## An Essay towards the Calculus of Functions Part I and II (Babbage) in Philosophical Transactions of the Royal Society of London, Volume 105, 1816 Part I pp. 1-22, 23-24 and Volume 106, Part II 179-256 WITH On the Fire-Damp of Coal Mines, and on Methods of Lighting the Mines So as to Prevent Its Explosion (Davy) & An Account of an Invention for Giving Light in Explosive Mixtures of Fire-Damp in Coal Mines, by Consuming the Fire-Damp(Davy) in Philosophical Transactions of the Royal Society of London, Volume 106, 1816, pp. 1-22, 23-24 WITH On the laws which regulate the polarisation of light by reflection from transparent bodies (Brewster) in Philosophical Transactions of the Royal Society of London, Volume 105, 1815, Parts I and II, pp. 125-159

1st Edition. FIRST EDITIONS of Charles Babbage's first papers as well as his most important contribution to mathematics, the calculus of functions. "The calculus of functions is undoubtedly Babbage's major mathematical invention. The subject... was taken up by [him] almost from its origin and developed by a series of ingenious generalizations" (Dubbey, The Mathematical Work of Charles Babbage, 51). Babbage's two papers formed a complete treatise on the subject; he "took a branch of mathematics barely considered by his predecessors and transformed it into a systematic calculus (ibid, 8).

Babbage became interested in the subject as early as 1809 and continued to develop it during his years at Cambridge. In these two papers, Babbage presented his major ideas on the subject and on the strength of these, was elected a fellow of the Royal Society. "Babbage believed that his new scheme would serve as a generalized calculus to include all problems capable of analytical formulation, and it is possible to see here a hint of the inspiration for his concept of the Analytical Engine.

"While the work on the engines and his other scientific, social and political activities caused him virtually to abandon mathematical research at the age of thirty, the calculus of functions was not taken up by other workers, and it is the aspect of Babbage's mathematical work that modern mathematicians find the most fascinating" (Dubbey 1989, 18-19). Many years later in his Passages from the Life of a Philosopher, Babbage referred to the calculus of functions as his "earliest step" and "one to which I would willingly recur if other demands on my time permitted" (Babbage 1864, 435).

ALSO INCLUDED: First edition of the first announcement and description of an invention some have argued rescued the Industrial Revolution, Humphrey Davy's Safety Lamp.

ALSO INCLUDED: First edition, first presentation of 'Brewster's Angle, "one of David Brewster's most important contributions to the science of physics" (Molecular Expressions Website). Item #442

CONDITION & DETAILS: Philosophical Transactions Volume for the year MDCCCXV (1815) and MDCCCXVI (1816) Ex-libris bearing only a miniscule "Athenaeum Library, Liverpool" stamp and at the foot (margin) of some of the plates. Quarto. (10.5 x 8.5 inches; 263 x 408mm). [12], 446, [20]; Volume 106 [14], 366, [12]. Volume I includes 8 page index. 16 copperplate engravings; Volume II includes and 8 page index and 21 copperplate engravings. The construction of Davy's lamp is depicted in one of the plates. Full volumes, complete. Handsomely rebound in aged calf. 5 raised bands at the spine, each gilt-ruled; gilt-tooled fleur de lis at the spine. Red and black, gilt-lettered spine labels. Tightly and solidly bound. New endpapers. Occassional light toning and foxing. By any measure, near fine condition.

**
Price:
$2,500.00
**