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Loci: Convergence

Mathematical Treasures

by Frank J. Swetz and Victor J. Katz

Introduction

Index to the Collection (alphabetical by author)

During the first half of the twentieth century, David Eugene Smith (1860-1944) was a moving force in the world of mathematics education.  As the chairman of the mathematics education department at Columbia University’s Teachers College, Smith led the way in teaching reforms attuned to the Progressive Education Movement.  He firmly believed that the teaching of mathematics should be closely associated with the history of the subject.  As an historian of mathematics, he wrote and lectured widely on the subject and also collected historical mathematical materials: texts, documents and artifacts.  Smith befriended the wealthy New York book publisher and bibliophile, George Arthur Plimpton (1855-1936).  While Plimpton was an avid collector of materials from the liberal arts that comprised “the tools of learning” for western civilization, under Smith’s influence Plimpton greatly enriched his collection with mathematical manuscripts and many early Renaissance texts on arithmetic.  When Plimpton died in 1936, he bequeathed his collection to Columbia University.  Similarly, beginning in 1931, David Eugene Smith began donating his extensive collection of mathematical memorabilia: historical texts; correspondence; portraits of famous mathematicians; signatures and concrete artifacts to the Columbia University Library.

Today, these two collections exist as rich resources for understanding the development of mathematics and the lives and work of many of the persons responsible for its advance.  These archives are available to researchers through the Rare Book and Manuscript Collection at Columbia University.  The Mathematical Association of America, in cooperation with the Columbia University Libraries, is pleased to display a selection of items, Mathematical Treasures, from these two separate collections.  The editors of Convergence would like to thank particularly Dr. Michael Ryan, Director of Rare Books and Manuscripts, and Jennifer Lee, Librarian for Public Service and Programs, for their assistance in making this display possible.

This article is still "under construction."  Page 2 contains the beginning of an index to the collection (alphabetical by author).  Each item is posted in this article at the standard web resolution of 72dpi.  But if you right-click on the name of the item, found in the first sentence of the item description, you can download the item as a tif file at a resolution of approximately 150-200dpi as well.  (Since these files are in the range of 3-5MB, the downloading may take some time.) That version should be suitable for most purposes in a classroom setting.  If you want a version in even higher resolution, please contact the authors or editor. (Note that if you just click on the name of the item, you will get the tif file on your screen, again after a long wait, but you may not be able to save it to your computer.)

Table Of Contents

  1. Introduction
  2. Index to the Collection
  3. Plimpton 322
  4. Ars Magna Title Page
  5. Al-Khwarizmi's Algebra
  6. Lilavati of Bhaskara
  7. De Divina Proportione, by Luca Pacioli
  8. Robert Recorde's Pathway to Knowledge
  9. The Treviso Arithmetic
  10. On Triangles, by Regiomontanus
  11. Isaac Barrow's Geometrical Lectures
  12. Jacob Bernoulli's Ars Conjectandi
  13. Rene Descartes' Treatise on Method
  14. Oronce Fine's Geometry
  15. Leonhard Euler's Algebra
  16. Simon Jacob's Rechenbuch
  17. Jacob Kobel's Geometry
  18. Margarita philosophica of Gregor Reisch
  19. Leonhard Euler's Calculus of Variations
  20. Adam Riese's Rechenbuch
  21. Omar Khayyam's Algebra
  22. The Grounde of Artes by Robert Recorde
  23. A Treatise of Algebra by John Wallis
  24. Boethius's Arithmetic
  25. Galileo's Siderius Nuncius
  26. Jordanus de Nemore's Arithmetica
  27. Galileo's Geometrical Compass
  28. Pacioli's Summa
  29. Albrecht Durer's Treatise on Mensuration
  30. Niccolo Tartaglia's Nova Scientia
  31. Gaspard Monge's Descriptive Geometry
  32. Isaac Barrow's edition of Archimedes, Apollonius, & Theodosius
  33. Leibniz - Bernoulli correspondence
  34. Christiaan Huygens' De Circuli Magnitudine Inventa
  35. Frans van Schooten's Exercitationes mathematicae
  36. Niccolo Tartaglia's General Trattato di Numeri et Misure
  37. Isaac Newton
  38. Zhoubi suanjing
  39. Jiuzhang suanshu
  40. Leonard Digges' Tectonicon
  41. Thomas Digges' Pantometria
  42. Qadi Zada al-Rumi's Geometry
  43. Opus Arithmetica of Honoratus
  44. Euclid's Elements in a 14th century manuscript
  45. Euclid's Elements in a manuscript from c. 1294
  46. Benedetto da Firenze's Trattato d'arismetriche
  47. Nasir al-Din al-Tusi's Commentary on Euclid's Elements
  48. Seki Kowa's Essentials of Mathematics
  49. Oliver Byrne's Euclid
  50. Johann Kepler's Rudolphine Tables
  51. Tycho Brahe's astronomical instruments
  52. Peter Apianus's trigonometry and geography
  53. Leonhard Euler's Integral Calculus
  54. Christopher Clavius's Opera Mathematica
  55. Giuseppe Alberti's Instruzioni pratiche per l’ingenero civile
  56. Johann Faulhaber's Academia Algebrae
  57. Robert Recorde's Whetstone of Witte
  58. Clavius's Epitome arithmetica practica
  59. Van Heuraet's Rectification of Curves
  60. Francesco Barozzi's Procli Diadochi
  61. Lagrange's Analytical Mechanics
  62. Marin Mersenne's Universal Geometry
  63. Euler's Analysis of the Infinite
  64. Lacroix's Calculus of Probability
  65. Maria Agnesi's Analytical Institutions
  66. Johann Kepler's Uralten Messekunst Archimedes
  67. Billingsley Euclid
  68. Laplace's Celestial Mechanics
  69. Boethius's Liber Circuli
  70. Christopher Clavius's edition of Euclid's Elements
  71. Kepler's Logarithms
  72. Desargues' Sundials
  73. Leonhard Zubler's Nova Instrumentum Geometricum
  74. Legendre's Elements of Geometry
  75. Oronce Fine's Le Sphere du Monde
  76. John Eyre's The Exact Surveyor
  77. Bartholomew Pitiscus's Trigonometry
  78. Francis Maseres's Doctrine of Permutations
  79. Isaac Barrow's edition of Euclid's Elements
  80. Kepler's Epitome of Astronomy
  81. Bettini's Aerarium Philosophiae Mathematicae
  82. Ramus's The Way to Geometry
  83. Franciscus Maurolycus's Arithmeticorum libri duo
  84. Jonas Moore's Arithmetick in Four Books
  85. Johann Scheubel's De Numeris
  86. Jan de Witt's Elements of Curves
  87. Francisco Feliciano's Libro di Arithmetica
  88. Johann Boschenstein's Rechenbuch
  89. Christian Wolff's Treatise of Algebra
  90. Michael Stifel's Arithmetica Integra
  91. Richard Sault's New Treatise of Algebra
  92. Simon Stevin's Oeuvres Mathematiques
  93. William Emerson's Treatise of Algebra
  94. Gerolamo Cardano's Practica Arithmetice
  95. Francesco Ghaligai's Practica D'Arithmetica
  96. Charles Bossut's Traite elementairede geometrie
  97. John Ward's Compendium of Algebra
  98. Gemma Frisius's Arithmeticae Methodus Facilis
  99. Antichissimo di Algorismo
  100. German protractor
  101. Austran weights
  102. English gauger's scale
  103. Austrian measuring rod
  104. English tally sticks
  105. Korean Sangi rods
  106. Italian compass
  107. Italian armillary sphere
  108. Italian astrolabe
  109. The George Arthur Plimpton Collection
  110. The David Eugene Smith Collection

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