## A History of Mathematics: From Mesopotamia to ModernityA History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader. |

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### Contents

1 | |

14 | |

Greeks and origins | 33 |

Greeks practical and theoretical | 57 |

Chinese mathematics | 78 |

Islam neglect and discovery | 101 |

Understanding the scientific revolution | 133 |

The calculus | 161 |

Geometries and space | 189 |

Modernity and its anxieties | 213 |

A chaotic end? | 235 |

Conclusion | 260 |

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algebra already angles answer appears Appendix Archimedes argument become calculation called century chapter Chinese circle claims classical completely consider construction continued course curve deal defined described detail discussion early easy equal equation Euclid example Exercise fact Fauvel and Gray figures follows formula geometry give given Greek idea important infinite interesting Islamic kind known language later least length less look machine mathematicians mathematics means measurement method multiply nature Newton original particular period position possible practical present problem produced proof proposition prove question ratio reader reason referred relation result roots rules seems seen sense side simple solution solve sources space square statement suppose texts theorem theory things thought tradition translation triangle true understand usual whole writing

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Page 260 - Only an alert and knowledgeable citizenry can compel the proper meshing of the huge industrial and military machinery of defense with our peaceful methods and goals, so that security and liberty may prosper together.

Page 36 - twas the 47 El. libri I. He read the Proposition. By G — , sayd he (he would now and then sweare an emphaticall Oath by way of emphasis) this is impossible! So he reads the Demonstration of it, which referred him back to such a Proposition; which proposition he read. That referred him back to another, which he also read. El sic deinceps [and so on] that at last he was demonstratively convinced of that trueth. This made him in love with Geometry.

Page 49 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.

Page 71 - In the bloom of beauty, and in the maturity of wisdom, the modest maid refused her lovers and instructed her disciples; the persons most illustrious for their rank or merit were impatient to visit the female philosopher; and Cyril beheld with a jealous eye the gorgeous train of horses and slaves who crowded the door of her academy.

Page 240 - Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Page 260 - Yesterday all the past. The language of size Spreading to China along the trade-routes; the diffusion Of the counting-frame and the cromlech; Yesterday the shadow-reckoning in the sunny climates. Yesterday the assessment of insurance by cards, The divination of water; yesterday the invention Of cartwheels and clocks, the taming of Horses.

Page 260 - The prospect of domination of the nation's scholars by Federal employment, project allocations, and the power of money is ever present — and is gravely to be regarded. Yet, in holding scientific research and discovery in respect, as we should, we must also be alert to the equal and opposite danger that public policy could itself become the captive of a scientifictechnological elite.

Page 42 - This king [Sesostris, ca. 1300 BC] moreover (so they said) divided the country among all the Egyptians by giving each an equal square parcel of land, and made this his source of revenue, appointing the payment of a yearly tax. And any man who was robbed by the river of a part of his land would come to Sesostris and declare what had befallen him; then the king would send men to look into it and measure the space by which the land was diminished, so that thereafter it should pay the appointed tax in...

Page 217 - This conviction of the solvability of every mathematical problem is a powerful incentive to the worker. We hear within us the perpetual call : There is the problem. Seek its solution. You can find it by pure reason, for in mathematics there is no ignorabimus.

Page 60 - Archimedes possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge, that though these inventions had now obtained him the renown of more than human sagacity, he yet would not deign to leave behind him any commentary or writing on such subjects; but, repudiating as sordid and ignoble the whole trade of engineering, and every sort of art that lends itself to mere use and profit, he placed his whole affection and ambition in those purer speculations where there can...