## A concise history of mathematics, Volumes 1-2 |

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Page 228

Jacobi based his theory of elliptic

series and called theta

u are quotients of theta

Jacobi based his theory of elliptic

**functions**on four**functions**defined by infiniteseries and called theta

**functions**. The doubly periodic**functions**an u, on u and dnu are quotients of theta

**functions**; they satisfy certain identities and addition ...Page 235

The first of these papers analyzed Dirichlet's conditions for the expansion of a

integrable.” But what does this mean? Cauchy and Dirichlet had already given

certain ...

The first of these papers analyzed Dirichlet's conditions for the expansion of a

**function**in a Fourier series. One of these conditions was that the**function**be “integrable.” But what does this mean? Cauchy and Dirichlet had already given

certain ...

Page 237

In his Gymnasial period Weierstrass wrote several papers on hyperelliptic

integrals, Abelian

contribution is his foundation of the theory of complex

series.

In his Gymnasial period Weierstrass wrote several papers on hyperelliptic

integrals, Abelian

**functions**, and algebraic differential equations. His best knowncontribution is his foundation of the theory of complex

**functions**on the powerseries.

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### Contents

The Beginnings | 1 |

Geometrical Patterns Developed by American Indians | 6 |

The Ancient Orient | 13 |

Copyright | |

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algebra ancient antiquity Apollonios appeared Arabic Archimedes arithmetic astronomy Babylonian mathematics became Bernoulli calculus calculus of variations Cantor Cauchy century A.D. circle classical complex numbers computational conception conic cubic cubic equations curves D’Alembert date back decimal deﬁned deﬁnite Descartes developed differential equations Diophantos discovery Egyptian Egyptian mathematics Euclid Euclidean Eudoxos Euler existence ﬁgures ﬁnd ﬁnite ﬁrst fractions functions Gauss Greek mathematics Hellenistic Hindu Hindu-Arabic numerals history of mathematics ideas Indian inﬁnite inﬁnitesimals inﬂuence integral known Lagrange Laplace later Leibniz mathe mathematicians matics method modern Newton Nineteenth Century notation number theory Oriental papers Paris Pascal period place value plane problems projective geometry published Pythagorean quadratic quadratic equations rational Riemann rigorous Roman Empire scientiﬁc sexagesimal so-called solution solved square symbols T. L. Heath texts theorem tion tradition translation triangle trigonometry vols Weierstrass Western Zeno’s