Mathematical Treasure: Selected Journal Articles by Charles Babbage

Author(s):

Frank J. Swetz (The Pennsylvania State University)

Charles Babbage (1791–1871) was an inventor and scientist as well as a mathematician, prolific writer, and friend and tutor of Ada Lovelace. Several of his articles were extracted from the journals and transactions in which they appeared and published as separate pamphlets for distribution by the author and other readers. Here we will note several of these works along with an independent publication related to his advocacy for the differential and integral calculus:

“Observations on the analogy which subsists between the calculus of functions and the other branches of analysis,” Philosophical Transactions 107, no. 107 (December 1817): 197–216.

First page of Babbage's article, “Observations on the analogy which subsists between the calculus of functions and the other branches of analysis.”

Additional pages:

Page 4 of Babbage's article, “Observations on the analogy which subsists between the calculus of functions and the other branches of analysis.”

Page 5 from Babbage's article, “Observations on the analogy which subsists between the calculus of functions and the other branches of analysis.”

Page 6 from Babbage's article, “Observations on the analogy which subsists between the calculus of functions and the other branches of analysis.”

Read the full article in the Accademia delle Scienze di Torino. Read the full article as it was originally published in Philosophical Transactions.

“On the application of analysis to the discovery of local theorems and porisms,” Transactions of The Royal Society of Edinburgh 9, no. 2 (1823): 337–352.

Title page for Babbage's article, “On the application of analysis to the discovery of local theorems and porisms.”

Sample pages:

First page of Babbage's article, “On the application of analysis to the discovery of local theorems and porisms.”

Page 2 of Babbage's article, “On the application of analysis to the discovery of local theorems and porisms.”

Page 3 from Babbage's article, “On the application of analysis to the discovery of local theorems and porisms.”

Plate 22 from Babbage's article, “On the application of analysis to the discovery of local theorems and porisms.”

Read the full article in the Accademia delle Scienze di Torino. Read the full article as it was originally published in Transactions of the Royal Society of Edinburgh.

Babbage’s Examples of the Solutions of Functional Equations was written in 1820 as part of the work of the Analytical Society, during a year in which he was also helping found the Royal Astronomical Society.

Title page of Babbage's short book, Examples of the solutions of functional equations (1820).

Sample pages:

Author's notice for Babbage's short book, Examples of the solutions of functional equations (1820).

First page of Babbage's short book, Examples of the solutions of functional equations (1820).

Page 2 from Babbage's short book, Examples of the solutions of functional equations (1820).

Page 3 from Babbage's short book, Examples of the solutions of functional equations (1820).

Read all 42 pages of the book in the Internet Archive.

“Observations on the notation employed in the calculus of functions,” Transactions of the Cambridge Philosophical Society 1 (1820): 63–76.

First page of the article by Babbage, “Observations on the notation employed in the calculus of functions."

Read the article in the Internet Archive.

“On the influence of signs in mathematical reasoning,” Transactions of the Cambridge Philosophical Society 2 (1827): 325–377. Preprinted in 1826 by J. Smith, Cambridge.

Title page for Babbage's article, “On the influence of signs in mathematical reasoning.”

Sample problems:

First page of Babbage's article, “On the influence of signs in mathematical reasoning.”

Page 2 of Babbage's article, “On the influence of signs in mathematical reasoning.”

Page 3 of Babbage's article, “On the influence of signs in mathematical reasoning.”

Read the article in the Internet Archive. Another copy was offered for sale ca 2023 by Jonathan Hill, Bookseller.

The images on this page depict items in the digital collections of the Accademia delle Scienze di Torino and were found by searching the catalogue of Museo Galileo.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Selected Journal Articles by Charles Babbage," Convergence (February 2023)

Convergence

Tags:

Philosophy of Mathematics