ARITHMOS

Readings

 

 

Arithmos XXXI: January 24-25, 2009

New Location - Mathematics Conference Room, Second Floor, Higgins Hall

Jakob Bernoulli - Ars Conjectndi

At least two translations are available:

Bernoulli, Scylla, The Art of Conecturing, Johns Hopkins, 2006

and an edition by Maseres from the 1700s, available here digitally in 50-page units.  We will use at most parts 1 to 4.

Concordance between Maseres and Scylla (.doc)

Block 01

Block 02

Block 03

Block 04

Block 05

Block 06

Block 07

Block 08

Block 09

Block 10

Block 11

Block 12

Block 13

I also have a photocopy of the original (Latin) 300-page 1715 edition, copied single side, two pages to a side.  That's about 150 sheets, only 75 if we double-side it.   

Arithmos XXV: September 6-7, 2008

Cauchy - Cours d'analyse

Selections from Chapters 3, 5 and 8 (.pdf, approx 35 pages, all in English)

Arithmos XXVIII: March 29-30, 2008

Cauchy - Cours d'analyse

1821 edition in French  - complete pdf file(11.8 MB)

1911 second edition from the Oeuvres  - complete pdf file (13.6 MB)

newly translated English edition (some Microsoft Word files, others pdf)

Introduction (pdf)

Preliminaries (pdf)

Ch 1 - Algebraic Analysis (pdf)

Ch 2 - Infinitely small and infinitely large (incomplete) (pdf)

Ch 6 - Series (incomplete)

first part (doc)

second part (pdf)

Ch 7 - imaginary expressions

part 1

part 2

part 3

Note III - Intermediate value theoerm

part 1

part 2 (incomplete)

Table of contents

 

 

Arithmos XXVII: January 26-27, 2008

Non-Western Mathematics: Readings from Katz' Sourcebook

Table of Contents - 4 pages in .pdf format

Pages 385-397 - 13 pages in .pdf on introduction and mathematical texts 

Pages 480-492 - 14 pages in .pdf on the Kerala school 

Arithmos XXV:  May 19-20, 2007

Heath's commentaries on Euclid's Elements

Part 1 - 20 pages in .pdf format

Part 2 - 20 pages in .pdf format

Part 3 - 6 pages in .pdf format

Arithmos XXIIII - January 27-28, 2007

Euler's Foundations of Calculus

Chapter 3 - On the Infinite and the Infinitely Small (8 double pages)

Chapter 4 - On the Nature of Differentials of Each Order (8 double pages)

Arithmos XXI - February 25-26, 2006

Gauss's Disquisitiones Arithmeticae

Front matter

Chapter 1 - Congruent numbers in general (4 pages)

Chapter 2 - Congruences of the first degree (24 pages)

Chapter 3 - Residues of powers (34 pages)

Chapter 4 - Congruences of the second degree (45 pages)

Arithmos XX December 3-4, 2005

Continuing Isaac Newton

 

Arithmos XVIIII (XIX to some) - September 10-11, 2005

Isaac Newton's  Arithmetica Universalis,

Part 1: (approximately 15 pages in .pdf format)

Part 2: (approximately 20 pages)

Part 3: (approximately 20 pages)

Part 4: (approximately 20 pages)

Part 5: (19 pages) - posted 5 days after the first 4 parts.

Three 18th century editions are available online in the Babson Collection at the Burndy Library at the Dibner Institute.

 

 

Arithmos XVIII - July 30-31, 2005

Euler's Introductio in Analysin Infinitorum,

Volume 1, Chapters 11, 13, 16, 17, 18

11.    On other infinite expressions for arcs and sines (15 p)

13.    On recurrent series (23 p)

16.    On the partition of numbers (27 p)

17.    Using recurrent series to find roots of equations (20 p)

18.    On continued fractions (25 p)

Student Center room 228

Present: Rob Bradley, Andy Perry, David Burns, Ross Gingrich, Jeff Suzuki, Fred Rickey, Chuck Rocca, Ed Sandifer, Larry D'Antonio and Lydia Novozhilova

 

 

 

 

 

Arithmos XVII - April 30-May 1, 2005

 

Euler's Introductio in Analysin Infinitorum,

Chapters 4, 7, 8, 11

Chapter 4 - On the development of functions in infinite series (14 p)

Chapter 7 - Exponentials and logarithms expressed through series (9 p)

Chapter 8 - On transcendental quantities which arise from the circle (15 p)

Chapter 11 - On other infinite expressions for arcs and sines (15 p)

 

Present:  Rob Bradley, Erik Tou, Chuck Rocca, Andy Perry, Fred Rickey, David Burns, Cindy Gubitose, Larry D'Antonio, Ed Sandifer

 

Here is a good on-line Latin dictionary

 

Arithmos XVI - February 12-13, 2005

 

Introductio in Analysin Infinitorum, Leonhard Euler

Preface and Translator's notes

Table of Contents

Chapter 1 - On Functions in General

Chapter 2 - On the Transformation of Functions

Chapter 6 - On Exponentials and Logarithms

Chapter 8 - On transcendental quantities which arise from the circle

For the most part, these copies are two book-pages per copy-page.

We also got to look at Duncan Melville's new photographs of Mesopotamian tablets and other artifacts.

Present:  Fred Rickey, Duncan Melville, Rob Bradley, Larry D'Antonio, Ed Sandifer, Andy Perry, David Burns, Chuck Rocca, Ron Kutz.

 

Preface

Table of Contents

 

  1. On functions in general (15 p)
  2. On the transformation of functions (21 p)
  3. On the transformation of functions by substitution (12 p)
  4. On the development of functions in infinite series (14 p)
  5. Concerning functions of two or more variables (11 p)
  6. On exponentials and logarithms (17 p)
  7. Exponentials and logarithms expressed through series (9 p)
  8. On transcendental quantities which arise from the circle (15 p)
  9. On trinomial factors (21 p)
  10. On the use of the discovered factors to sum infinite series (17 p)
  11. On other infinite expressions for arcs and sines (15 p)
  12. On the development of real rational functions (12 p)
  13. On recurrent series (23 p)
  14. On the multiplication and division of angles (24 p)
  15. On series which arise from products (28 p)
  16. On the partition of numbers (27 p)
  17. Using recurrent series to find roots of equations (20 p)
  18. On continued fractions (25 p)

 

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