Part I -- 1 Intoduction: Purpose and plan of the inquiry -- 2 The opposition of logistic and arithmetic in the Neoplatonist -- 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 factions -- 6 The concept of arithmos -- 7 The ontological conception of the arithmoi in Plato -- 8 The Aristotelian critique and the possibilituy of a theoretical logistic -- Part II -- 9 On the difference between ancient and modern conceptualization -- 10 The Arirhmetic of Diophantus as theoretical logistic. The concept of eidos in Diophantus -- 11 The formalism of Vieta and the tranforamation of the arithmos concept -- 12 The concept of "number" -- 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 equatuions 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 reckogning by species -- V. Concerning the laws of zetetics -- VI. Concepting 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.