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Index
Title Page
Copyright Page
Table of Contents
Author’s note
Translator’s note
Short titles frequently used
Part I
1 Introduction: Purpose and plan of the inquiry.
2 The opposition of logistic and arithmetic in the Neoplatonists.
3 Logistic and arithmetic in Plato.
4 The role of the theory of proportions in Nicomachus, Theon, and Domninus.
5 Theoretical logistic and the problem of fractions.
6 The concept of arithmos.
7 The ontological conception of the arithmoi in Plato.
A. The science of the Pythagoreans.
B. Mathematics in Plato—logistike and dianoia.
C. The arithmos eidetikos.
8 The Aristotelian critique and the possibility of a theoretical logistic.
Part II
9 On the difference between ancient and modern conceptualization.
10 The Arithmetic of Diophantus as theoretical logistic. The concept ofeidos in Diophantus
11 The formalism of Vieta and the transformation of thearithmos concept.
A.The life of Vieta and the general characteristics of his work.
B.Vieta’s point of departure: the concept of synthetic apodeixisin Pappus and in Diophantus.
C.The reinterpretation of the Diophantine procedure by Vieta:
1. The procedure for solutions “in the indeterminate form” as an analogue to geometric analysis.
2. The generalization of the eidos concept and its transformation into the “symbolic” concept of the species.
3. The reinterpretation of the katholou pragmateia as Mathesis Universalis in the sense of ars analytice.
12 The concept of “number.”
A. In Stevin.
B. In Descartes.
C. In Wallis.
Notes
Part I, Notes 1–125
Part II, Notes 126–348
Appendix Introduction to the Analytical Art,by François Viète (Vieta). Letter to Princess Mélusine.
I. On the definition and division of analysis and those things which are of use to zetetics.
II. On the stipulations governing equations and proportions
III. Concerning the law of homogeneity and the degrees and genera of the magnitudes that are compared.
IV. On the precepts of the reckoning by species.
V.Concerning the laws of zetetics.
VI. Concerning the investigation of theorems by means of the poristic art.
VII.Concerning the function of the rhetic art.
VIII.The symbolism in equations and the epilogue to the art.
Index of names
Index of topics
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