Greek Mathematical Thought and the Origin of Algebra

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Courier Corporation, 1992 - Mathematics - 360 pages
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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 — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.
 

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Contents

Purpose and plan of the inquiry
3
The opposition of logistic and arithmetic in
10
Logistic and arithmetic in Plato
17
The role ofthe theory ofproportions
26
Theoretical logistic and the problem
37
fractions Ox EZ
46
The ontological conception of the arithmoi
61
B Mathematics in Platologistilee and dianoia
69
O The Arithmetic ofDiophantus as theoretical
126
tranfinmation of the arithmos concept
150
I2 The concept of number
186
NOTES
217
Part I Notes 1125
227
Part II Notes 126348
242
Introduction to the Analytical Art by Francois Viete
313
Concerning the investigation of theorems by means
345

The arithmos eidetileos
79
of a theoretical logistic
100
On the difierence between ancient and modem
117

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