Greek Mathematical Thought and the Origin of Algebra Book

	Author's note
	Translator's note
	Short titles frequently used
1	Introduction: Purpose and plan of the inquiry	3
2	The opposition of logistic and arithmetic in the Neoplatonists	10
3	Logistic and arithmetic in Plato	17
4	The role of the theory of proportions in Nicomachus, Theon, and Domninus	26
5	Theoretical logistic and the problem of fractions	37
6	The concept of arithmos	46
7	The ontological conception of the arithmoi in Plato	61
A	The science of the Pythagoreans	63
B	Mathematics in Plato - logistike and dianoia	69
C	The arithmos eidetikos	79
8	The Aristotelian critique and the possibility of a theoretical logistic	100
9	On the difference between ancient and modern conceptualization	117
10	The Arithmetic of Diophantus as theoretical logistic. The concept of eidos in Diophantus	126
11	The formalism of Vieta and the transformation of the arithmos concept	150
A	The life of Vieta and the general characteristics of his work	150
B	Vieta's point of departure: the concept of synthetic apodeixis in Pappus and in Diophantus	151
C	The reinterpretation of the Diophantine procedure by Vieta	161
1	The procedure for solutions "in the indeterminate form" as an analogue to geometric analysis	161
2	The generalization of the eidos concept and its transformation into the "symbolic" concept of the species	163
3	The reinterpretation of the katholou pragmateia as Mathesis Universalis in the sense of ars analytice	178
12	The concept of "number."	186
A	In Stevin	186
B	In Descartes	197
C	In Wallis	211
	Part I, Notes 1-125	227
	Part II, Notes 126-348	242
	Appendix. Introduction to the Analytical Art
	Appendix. Letter to Princess Melusine	315
	Appendix I. On the definition and division of analysis and those things which are of use to zetetics	320
	Appendix II. On the stipulations governing equations and proportions	322
	Appendix III. Concerning the law of homogeneity and the degrees and genera of the magnitudes that are compared	324
	Appendix IV. On the precepts of the reckoning by species	328
	Appendix V. Concerning the laws of zetetics	339
	Appendix. VI. Concerning the investigation of theorems by means of the poristic art	345
	Appendix VII. Concerning the function of the rhetic art	346
	Appendix VIII. The symbolism in equations and the epilogue to the art	347
	Index of names	355
	Index of topics	359