HERSCHEL (John Frederick William). A Collection of Examples of the Applications of the Calculus of Finite Differences. Cambridge: Printed by J. Smith, Printer to the University, 1820. First edition, iv, [2], 171, [1]pp., some prelims foxed. [Bound with:] BABBAGE (Charles) Examples of the Solutions of Functional Equations. s.n., 1820]. First edition, [4], 42pp., one engraved plate, some light spotting. 2 works in one, 8vo (225 x 145 mm), orig. boards, rebacked with new printed paper label, uncut. [Sold with:] PEACOCK (George) A Collection of Examples of the Applications of Differential and Integral Calculus.1820

Cambridge: Printed by J. Smith, Printer to the University, First edition, 8vo (220 x 140 mm), viii, 506pp., 6 folding diagram plates to rear, some occasional light spotting, orig. boards, printed paper label to spine, rubbed, uncut. While at Cambridge Babbage and his friends in the Analytical Society fought a battle with the Cambridge establishment to replace the Newtonian dot notation for the calculus with the more powerful Leibnizian dx/dy notation. To this end, Babbage, Herschel and Peacock translated Lacroix's elementary treatise on the calculus which, like all continental works, followed Leibniz. The change over continued to move slowly and Babbage decided it was necessary to provide some worked examples, which took the form of the present works. Within a few years Babbage had won the day and British mathematicians, no longer impeded by an imperfect notation, began to catch up with their continental rivals.