*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

*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)

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, 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)
- 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)
*Arithmeticae practicae* of Gemma Frisius (1540/1567) (posted 02/11/19)
*Ptolemaei mathematicae* (*Almagest* in Greek/Latin, 1549) (posted 03/11/19)
- 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)
- 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)
- 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)
- 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)
- Seth Partridge's Double Scale Slide Rule (1692) (posted 05/27/19)
*De Locis Solidis* of Vincenzo Viviani (1701) (posted 03/09/19)
- Works of Isaac Newton (1711)
- James Hodder's
*Arithmetick* (1719, original 1661) (posted 03/20/19)
- John Keill's
*Euclid's Elements* and other works (1723/1782)
- Newton's
*Fluxions* owned by De Morgan (1740) (posted 02/25/19)
- Critical Edition of Newton's
*Principia* (1739-1742) (posted 05/28/19)
- Two Works of Joseph Fenn (1769/1772) (posted (03/17/19)
*Of the Parabola *(late 18th century) (posted 02/19/19)
- Georg Vega's Lectures on Applied Mathematics (1788, 1819) (posted 05/29/19)
- Lazare Carnot on
*Infinitesimal Calculus* (1797) and *Geometry* (1801) (posted 03/09/19)
- Charles Bossut's
*Cours de Mathématiques *(1800) (posted 03/08/19)
- Joseph Nicolas Nicollet's
*Traité* *elémentaire [et] synthétique des sections coniques* (1809) (posted 02/10/19)
- 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)
- Ada Lovelace's Notes on the Analytic Engine (1843) (posted 05/31/19)
- Works of Charles Hermite (1873/1885/1905) (posted 02/24/19)
- George Boole on the Laws of Thought (1874)
- Weierstrass lecture notes (1879-1881) (posted 02/17/19)
- Works of Paul du Bois-Reymond (1887/1912) (posted 02/21/19)
- Works of Paul Bachmann (1892/1894/1925) (posted 02/22/19)
- Lewis Carroll's
*Symbolic Logic* (1896) (posted 03/23/19)
- 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)
- 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)