## Greek Mathematical Thought and the Origin of AlgebraImportant 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 |

### Other editions - View all

Greek Mathematical Thought and the Origin of Algebra Jacob Klein,Eva Brann No preview available - 1976 |

### Common terms and phrases

1rpds Ad.-Tann algebra analysis analytic art ancient Apollonius Aristotle arithmetic Arithmetica arithmos belongs calculation called Chap character Charmides concemed concept of number conjoined countable counting cube deﬁned deﬁnition Descartes dianoia Diophantus division Domninus edition eide eidetic eidos equation especially Euclid fact ﬁeld ﬁfth ﬁgures ﬁnally ﬁnd ﬁnding ﬁrst fractional furthermore genus geometric Gorgias Greek Greek mathematics homogeneous Hultsch Iamblichus indivisible inﬁnitely insofar Isagoge kind logistice lower ladder magnitude mathematical mathesis universalis means Metaphysics mode modem monads multiplied multitude namely Neoplatonic Nicomachus nombre Note numbers objects of sense ontological Pappus Pauly-Wissowa Philebus plane plane-plane Plato poristic possible Posterior Analytics precisely problem procedure Proclus pure Pythagorean quae quam quantity quod ratios realm reference reﬂection relation rung says scholium scientiﬁc signiﬁcance solid solution square squared-square Stevin symbolic Tannery Theaetetus Theon theoretical logistic theory of proportions things tion tradition understanding understood units Vieta Wallis zetetic