...Our patron, Nicole Oresme, reviewing the last session's
proceedings.

Daniel
J. Curtin (Northern Kentucky University) and Daniel
E. Otero (Xavier University) have organized the **Ohio River
Early
Sources in Mathematical Exposition (ORESME) Reading Group**.
The Reading Group has been bringing together scholars interested in
the history
of mathematics from the Cincinnati tri-state area twice a year since
1998
to read original source materials in mathematics. The
organization was named
after the French Scholastic philosopher Nicole
Oresme (1323-1382)
whose "latitude of forms" constituted early graphical
representations of
mathematical functions, long before Descartes. The Reading
Group was inspired
by the experience the organizers shared during the summers of
1995-1997
at the Institute on the History of Mathematics and its Use in
Teaching
held at American University (Washington, DC), and was established
under
the guidance of Fred Rickey, one of the organizers of the
Institute and
an erstwhile Ohioan.

Individuals interested in participating in ORESME's meetings are encouraged to contact either of the organizers.

Plans are to extend our discussion on the
foundations of analysis by reading from Bernhard Riemann's *Habilitationschrift*
of 1854.

** **

The thirty-first meeting was held on **October 25-26, 2013**,
at Xavier University. We continued the thread begun at the last meeting by reading
from the work of** Karl Weierstrass** (1815-1897). Along with Cauchy,
Weierstrass has long been regarded as one of the central figures in the rigorization
of analysis in the nineteenth century. We read two pieces "by" Weierstrass
(given that the first was actually written by his student, H. A. Schwarz):

*Differentialrechnung, Ausarbeitung der Vorlesung an dem Königlichen Gewerbeinstitut zu Berlin im Sommersemester 1861 von H. A. Schwarz*(*Differential calculus, an elaboration of lecture notes at the Royal Technical Institute in Berlin in the summer semester of 1861 by H. A. Schwarz*), as excerpted in*Eléments d'analyse de Karl Weierstrass,*by Paul Dugac,*Archive for Hist. Exact Sci.,*vol. 10, No. 1/2 (28.VI.1973), 118-125;*Über continuirliche functionen eines reellen arguments, die für keinen werth des letzteren einen bestimmten, differentialquotienten besitzen*(*On continuous functions of a real argument which possess derivatives at not a single of their values*), Königl. Akad. Wiss. (1872),*Mathematische Werke II*, 71-74.

This task was made far more challenging by the fact that neither of these pieces are available in their entirety in English translation and facility with German is weak among the members of the seminar. So Wiebke Diestelkamp (U Dayton, and current President of the MAA Ohio Section) agreed to produce a rough translation for us of both pieces. For this we acknowledge her kind assistance.

The thirtieth meeting was held **January 25-26, 2013**, at Northern
Kentucky University (which, incidentally, marked the 15th anniversary of the
ORESME Reading Group!). We recognized the recent publication by Rob Bradley
and Ed Sandifer, the co-founders of our sister seminar Arithmos, of *Cauchy's
Cours d'Analyse* (Springer, 2009) by reading from their translation of these
highly influential lecture notes by **Augustin-Louis Cauchy** (1789-1857)
for a course that he never gave (!) at the École Polytechnique. It is
in these lecture notes that Cauchy first introduced the concept of limits into
the calculus. We read the following selections from the *Cours d'Analyse*:

- Introduction - p.1-3
- Preliminaries, p. 5-7, number and quantity, numerical value (i.e. absolute value) and the definition of the limit, which surprisingly is done in the didactic style - no epsilons!
- Chapter 1 - p. 17-20 Functions. Note in section 1.2 that he describes an "algebra" of 11 basic functions. No "arbitrary rule" relating 2 sets. This is a practical notion of function.
- Chapter 2 - p. 21 (definition of infinitely small) and p. 26-28 continuity of functions. Also: p. p. 38-41, the second epsilon proof in the book; follow this up with Theorem IV, which is a corollary and will be referred to below, on p. 92.
- Chapter 5, p. 71-75; distributive functions and a theorem (Theorem 2) that he will use to sum the binomial series.
- Chapter 6, p 85-90, convergence and divergence of series, Cauchy criterion, the famous false theorem, and p. 91-93, root, ratio and condensation tests.
- Chapter 7 - p. 122-127, modulus and argument, p. 132-133, roots of unity.

The twenty-ninth meeting was held **September 21-22, 2012**,
at Xavier University. We celebrated the bicentennial anniversary of the
publication of* Théorie Analytique des Probabilité*s by** Pierre-Simon
de Laplace** (Courcier, Paris, 1812; 2nd ed., 1814; supplements in 1816,
1818, 1820, contained in 3rd ed., 1820; reprinted with a fourth supplement,
1825) by reading a portion (Chapter IV, Section 18) of this seminal work, the
section in which he presents his version of the Central Limit Theorem, a result
that lies at the foundation of much of modern statistical methodology. Conveniently,
one of our members, Dick Pulskamp, recently wrote a piece for publication on
*TAP*, which was ideal for helping us understand the context and content
of Laplace's work. We also consulted these supplementary texts:

• E.C. Molina, "The Theory of Probability: Some Comments on Laplace's Théorie Analytique", Bull. AMS 36 (1930), 369-392.

• Anders Hald,A History of Mathematical Statistics from 1750 to 1930, Wiley, 1988, sections 17.1-17.2.

The twenty-eighth meeting was held **January 20-21, 2012**, at Northern
Kentucky University. We took up two selections of that giant of modern
mathematics, **David** **Hilbert** (1862-1943):

• his proof of the Hilbert Basis Theorem (as Hilbert understood it, any ideal in the ring of polynomials in n variables with rational coefficients is finitely generated), which appears in the paperÜber die Theorie der algebriaschen Formen[On the theory of algebraic forms], original pub. asMath. Annalen,36(1890), 473-534; our English translation was by M. Ackerman inLie Groups: History, Frontiers and Applications, Math Sci Press, 1978;

• one of his most popular works,Grundlagen der Geometrie, Teubner, 1899, the first edition of a work that has seen no fewer than 19 editions (!!); the English translation we used was the "authorized" translation of E.J. Townsend:Foundations of Geometry, Open Court, 1910.

The twenty-seventh meeting was held **September 23-24, 2011**,
at Xavier University. We extended our study of the history of modern algebra
by turning to the work that started it all: **Evariste Galois'**
*Mémoire sur les conditions de résolubilité des équations par radicaux*,
written days before his too-early death in 1831 (pub. posthumously by Joseph
Liouville in his* Journal de mathématiques pure et appliquées*, 1846,
pp. 417-433). An English translation appears as an appendix in Harold M. Edwards'
*Galois Theory* (Springer, 1984).

The twenty-sixth meeting was held **February 25-26, 2011**,
at Northern Kentucky University. This meeting was a natural follow-up
to the previous meeting, continuing a line of reasoning first begun by Ernst
Kummer, with his ideal complex numbers. We undertook a a study of the
evolution of the concept of an ideal (in a ring) by reading from **Richard
Dedekind's** first exposition in the Supplement to the 2nd (1871) edition
of Dirichlet's *Vorlesungen über Zahlentheorie* (*Lectures on Number
Theory*). The relevant sections have appeared in a recent English translation
by Jeremy Avigad (Carnegie Mellon University). Together with the German originals
for this text and the revised texts that Dedekind provided for the 3rd (1879)
and 4th (1894) editions of Dirichlet's textbook, we will also draw from two
papers by Harold M. Edwards, who wrote extensively on this subject in the early
1980s. Here's a full bibliographic list:

• Richard Dedekind. Supplement X von Dirichlets

Vorlesungen über Zahlentheorie, 2. Auflage, 1871.

• Jeremy Avigad. Dedekind's 1871 version of the theory of ideals. Carnegie Mellon Technical Report CMU-PHIL-162, 2004.

• Richard Dedekind. Supplement XI von DirichletsVorlesungen über Zahlentheorie, 3. Auflage, 1879.

• Richard Dedekind. Supplement XI von DirichletsVorlesungen über Zahlentheorie, 4. Auflage, 1894.

• H.M. Edwards. The genesis of ideal theory.Arch. Hist. Exact Sci.23, 1980, 321-378.

• H.M. Edwards. Dedekind's invention of ideals.Bull. London Math.Soc.15(1), 1983, 8-17.

The twenty-fifth meeting was held **October 8-9, 2010**, at Xavier
University. We read *Zur Theorie der complexen Zahlen* (*On
the theory of complex numbers)*, J. Reine Angew. Math. 35 (1847) 319-326
[Collected Papers, A. Weil (ed.), pp. 203-210], in its English translation as
found in Smith, *A Source Book in Mathematics*, 119-126. The paper
presents **Ernst Kummer**'s first description of his invention
of ideal complex numbers, famously used to illustrate that unique factorization
of integers into primes is not always available in certain rings of algebraic
integers.

The twenty-fourth meeting was held **January 29-30, 2010**, at
Northern Kentucky University. We read from two papers by the Scottish
mathematician** Joseph HM Wedderburn** (1882-1948): *A Theorem
on Finite Algebras*, Trans. AMS, Vol. 6, No. 3 (Jul., 1905), pp. 349-352;
and *Non-Desarguesian and Non-Pascalian Geometries*, Trans. AMS, Vol.
8, No. 3 (Jul., 1907), pp. 379-388. The first of these papers includes
three proofs (!) of the celebrated theorem that carries Wedderburn's name, that
every finite division algebra is a field; the second proves the existence of
finite geometries in which Desargues's Theorem fails. (As it turned out, we
had little time to explore the second of these two papers.)

The twenty-third meeting was held** October 2-3 , 2009**, at
Xavier University: to celebrate the bicentennial of its publication, we read
the paper that made** Carl Friedrich Gauss** (1777-1855) famous
as something other than a mathematical prodigy, his work on the computation
of the orbit of Ceres (in which he successfully predicted where astronomers
would be able to relocate it, within a half a degree of arc, after its passage
behind the Sun). Our attention focuses not on the astronomical calculation but
on his work in this same paper wherein he lays out his method of least squares
for minimizing measurement errors and the function that describes the probability
distribution now named after him. We read Section III of Book II of his *Theoria
motus corporum coelestium in sectionibus conicis solem ambientum* (Hamburg,
1809) in the 1857 English translation, *Theory of the motion of the heavenly
bodies moving about the sun in conic sections*, by Charles Henry Davis (available
in a 2004 Dover reprint).

The twenty-second meeting was held **January 16-17, 2009**, at
Northern Kentucky University. We read from the work of **Bernard
Bolzano** on the foundations of analysis. In particular, we read an English
translation of his seminal 1817 paper *Rein analytischer Beweis des Lehrsatzes,
das zwichen je zwei Werthen, die ein entgegengesetzes Resultat gewahren, wenigstens
eine reele Wurzel der Gleichung liege* (*A Purely Analytic Proof of the
Theorem that between and two Values which give Results of Opposite Sign, there
lies at least one real Root of the Equation*) from Steve Russ' *The Mathematical
Works of Bernard Bolzano* (Oxford U. Pr., 2004).

The twenty-first meeting was held **September 19-20, 2008**,
at Xavier University. In a departure from tradition, our topic was not
an important work of an individual mathematician, but rather a survey of the
development of a central idea that required many decades to take shape, **the
determinant.** We followed (essentially) the work of Thomas Muir (1844-1934),
the Scottish mathematician famous for a monumental multi-volume work,* The
Theory of Determinants in the Historical Order of Development* (Macmillan,
1890, 1906) which to this day remains the authority on the subject. We
also read a single modern paper, by Bruce Hedman, concerning Maclaurin's contributions.

READINGS

1. Leibniz,*
Specimen Analyseos novae, qua errores vitantur, quasi manu ducitur, et
facile progressiones invenientur* [*A Model for a new kind of
Analysis, by which error is avoided, the mind is led as if by the hand,
and patterns are easily discovered*], Leibnizens mathematische
Schriften, C.I. Gerhardt, ed., Part II, Volume 3, Berlin, 1863, pp. 7-8.
Unpub. ms., dated June 1678.

2. Muir, pp. 6-10: a description of the following ms.

3. Leibniz,*
Brief an de L'Hosptial, VI*, Hanover, 28 Avril 1693 [*Letter to
L'Hôpital, VI*, Hannover, 28 April 1693], Leibnizens mathematische
Schriften, C.I. Gerhardt, ed., Part I, Volume 2, Berlin, 1850, pp.
238-241.

4. Hedman,* An
earlier date for "Cramer's rule"*, Historia Mathematica 26 (1999) 4,
365-368: a relatively new piece of scholarship which argues the
advertised claim.

5. Maclaurin,
From* Treatise of Algebra*, 2nd ed., London, 1756, Chap. XII. pp.
81-85.

6. Muir, pp. 11-14: a description of the following two pieces.

7. Cramer, From*
Introduction a l'Analyse des Lignes Courbes algébriques* [*An
Introduction to the Analysis of algebraic Curved Lines*], Genève,
1750, pars. 37-38, pp. 57-60.

8. Cramer, From*
Introduction a l'Analyse des Lignes Courbes algébriques* [*An
Introduction to the Analysis of algebraic Curved Lines*], Genève,
1750, App. No. I, pp. 656-659.

9. Muir, pp. 14-17: a description of the following excerpt.

10. Bézout,*
Recherches sur le degré des équations résultantes de l'évanouissement
des inconnues, et sur les moyens qu'il convient d'employer pour trouver
ces équations* [*Researches on the degree of equations resulting
from the vanishing of unknowns, and on the means which are convenient to
use in order to solve these equations*], Hist. de l'Acad. Roy. des
Sciences, Paris, 1764, pp. 288-295.

11. Muir, pp. 17-24: a description of the following excerpt.

12. Vandermonde,
From* Mémoire sur l'élimination* [A memoir on elimination], Hist.
de l'Acad. Roy. des Sciences, Paris, 1772, 2° partie, pp. 516-525.

13. Muir, pp. 24-33: a description of the following paper.

14. Laplace,*
Recherches sur le calcul intégral et sur le système du monde, Sec. IV*
[*Researches on integral calculus and the system of the world, Sec.*],
Hist. de l'Acad. Roy. des Sciences, Paris, 1772, 2° partie, pp.
294-304.

15. Muir, pp. 63-66: a description of the following excerpt.

16. Gauss, From*
Disquisitiones Arithmeticae* [Investigations in Arithmetic],
Leipzig, 1801, Sect. V, Pars. 153-159, 266-270, in the English edition
by Arthur A. Clarke, rev. by William C. Waterhouse, Cornelius Greither,
and A. W. Grootendorst, Springer, New York, 1986, pp. 108-115, 292-297.

17. Muir, pp. 80-92: a description of the following excerpt.

18. Binet, From*
Mémoire sur un système de formules analytiques, et leur application à
des considérations géométriques* [*A memoir on a system of
analytical formulas and their application to geometric considerations*],
Journal de l'Ecole Polytechnique, 1812, T. IX, Cah. 16, pp. 280-302.

19. Muir, pp. 92-131: a description of the following excerpt.

20. Cauchy,*
Mémoire sur les fonctions qui ne peuvent obtenir que deux valuers égales
et de signes contraires par suite des transpositions opérées entre les
variables qu'elles renferment* [*A memoir on functions that can
have but two equal values, and on the contrary signs they must hold
because of transpositions performed between the variables*],*
Oeuvres de Cauchy*, Ser. II, T. 1, pp. 91-169.

21. Muir, pp. 176-178: a description of three papers, the third of which follows here.

22. Jacobi,*
Ueber die Pfaffshce Methode, eine gewöhnliche lineäre
Differential-gleichung zwischen 2n Variabeln durch ein System von n
Gleichungen zu integriren* [*On Pfaff's Method, an ordinary linear
Differential equation between 2n Variables in terms of a System of n
equations to integrate*],* Werke*, IV, pp. 17-29. Special thanks
to Danny Otero, Dick Pulskamp and Chuck Holmes for preparing English
translations of the materials above from, respectively, Latin, French
and German originals.

The twentieth meeting (and our 10th anniversary!) was held **January
25-26, 2008**, at Xavier University. We read three papers by**
Ernst Zermelo** (1871-1953) in celebration of the 100th anniversary of
his publication of the axioms of set theory and a proof of the axiom of choice.
The papers were: *Beweis, daß jede Menge wohlgeordnet werden kann*, Math.
Ann. 59 (1904), no. 4, 514--516 (an English translation of the original text
of this paper, part of a letter to Hilbert dated 24 Sep 1904, has the title
*Proof that every set can be well-ordered*, in Jean van Heijenoort's *From
Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931*, Harvard,
1967); *Neuer Beweis für die Möglichkeit einer Wohlordnung*, Math. Ann.
65 (1907), no. 1, 107--128 (an English translation of this later version of
the well-ordering property for sets has the title *A new proof of the possibility
of a well-ordering*, in Jean van Heijenoort's *From Frege to Gödel: A Source
Book in Mathematical Logic, 1879-1931*, Harvard, 1967); and *Untersuchungen
über die Grundlagen der Mengenlehre. I*, Math. Ann. 65 (1908), no. 2, 261--281
(an English version of this paper that lays out the axioms for set theory has
the title *Investigations in the foundations of set theory. I*, also in
Jean van Heijenoort's *From Frege to Gödel: A Source Book in Mathematical
Logic, 1879-1931*, Harvard, 1967).

The nineteenth meeting was held **October 5-6, 2007**, at Northern
Kentucky University. This was the second meeting in celebration of the
**Leonhard Euler** tricentennial. We read from Euler's *Introductio
in analysin infinitorum* (*Introduction to the analysis of the infinite*),
translated by John D. Blanton (Springer-Verlag, 1988). The selections
from Book One: Chapter I. On Functions in General; Chapter VI. On Exponentials
and Logarithms; Chapter VII. Exponentials and Logarithms Expressed through Series;
Chapter VIII. On Transcendental Quantities Which Arise from the Circle; Chapter
XVII. On using recurrent series to find roots of equations; and Chapter XVIII
On continued fractions; and from Book Two: Chapters I and II.

The eighteenth meeting was held **January 26-27, 2007**, at Xavier
University. This was the first of two meetings planned to celebrate the
Euler tricentennial. We read selections (from v.1, Sections I.xxi - I.xxiii
on logarithms; II.v on series; IV.viii on square roots of binomials; IV.x -
IV.xv on cubics and quartics; from v.2, Sections IV - VII on solutions to Pell's
equation) from **Leonhard Euler**'s *Vollständige Anleitung zur
Algebra* (St. Petersburg Akademie der Wissenschaften, 1770), available in
a 1984 Springer reprint of John Hewlett's 1828 English translation as *Elements
of Algebra*.

The seventeenth meeting was held **September 15-16, 2006**, at
Northern Kentucky University. The topic of the meeting was the work and
career of** Alan Turing**. We read two of his most important
papers, *Computing machinery and intelligence*, in *Mind* (new series),
vol. 59, no. 236 (Oct 1950), pp. 433-460, in which Turing presents what is known
today as the Turing test for artificial intelligence; and *On computable numbers,
with an application to the Entscheidungsproblem*, *Proc. London Math. Soc.*
(2) 42 (1936), 230-265, in which Turing explores a definition of computability.

The sixteenth meeting was held **January 20-21, 2006**, at the
University of Cincinnati, hosted by Charles Groetsch, one of the founding members
of the Reading Group. The topic of the meeting was the famous and important
work of **Galileo Galilei** (1564-1642) on kinematics, as it appeared
in Days Three and Four of his *Discorsi e dimonstrzioni mathematiche intorno
a due nuove scienze* (*Discourses and Mathematical Demonstrations Concerning
Two New Sciences*), published posthumously in 1654 and available in English
translation by Stillman Drake (U. Wisc. Pr., 1974).

The fifteenth meeting was held **October 21-22, 2005**, at Northern
Kentucky University. The focus of the meeting was the mathematical career
of** Hermann Wey**l (1885-1955). We read his book on *Symmetry*
(Princeton University Press, 1952, reprinted in 1982 and 1989).

The fourteenth meeting was held **January 28-29, 2005**, at Xavier
University. The readings included the paper in which** John von Neumann**
first proved the Minimax Theorem and launched the serious mathematical theory
of games: *Zur Theorie der Gesellschaftspiele* (Math. Annalen 100 (1928),
295-320), translated as *On the theory of games of strategy* by Sonya Bargmann,
in *Contributions to the Theory of Games*, IV (Annals of Mathematics Studies
40), A. W. Tucker and R. D. Luce, eds., Princeton U. Pr., 1950, pp. 13-42; additionally,
the paper that started von Neumann thinking about games of strategy: Emile Borel,
*La théorie du jeux et les équations intégrales à noyau symétriques* (C.
R. Math. Acad. Sci. Paris, vol. 173 (1921), 1304-1308) , translated as *Theory
of games and integral equations with skew symmetric kernels* by Leonard J.
Savage, *Econometrica*, vol. 21, no. 1 (Jan 1953), 97-100. For details
see Danny Otero's report of the meeting.

The thirteenth meeting was held **September 17-18, 2004**, at
Northern Kentucky University. The readings were two papers by Maj. **Percy
MacMahon**: *The design of repeating patterns, Part I* ( Proc. Royal
Soc. London, Ser. A, vol. 101, no. 708 (Apr 1, 1922), 81-94) , and *On the
thirty cubes that can be constructed with six differently coloured squares*
(Proc. London Math. Soc. 24 (1893), 145-155). For details see Danny Otero's
report of the meeting.

The twelfth meeting was held **January 30-31, 2004**, at Xavier
University. The readings were: the Preface, and Chapters 1, 6, and 11 from**
George Polya**'s *Mathematics and Plausible Reasoning* (1954); the
Preface and Appendix to vol 1, and Chapters 13-14 of vol. 2 from *Mathematical
Discovery* (1961). This was the second meeting on the work of Polya, and
we focused deliberately on his work in teaching mathematics. For details see
Danny Otero's report of the meeting.

The eleventh meeting was held **September 26-27, 2003**, at Northern
Kentucky University. The reading was the Introduction and first Chapter of**
George Polya**'s *Combinatorial Enumeration of Groups, Graphs and Chemical
Compounds* (Springer, 1987), the English version with R. C. Read of a translation
of his influential 1937 paper *Kombinatorische Anzahlbestimmungen fur Grüppen,
Graphen und chemische Verbindungen* (Acta Math., 68, 145-254) in which the
eponymous Enumeration Theorem first appears. This is the first of two meetings
devoted to Polya. For deatils see Danny Otero's report of the meeting.

The tenth meeting was held **January 24-25, 2003**, at Xavier
University. The readings were by** E. H. Moore**: first, his *A
doubly infinite system of simple groups *(in *Mathematical Papers Read
at the *[1893]* International Mathematical Congress*, Macmillan,1896),
in which he contributed to early work on the classification of finite groups;
and also *On the foundations of mathematics* (Science, vol. XVII, no. 428
(March 13, 1903)), Moore's Presidential address upon retirement from that AMS
post. For details see Danny Otero's report of the meeting.

The ninth meeting was held **September 20-21, 2002,** at the
University of Louisville. Michael J. Crowe, Distinguished Scholar in Residence
and our special guest, led the discussion of work of **Hermann Grassmann**
and, more generally, on the history of vector analysis. Danny Otero's report of the meeting. It includes links to Crowe's notes
"A History of Vector Analysis."

The eighth meeting was held **May 10-11, 2002**at Xavier University.
The reading was** L. E. Dickson**'s (1874-1954), *Recent progress
on Warings's Theorem and its generalizations* (Bull. Amer. Math.Soc., 39,
701-727). For more, see Danny Otero's report of the meeting.

The seventh meeting was held **September 14-15, 2001**,at NKU.
We read three papers and a letter of** Georg Cantor** dating from
the 1880s and 1890s on his transfinite numbers. For more, see Danny Otero's
report of the meeting.

The sixth meeting was held **January 26-27, 2001**,at XU.
We read a paper by the British mathematician** William Burnside**
that was influential in the development of group theory at the beginning of
the 20th century. The paper, *On an unsettled question in thetheory
of discontinuous groups* (Quart. J. of Pure and Applied Math. 33 (1902) 230-238),
introduced what is now known as the Burnside problem: are all finitely generated
torsion groups finite? For more, see Danny Otero's reportof the meeting.

There was **no meeting in Fall 2000**. The
members decided to support instead the Midwest History of Mathematics
Conference at NKU, October 13-14, 2000.

Our fifth meeting was held **March 24-25, 2000**, at Miami University,
hosted by members David Kullman and Chuck Holmes. John Fauvel of the Open
University (UK) was our special guest, and led us in a reading of **Isaac
Newton**'s "De Analysi" (1669) [in *The Mathematical Papers of Isaac
Newton*, D.T. Whiteside, ed., Cambridge, 1967-, vol. 1, pp. 206-247]. In
lieu of a formal report, we have photos of the meeting taken by our illustrious guest, John
Fauvel.

Our fourth meeting was held at NKU on **September
17-18,1999**. We completed our study of Klein and his
Erlangerprogramm. See Danny Otero's report
of the meeting.

Our third meeting was again at Xavier, **January 29-30,1999**.
This was the first of two meetings on** Felix Klein**'s Erlangerprogramm. The primary
reading was Haskell's translation *A Comparative Review of Recent Researches
in Geometry*, (Bull. NY Math.Soc. 2 (1892-3), 215-249). Dick Davitt prepared
a preliminary bibliography
of Klein and the Erlangerprogramm for the members. See Danny Otero's
report of the meeting.

The second meeting took place on **September 18-19, 1998**, at
Northern Kentucky University. The paper *Sur une courbe continue sans
tangente obtenue par une construction géométrique élémentaire*,* *(Archiv
fur Matematik, Astronomi och Fysik, 1 (1904) 681-702, [trans.by Ilan Vardi in
*Classics on Fractals*, Gerald Edgar, ed. (Addison-Wesley, 1993)]), in
which **Helge von Koch** presented the Koch Snowflake,
was the topic of the meeting. This material is reprinted, with some additions,
in *Une méthode géométrique élémentaire pour l'étude de certaines questiones
de la théorie des courbes planes* (ActaMathematica, 30 (1906), 145-174).
The last
four pages are available here in JPEG format. Dick Pulskamp's
translation is available in dvi format. Here is a
translation of some additional material, not in the 1904 paper, proving
the curve is simple.

The inaugural meeting of ORESME was held **January 30-31, 1998**,
at Xavier University. We read** William Fogg Osgo****od**'s paper, *A Jordan Curve of Positive
Area* (Trans. AMS, 4 (1903) 107-112). See Danny Otero's report of the meeting.