Greek Mathematical Thought and the Origin of AlgebraCourier Corporation, 1992-01-01 - 360 psl. Important study focuses on the revival and assimilation of ancient Greek mathematics in the 13th16th 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. |
Turinys
Purpose and plan of the inquiry | 3 |
The opposition of logistic and arithmetic in | 10 |
Logistic and arithmetic in Plato | 17 |
The role of the theory of proportions | 26 |
Theoretical logistic and the problem | 37 |
The concept of arithmos | 46 |
The ontological conception of the arithmoi | 61 |
of a theoretical logistic | 100 |
The formalism of Vieta and | 150 |
The concept of number | 186 |
NOTES | 217 |
Part I Notes 1125 | 227 |
Part II Notes 126348 | 242 |
Introduction to the Analytical Art by François Viète | 313 |
Concerning the function of the rhetic art | 346 |
| 355 | |
On the difference between ancient and modern | 117 |
IO The Arithmetic of Diophantus as theoretical | 126 |
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Pagrindiniai terminai ir frazės
Ad.-Tann algebra analysis analytic art ancient Aristotle arithmetic Arithmetica arithmos calculation Chap character Charmides concept of number counting cube definition Descartes dianoia Diophantine Diophantus eide eidos equation especially Euclid fractional furthermore genus geometric Geschichte Gorgias Greek Greek mathematics homogeneous Hultsch Iamblichus indivisible insofar Isagoge kind ladder magnitudes logistice Mathematica mathematical mathesis universalis means Metaphysics metic mode modern monads multiplied multitude namely Neoplatonic Nicomachus nombre Note numbers objects of sense ontological Pappus Pauly-Wissowa Philebus plane plane-plane Plato possible Posterior Analytics precisely problem Proclus pure Pythagorean quae quam quantity quod ratios realm relation rung says scholium solid solution square squared-square Stevin symbolic Tannery Theaetetus Theon theoretical logistic theory of proportions things tion tradition understanding understood units Vieta Wallis zetetic ἀριθμὸς γὰρ δὲ διὰ εἶναι ἐν καὶ κατὰ μὲν μὴ ὅτι περὶ πλῆθος πρὸς τὰ τε καὶ τῇ τὴν τῆς τὸ τοῦ τῶν ὡς