*Editors:* Amy Ackerberg-Hastings, Janet Barnett, Janet Beery (through 1/31/19)

*Associate Editors:* Paul Bialek, Eugene Boman, Maureen Carroll, Lawrence D'Antonio, Sloan Despeaux, Victor Katz (through 1/31/19), Michael Molinsky, Elyn Rykken, Randy Schwartz, Amy Shell-Gellasch, Jody Sorensen, Gary Stoudt, Erik R. Tou, Laura Turner

*Founding Editors:* Victor Katz, Frank Swetz

### Articles

Bringing Historical Methods for Astronomical Measurements into the Classroom by Seán P. Madden, Jocelyne M. Comstock, and James P. Downing (posted 10/14/2019)

Student activities that combine data collection with astronomical measurement methods attributed to Eratosthenes, Ptolemy, and Galileo.

Here's Looking at Euclid by Sid Kolpas and Stu Ockman (posted 09/16/2019)

A mathematical crossword puzzle with historical overtones.

To Simplify, or Not To Simplify? A Lesson from Medieval Iraq by Valerio De Angelis and Jeffrey A. Oaks (posted 09/02/2019)

A case where not simplifying fractions explains a curious rule for computing cube roots from medieval Arabic mathematics, with student exercises.

*MAA Convergence* is Sweet Sixteen!

As *Convergence* marks its 16th volume, we recognize its long-term former editors by compiling their contributions to the journal’s content and by presenting a brief history of the journal.

Servois' 1817 "Memoir on Quadratures" translated by Robert E. Bradley and Salvatore J. Petrilli, Jr. (posted 05/20/2019)A readers' guide and complete English translation of Servois' 1817 contribution to a debate on numerical integration.

HOM SIGMAA 2019 Student Paper Contest Winner (posted 04/23/2019)Read the winning entry, "Omar Khayyam's Successful Replacement of Euclid's Parallel Postulate" by Amanda Nethington, from the 16th annual edition of this contest.

Teaching Mathematics with Ephemera: John Playfair's Course Outline for Practical Mathematics by Amy Ackerberg-Hastings (posted 04/22/2019)

Ephemera are a category of primary source that may prove especially engaging for students. The article provides examples of ephemera, a sample analysis of one piece of ephemera, and suggestions for incorporating this form of primary source into mathematics classrooms.

Using the Publimath Database to Bring History into our Teaching by Hombeline Languereau and Anne Michel-Pajus (posted 04/08/2019)

Description, with user instructions, of a French online resource cataloging research articles and projects for using history to teach mathematics.

More Than Just a Grade: The HOM SIGMAA Student Contest Fosters Writing Excellence at UMKC by Richard Delaware (posted 02/10/2019)

Advice on promoting excellence in student research and writing in the history of mathematics.

Ongoing Series

A Series of Mini-projects from **TR**ansforming **I**nstruction in **U**ndergraduate **M**athematics via **P**rimary **H**istorical **S**ources, by Janet Barnett, Kathy Clark, Dominic Klyve, Jerry Lodder, Danny Otero, Nick Scoville, and Diana White

- The Derivatives of the Sine and Cosine Functions: A Mini-Primary Source Project for Calculus I, by Dominic Klyve
- Why be so Critical? Nineteenth Century Mathematics and the Origins of Analysis: A Mini-Primary Source Project for Introductory Analysis Students, by Janet Heine Barnett
- Connecting Connectedness: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
- Generating Pythagorean Triples: A Mini-Primary Source Project for Mathematics Majors, Elementary Teachers and Others, by Janet Heine Barnett
- Euler's Rediscovery of
*e:* A Mini-Primary Source Project for Introductory Analysis Students, by Dave Ruch
- How to Calculate \(\pi\): Machin's Inverse Tangents, A Mini-Primary Source Project for Calculus II Students, by Dominic Klyve
- Henri Lebesgue and the Development of the Integral Concept: A Mini-Primary Source Project for Undergraduate Analysis Students, by Janet Heine Barnett
- Seeing and Understanding Data: A Mini-Primary Source Project for Students of Statistics, by Charlotte Bolch and Beverly Woods
- The Origin of the Prime Number Theorem: A Primary Source Project for Number Theory Students, by Dominic Klyve (posted 03/06/2019)
- The Cantor Set Before Cantor: A Mini-Primary Source Project for Analysis and Topology Students, by Nicholas A. Scoville (posted 05/03/2019)
- Euler’s Calculation of the Sum of the Reciprocals of the Squares: A Mini-Primary Source Project for Calculus II Students, by Kenneth M Monks (posted 08/06/2019)
- Completing the Square: From the Roots of Algebra, A Mini-Primary Source Project for Students of Algebra and Their Teachers, by Daniel E. Otero (posted 09/30/2019)
- Regression to the Mean: A Mini-Primary Source Project for Statistics Students, by Dominic Klyve (posted 12/04/2019)

Math Origins, by Erik R. Tou

How were concepts, definitions, and theorems familiar to today's students of mathematics developed over time?

Mathematical Treasures

Mathematical Treasures at the Linda Hall Library, by Cynthia J. Huffman Description of the physical and digital history of science collections of the Linda Hall Library in Kansas City. At least 75 of LHL's digitized rare books relate to the history of mathematics and can be used in classrooms.

Mathematical Treasures from the Linda Hall Library added during 2019:

Mathematical Treasures, by Frank J. Swetz

Index to Mathematical Treasures Collection: Images of historical texts and objects from libraries, museums, and individuals around the world for use in your classroom!

Mathematical Treasures added during 2019:

- Egyptian Wooden Codex (6th or 7th century) (posted 02/17/19)
- Gerbert's
*Geometriae* (12th century copy of c. 1000 CE original)
*Sphaera Mundi* of Abraham bar Hiyya (1546, original 11th or 12th century) (posted 05/15/19)
- Adelard's Translation of Euclid's
*Elements* (12th-14th centuries) (posted 08/22/19)
- Sacrobosco's
*Sphaera mundi* (c. 1256-1270 manuscript) (posted 02/26/19)
- Isadore of Seville's
*Etymologiae *(c. 1265) (posted 02/10/19)
*Liber abaci* of Leonardo of Pisa (14th cent. copy of 1202 original) (posted 03/06/19)
- John Peckham's
*Perspectiva* (1556, original 13th century) (posted 05/16/19)
- Muscarello's
*Algorismus* from Southern Italy (c. 1478) (posted 02/18/19)
- The Arithmetic of Piero Borghi (1491, original 1484)
- Luca Pacioli's
*Summa de arithmetica, geometria, … * (1494) (posted 02/10/19)
- Arithmetic of Juan Martinez Siliceo (1514)
- First Printed Greek Euclid's Elements (1533)
- Johannes Stöffler's
*Art of Measurement *(1536)
*Arithmeticae practicae* of Gemma Frisius (1540/1567) (posted 02/11/19)
- Oronce Fine's
*De mundi sphaera** *(1542)
*Ptolemaei mathematicae* (*Almagest* in Greek/Latin, 1549) (posted 03/11/19)
- Charles de Bovelles's
*Practical Geometry* (1555)
- Robert Recorde's
*Castle of Knowledge* (1556) (posted 02/27/19)
- First Euclid's
*Elements* in Greek and Latin (1558) (posted 05/11/19)
*Scholarum mathematicarum* of Peter Ramus (1559) (posted 03/08/19)
- Juan de Ortega's
*Tractado Subtilissimo d’arismetica** * (1563)
- Pietro Cataneo's
*Le pratiche della due prime matematiche *… (*Practice of the two basic Mathematics*) (1567)
- First Spanish Euclid's
*Elements* (1576)
- Danti on Euclid's
*Optics* (1573) and the Astrolabe (1578) (posted 05/17/19)
- Marchesi's
* Handbook of Commercial Arithmetic *(1578) (posted 02/10/19)
- al-Tusi's printed Arabic edition of Euclid's Elements (1594)
- Van Ceulen's
*On the Circle *(1596)
- Peurbach's
*New Theory of the Planets *(c. 16th century) (posted 02/19/19)
- Guidobaldo del Monte's
*Perspectiva* (1600) (posted 05/17/19)
- Tycho Brahe's
*Astronomiae instauratae mechanica *(1602) (posted 05/20/19)
- Galileo's
*Siderius nuncias* with author's signature (1610) (posted 02/10/19)
- Two Portraits of John Napier (1550-1617) (posted 05/18/19)
- John Napier,
*A Declaration of the Admirable Table of Logarithmes * (1618)
- Kepler's
*Harmony of the Worlds* (1619) (posted 05/21/19)
- Metius on Geography and Measurement (1624) (posted 05/22/19)
- Student notes from lectures of Rhodius, University of Wittenberg (1629) (posted 02/10/19)
- Christoph Scheiner's pantograph and sunspot device (1631)
- Marginal note by Galileo in his
*Dialogue* (1632) (posted 05/23/19)
- Philip Lansberge's Astronomical Tables (1632) (posted 05/24/19)
- Philip Lansberge's Quadrant (1635) (posted 05/24/19)
- Letter from Torricelli to Mersenne (1645)
- Riccioli's New Almagest (1651) (posted 05/25/19)
- Mathematical Works of Caroli Rinaldini (1655) (posted 05/26/19)
- Graunt's Early Statistics on Mortality (1662)
- Cardinal Ricci on Maxima & Minima (1668) (posted 03/07/19)
- van Schooten's Latin edition of Descartes's Geometry (1683, original 1649)
- Seth Partridge's Double Scale Slide Rule (1692) (posted 05/27/19)
*De Locis Solidis* of Vincenzo Viviani (1701) (posted 03/09/19)
- Edward Hatton's
*The Merchant’s Magazine or Trades Man’s Treasury *(1707, original 1701)
- Works of Isaac Newton (1711)
- James Hodder's
*Arithmetick* (1719, original 1661) (posted 03/20/19)
- Colin Maclaurin's
*Geometria Organica *(1720)
- John Keill's
*Euclid's Elements* and other works (1723/1782)
- Girolamo Saccheri's
*Euclid Vindicated of All Errors *(1733)
- L’Abbé Deidier's
*L’Arithmetique des* *G**éom**étres* (1739)
- Newton's
*Fluxions* owned by De Morgan (1740) (posted 02/25/19)
- Critical Edition of Newton's
*Principia* (1739–1742) (posted 05/28/19)
- John Stewart's early text based on Newton's calculus (1745)
- Signature and portrait of Colin Maclaurin (early 18th century, 1814), contributed by Sid Kolpas (posted 09/02/19)
- Gabriel Cramer's
*Introduction a l’Analyse des Lignes Courbes Algebriques** *(1750)
- Juan Bautista Corachán's Arithmetic for Merchants (1757, original 1699)
- Benjamin Franklin's "Magic Square of Squares" discussed in
*Gentleman's Magazine* (1768), contributed by Sid Kolpas (posted 11/08/19)
- Two Works of Joseph Fenn (1769/1772) (posted (03/17/19)
*Of the Parabola *(late 18th century) (posted 02/19/19)
- Euler's
*Institutiones Calculus Differentialis *(1787)
- Georg Vega's Lectures on Applied Mathematics (1788, 1819) (posted 05/29/19)
- Chauncey Lee's
*The American Accomptant* (1797), contributed by Sid Kolpas (posted 09/02/19)
- Charles Bossut's
*Cours de Mathématiques** *(1800) (posted 03/08/19)
- Lazare Carnot on
*Infinitesimal Calculus* (1797) and *Geometry* (1801) (posted 03/09/19)
- N. R. Tomlinson's ciphering book from the Royal [Naval] Academy, Portsmouth (1806)
- Joseph Nicolas Nicollet's
*Traité* *elémentaire [et] synthétique des sections coniques* (1809) (posted 02/10/19)
- Pierre-Simon Laplace's
*Théorie Analytique des Probabilités *(1812)
- John Graham's
*The Farmers’ and Mechanics’ Assistant or Companion, or A New System of Decimal* *Arithmetic* (1824)
- Abraham Lincoln's Cipher Book (ca. 1825)
- Works of Siméon-Denis Poisson (1831/1833/1835) (posted 03/24/2019)
- First Edition of Liouville's Journal (1836) (posted 05/30/19)
- Liouville's
*Journal de Mathématiques Pures et Appliquées* (founded 1836) (posted 03/22/19)
- Augustus De Morgan's "Induction (Mathematics)" (1838), contributed by Sid Kolpas (posted 02/16/19)
- John Napier's
*De Arte Logistica* (1839)
- Nicholas Lobachevsky's
*Theorie der Parallellinien* (1840)
- Ada Lovelace's Notes on the Analytic Engine (1843) (posted 05/31/19)
- Bernhard Riemann's Inaugural Address at Göttingen (1854/1867)
- Works of Charles Hermite (1873/1885/1905) (posted 02/24/19)
- George Boole on the Laws of Thought (1874)
- Letter by Florence Nightingale (1875), contributed by Anna Bargagliotti and Rebecca Nichols (posted 09/02/19)
- Weierstrass lecture notes (1879-1881) (posted 02/17/19)
- Works of Paul du Bois-Reymond (1887/1912) (posted 02/21/19)
- Herman Hollerith's tabulating machine discussed in
*Scientific American* (1890), contributed by Sid Kolpas (posted 11/07/19)
- Works of Paul Bachmann (1892/1894/1925) (posted 02/22/19)
- Lewis Carroll's
*Symbolic Logic* (1896) (posted 03/23/19)
- Postcard written by Charles Dodgson (aka Lewis Carroll, 1896), contributed by Sid Kolpas (posted 09/02/19)
- Henry F. Baker's
*Abel's Theorem and Allied Theory* (1897)
*Oeuvres mathématiques de Riemann* (1898) (posted 02/23/19)
*Collected Mathematical Papers* of J. J. Sylvester (1904)
- Henri Lebesgue's
*Leçons sur l'intégration* (1904) (posted 03/15/19)
- G. H. Hardy's
*Orders of Infinity* (1910) (posted 02/20/19)
- Bonola's Non-Euclidean Geometry (1912)
- Works of Hermann Weyl (1913/1918/1919) (posted 03/21/19)
- Albert Einstein's paper on Riemannian geometry (1928)
- Henry F. Baker's
*Principles of Geometry* (1929/1933)
- Bruce Rogers’s
*Elements of Geometry Book I* (1944), contributed by Sid Kolpas (posted 02/16/19)