## The World of Mathematics, Volume 1Vol. 1 of a monumental four-volume set includes a general survey of mathematics; historical and biographical information on prominent mathematicians throughout history; material on arithmetic, numbers and the art of counting, and the mathematics of space and motion. Nontechnical articles by and about scores of eminent mathematicians as well as literary figures, economists, biologists. and many other thinkers. Informative commentary by noted mathematics scholar James R. Newman precedes essays by Eric Temple Bell, W. W. Rouse Ball, Leonhard Euler, Bertrand Russell, Alfred North Whitehead, many others. Numerous figures. |

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### Contents

III | 4 |

IV | 73 |

V | 74 |

VI | 75 |

VII | 169 |

VIII | 170 |

X | 179 |

XI | 180 |

XLVI | 420 |

XLVII | 430 |

XLVIII | 432 |

L | 442 |

LI | 465 |

LII | 467 |

LIV | 488 |

LV | 489 |

XIII | 188 |

XIV | 189 |

XV | 212 |

XVI | 218 |

XVII | 220 |

XIX | 235 |

XX | 239 |

XXII | 254 |

XXIII | 255 |

XXV | 277 |

XXVII | 286 |

XXVIII | 288 |

XXX | 294 |

XXXI | 295 |

XXXIII | 340 |

XXXIV | 341 |

XXXVI | 366 |

XXXVII | 368 |

XXXIX | 377 |

XL | 381 |

XLII | 395 |

XLIII | 402 |

XLIV | 417 |

XLV | 418 |

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### Common terms and phrases

abstract algebra analytical geometry Archimedes arithmetic astronomy axioms Bertrand Russell bilateral symmetry calculation called Cayley century circle conception cross-ratio cube curve deﬁned deﬁnition Desargues Descartes digits Diirer Diophantus discovered discovery distance equal equation Euclid Euclidean geometry Euler example expressed fact ﬁeld ﬁgure ﬁnally ﬁnd ﬁnding ﬁnger ﬁnite ﬁrst ﬁve ﬁxed ﬂuid Gauss given Greek Greek mathematics ideas inﬁnite inﬁnitesimal inﬂuence integers invented Kepler Leibniz length letters logic mathe mathematicians mathematics matics means measure method motion multiply nature Newton non-Euclidean geometry notation philosophy physical plane polygon position prime Principia problem projective geometry proof properties proved Pythagoras Ramanujan rational numbers reason reﬂection regular polygon result right angles roots rotations scientiﬁc sides signiﬁcance space sphere square straight line suppose surface Sylvester symmetry theorem theory of numbers things thought tion triangle University velocity write