## The Legacy of Mario Pieri in Geometry and Arithmeticby Ivor Grattan-Guinness One of the distortions in most kinds of history is an imbalance between the study devoted to major figures and to lesser ones, concerning both achievements and influence: the Great Ones may be studied to death while the others are overly ignored and thereby remain underrated. In my own work in the history of mathematics I have noted at least a score of outstanding candidates for neglect, of whom Mario Pieri (1860–1913) is one. A most able contributor to geometry, arithmetic and mathematical analysis, and mat- matical logic during his rather short life, his work and its legacy are not well known. The main reason is that Pieri worked “in the shadow of giants,” to quote one of the authors 1 of this volume. Born into a scholarly family in Lucca, Pieri was educated briefly at the University of Bologna and principally at the prestigious Scuola Normale Superiore, in Pisa; under the influence of Luigi Bianchi (1856–1928) he wrote there his doctoral dissertations on al- braic and differential geometry. During his twenties came appointments in Turin, first at the military academy and then also at the university, where he fell under the sway of Corrado Segre (1863–1924) in algebraic geometry, and Giuseppe Peano (1858–1932) in the foundations of arithmetic, mathematical analysis, and mathematical logic. From 1900 to 1908 he held a chair at the University of Catania before moving to Parma, where he died from cancer. |

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### Contents

XIV | 47 |

XV | 50 |

XVII | 54 |

XVIII | 58 |

XIX | 61 |

XX | 62 |

XXI | 123 |

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XXIV | 128 |

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XXXI | 178 |

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XXXIX | 271 |

XLI | 274 |

XLII | 277 |

XLIII | 278 |

XLV | 282 |

XLVI | 283 |

XLVII | 284 |

XLVIII | 286 |

XLIX | 287 |

L | 289 |

LI | 290 |

LII | 291 |

LXI | 326 |

LXII | 331 |

LXIII | 332 |

LXIV | 333 |

LXV | 335 |

LXVI | 338 |

LXVII | 343 |

LXVIII | 347 |

LXIX | 349 |

LXX | 350 |

LXXI | 351 |

LXXII | 353 |

LXXIII | 357 |

LXXIV | 363 |

LXXVI | 367 |

LXXVII | 369 |

LXXVIII | 370 |

LXXIX | 372 |

LXXX | 374 |

LXXXII | 375 |

LXXXIV | 376 |

LXXXV | 377 |

LXXXVI | 378 |

LXXXVII | 379 |

LXXXIX | 381 |

XCII | 382 |

XCIII | 392 |

XCIV | 393 |

XCVI | 397 |

XCVII | 398 |

XCVIII | 399 |

XCIX | 401 |

C | 458 |

463 | |

### Other editions - View all

The Legacy of Mario Pieri in Geometry and Arithmetic Elena Anne Marchisotto,James T. Smith No preview available - 2011 |

The Legacy of Mario Pieri in Geometry and Arithmetic Elena Marchisotto,Elena Anne Marchisotto,James T. Smith No preview available - 2007 |

### Common terms and phrases

Academy Accademia dei Lincei Alfred Tarski algebraic geometry angle arithmetic Arrighi axiomatization axioms axis belong Bologna Burali-Forti Campetti Castelnuovo Catania no date Cesare Burali-Forti Cited in 1.3 coincide collinear congruent Corrado Segre Couturat D’Ovidio Dedekind defined definition descriptive geometry distinct points earned the laureate elementary geometry Enriques equidistant Euclidean geometry example Federigo Enriques follows foundations of geometry Giuseppe Peano hence Hilbert hypothesis internal intersect inversive geometry isometry Italian Klein letter logic Loria Lucca maps Mario Pieri matematica mathematicians mathematics middle schools natural numbers noncollinear points normal noted Padoa paper parallel Parma Pasch perpendicular Pincherle Pisa plane ABC Point and Motion Point and Sphere point different points A,B,C postulates principle professor projective geometry Proof published real numbers Reale Accademia relation Roero rotation Scuola segment Staudt symmetric Tarski theorem theory transformation translation Turin University of Catania wrote

### Popular passages

Page 426 - Foundations of analysis; the arithmetic of whole, rational, irrational, and complex numbers.

Page 430 - Der barycentrische Calcul ein neues Hülfsmittel zur analytischen Behandlung der Geometrie dargestellt und insbesondere auf die Bildung neuer Classen von Aufgaben und die Entwickelung mehrerer Eigenschaften der Kegelschnitte angewendet von August Ferdinand Möbius Professor der Astronomie zu Leipzig.