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Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th?16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.
Print version: Klein, Jacob, 1899-1978. Greek mathematical thought and the origin of algebra. New York : Dover Publications, 1992 (DLC) 92020992 (OCoLC)26094892
"Unabridged and unaltered republication of the edition published by the M.I.T. Press, Cambridge, Massachusetts, in 1968"--Title page verso.
Description:
1 online resource (xv, 360 pages)
Contents:
1. Introduction: Purpose and plan of the inquiry --
2. opposition of logistic and arithmetic in the Neoplatonists --
3. Logistic and arithmetic in Plato --
4. role of the theory of proportions in Nicomachus, Theon, and Domninus --
5. Theoretical logistic and the problem of fractions --
6. concept of arithmos --
7. ontological conception of the arithmoi in Plato --
A. science of the Pythagoreans --
B. Mathematics in Plato --
logistike and dianoia --
C. arithmos eidetikos --
8. Aristotelian critique and the possibility of a theoretical logistic --
9. On the difference between ancient and modern conceptualization --
10. Arithmetic of Diophantus as theoretical logistic. The concept of eidos in Diophantus --
11. formalism of Vieta and the transformation of the arithmos concept --
A. life of Vieta and the general characteristics of his work --
B. Vieta's point of departure: the concept of synthetic apodeixis in Pappus and in Diophantus --
C. reinterpretation of the Diophantine procedure by Vieta --
1. procedure for solutions "in the indeterminate form" as an analogue to geometric analysis --
2. generalization of the eidos concept and its transformation into the "symbolic" concept of the species --
3. reinterpretation of the katholou pragmateia as Mathesis Universalis in the sense of ars analytice --
12. concept of "number." --
A. In Stevin --
B. In Descartes --
C. In Wallis. Appendix. Introduction to the Analytical Art / Francois Viete (Vieta) --
Appendix. Letter to Princess Melusine --
Appendix I. On the definition and division of analysis and those things which are of use to zetetics --
Appendix II. On the stipulations governing equations and proportions --
Appendix III. Concerning the law of homogeneity and the degrees and genera of the magnitudes that are compared --
Appendix IV. On the precepts of the reckoning by species --
Appendix V. Concerning the laws of zetetics --
Appendix. VI. Concerning the investigation of theorems by means of the poristic art --
Appendix VII. Concerning the function of the rhetic art --
Appendix VIII. The symbolism in equations and the epilogue to the art.
Other Titles:
Griechische Logistik und die Entstehung der Algebra.
Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th?16th centuries, via Arabic science, and the 16th-century development of symbolic algebra. This brought about the crucial change in the concept of number that made possible modern science. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.
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