Dover Publications Inc. Edition Statement 2nd Revised ed. Illustrations note Illustrations, unspecified. The perspective that enabled Sir Thomas Heath to understand the Greek genius -- deep intimacy with languages, literatures, philosophy, and all the sciences -- brought him perhaps closer to his beloved subjects, and to their own ideal of educated men than is common or even possible today. Heath read the original texts with a critical, scrupulous eye and brought to this definitive two-volume history the insights of a mathematician communicated with the clarity of classically taught English. The linkage and unity of mathematics and philosophy suggest the outline for the entire history. Interspersed are sections devoted to the history and analysis of famous problems: squaring the circle, angle trisection, duplication of the cube, and an appendix on Archimedes's proof of the subtangent property of a spiral. The coverage is everywhere thorough and judicious; but Heath is not content with plain exposition: It is a defect in the History of Greek Mathematics: From Aristarchus to Diophantus: From Aristarchus to Diophantus v. 2 histories that, while they state generally the contents of, and the main propositions proved in, the great treatises of Archimedes and Apollonius, they make little attempt to describe the procedure by which the results are obtained. I have therefore taken pains, in the most significant cases, to show the course of the argument in sufficient detail to enable a competent mathematician to grasp the method used and to apply it, if he will, to other similar investigations. Mathematicians, then, will rejoice to find Heath back in print and accessible after many years. Historians of Greek culture and science can renew acquaintance with a standard reference; readers in general will find, particularly in the energetic discourses on Euclid and Archimedes, exactly what Heath means by impressive and awe-inspiring. Thomas Little Heath was unusual for an authority on many esoteric, and many less esoteric, subjects in the history of mathematics in that he was never a university professor. The son of an English farmer from Lincolnshire, Heath demonstrated his academic gifts at a young age; studied at Trinity College, Cambridge, from to ; came away with numerous awards; and obtained the top grade in the English Civil Service examination. From that foundation, he went to work in the English Treasury, rose through the ranks, and bywas permanent secretary to the Treasury, effectively the head of its operations. He left that post in at the end of the first World War, worked several years at the National Debt office, and retired in During all of that time, however, he became independently one of History of Greek Mathematics: From Aristarchus to Diophantus: From Aristarchus to Diophantus v. 2 world's leading authorities on the history of mathematics, especially on the history of ancient Greek mathematics. Heath's three-volume edition of Euclid is still the standard, it is generally accepted that it is primarily through Heath's great work on Archimedes that the accomplishments of Archimedes are known as well as they are. Dover has reprinted these and other books by Heath, preserving over several decades a unique legacy in the history of mathematical scholarship. Stahl "Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry. A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus

In this paper, after examining the relevance of various interpretations given for the famous problem II 8 in the context of modern algebra or geometry, we focus on a close reading of the ancient text of some problems of Arithmetica in order to investigate Diophantos' solving practices. This inquiry reveals certain pointers, which enable us to create History of Greek Mathematics: From Aristarchus to Diophantus: From Aristarchus to Diophantus v. 2 framework for defining the generality of Diophantos' methods. This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Acerbi, F. Ball Rouse, W. Fourth Edition. Reprinted, New York: Dover. Bashmakova, I. English edition by the Mathematical Association of America, Chemla, K. Jahnke et al [eds. Christianidis, J. Google Scholar. Euler, L. Fifth Edition. Reprinted, New York: Springer-Verlag. Franci, R. Heath, Th. A Study in the History of Greek Algebra. Second Edition. Reprinted, New York: Dover Publications. II, From Aristarchus to Diophantus. New York: Springer. Klein, J. Cambridge, Mass: The M. Kline, M. New York: Oxford University Press. Knorr, W. Menger, K. Dordrecht: Reidel. Mueller, I. Cambridge, MA. Netz, R. Cambridge: Cambridge University Press. Radford, L. Rashed, R. Paris: Les Belles Lettres. Sesiano, J. Scholz [Hrsg. Mannheim: History of Greek Mathematics: From Aristarchus to Diophantus: From Aristarchus to Diophantus v. 2. Struik, D. Cambridge, Mass: Harvard University Press. Tannery, P. Stuttgart: B. Waerden, B. Berlin: Springer-Verlag. Download references. Experimental School of University of Macedonia, P. Box04, Thessaloniki, Greece. Correspondence to Yannis Thomaidis. Reprints and Permissions. Thomaidis, Y. Exact Sci. Download citation. Received : 30 May Published : 19 July Issue Date : October Search SpringerLink Search. Immediate online access to all issues from Subscription will auto renew annually. References 1. English edition by the Mathematical Association of America, 4. Rights and permissions Reprints and Permissions. About this article Cite this article Thomaidis, Y. A Framework for Defining the Generality of Diophantos' Methods in ``Arithmetica'' | SpringerLink

Equations in the book are presently called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. Diophantus also appears to know that every History of Greek Mathematics: From Aristarchus to Diophantus: From Aristarchus to Diophantus v. 2 can be written as the sum of four squares. If he did know this result in the sense of having proved it as opposed to merely conjectured ithis doing so would be truly remarkable: even Fermat, who stated the result, failed to provide a proof of it and it was not settled until Joseph Louis Lagrange proved it using results due to Leonhard Euler. Arithmetica was originally written in thirteen books, but the Greek manuscripts that survived to the present contain no more than six books. Arithmetica became known to History of Greek Mathematics: From Aristarchus to Diophantus: From Aristarchus to Diophantus v. 2 in the Islamic world in the tenth century [5] when Abu'l-Wefa translated it into Arabic. Cum comm. C laude G aspar Bacheti et observationibus P ierre de Fermat. Tolosaedoi : From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Retrieved 11 April Dictionary of World Biography. Salem Press. Retrieved 6 July Only six of the thirteen books of the Arithmetica of Diophantus ca. The remaining books were believed to be lost, until the recent discovery of a medieval Arabic translation of four of the remaining books in a manuscript in the Shrine Library in Meshed in Iran see the catalogue [Gulchin-i Ma'anipp. The manuscript was discovered in by F. Retrieved 9 October A History of Mathematics Second ed. Note the omission of Diophantus and Pappus, authors who evidently were not at first known in Arabia, although the Diophantine Arithmetica became familiar before the end of the tenth century. Abu'l-Wefa was a capable algebraist as well as a trigonometer. He commented on al-Khwarizmi's Algebra and translated from Greek one of the last great classics, the Arithmetica of Diophantus. Ancient Greek and Hellenistic mathematics Euclidean geometry. Angle trisection Doubling the cube Squaring the circle Problem of Apollonius. Circles of Apollonius Apollonian circles Apollonian gasket Circumscribed circle Commensurability Diophantine equation Doctrine of proportionality Golden ratio Greek numerals Incircle and excircles of a triangle Method of exhaustion Parallel postulate Platonic solid Lune of Hippocrates Quadratrix of Hippias Regular polygon Straightedge and compass construction Triangle center. Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon. Apollonius's theorem. Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Menelaus's theorem Pappus's area theorem Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus. Cyrene Library of Alexandria Platonic Academy. Ancient Greek astronomy Greek numerals Latin translations of the 12th century Neusis construction. Categories : 3rd-century books Ancient History of Greek Mathematics: From Aristarchus to Diophantus: From Aristarchus to Diophantus v. 2 mathematical works History of algebra. Hidden categories: Articles needing additional references from July All articles needing additional references Articles containing Ancient Greek to -language text Use dmy dates from April Namespaces Article Talk. Views Read Edit View history. Help Learn to edit Community portal Recent changes Upload file. Download as PDF Printable version. Wikimedia Commons. In Elements Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Pons asinorum Pythagorean theorem Thales's theorem Theorem of the gnomon.