The 18th-century heritage: mechanics around 1800

Abstract

After an attempt in the last two chapters to survey the vast amount of work done in and around the calculus, I come now to the even vaster and more complicated developments in mechanics. This subject was very much at the heart of 18th-century mathematics, and the quantity of the research is as awe-inspiring as its mathematical and historical complications. For example, the quantity and range of Euler’s work alone is bewildering; not only the central questions of general principles but also a spectrum of special cases from sounding bells to swinging chains, the motion of elastic lines and membranes, the design of ships and of spectacles, the performance of machines and microscopes, the bending of rods and the buckling of columns, and so on and on—right across the five divisions of mechanics indicated in Figure 121.1. Further, mechanics provided the imperative for the mathematics: in Euler’s case again, partial differential equations were of importance to him because of the vibrating string and other problems from the 1740s; his first paper “purely” concerned with solving such equations was 1766b (although much of his textbook Integral (1768–1770) was written by then).