Renaissance engineers, from Brunelleschi on, had huge technical ambitions, and social ambitions too: for some of them, what we would call engineering was not just a craft practice like carpentry, stone masonry, or bee-keeping, but a tool of unlimited power over nature. With the Renaissance mastering of Archimedes in the middle decades of the 16th century, these ambitions were aided by a much more powerful argument: mathematical engineering is a mathematical science, a new science. Tartaglia's treatise on projectile motion of 1537 was the first to claim projectile motion to be a "new science" (although it was not until 1638 that a tenable "new science" of projectile motion was published). The ambition of such 'mere mechanics' to do true and certain and gentlemanly 'science' was not easily realised, however - on technical, philosophical, and social grounds. Dr Bursill-Hall will argue that, although generally only a mediocre mathematician per se, Galileo had the good luck to understand the significance of the spy-glass, and saw the arguments that made the leap from ambitious Archimedean mechanics to a mathematical natural philosophy and a new science.
