When did modern science arise? This is a question which has received divergent answers. Some would say that it started in the High Middle Ages , or that it began with th ‘via moderna’ of the fourteenth century. More widespread is the idea that the Italian Renaissance was also the re-birth of the sciences. In general, Copernicus is then singled out as the great revolutionary, and the ‘scientific revolution’ is said to have taken place during the period from Copernicus to (...) Newton. Others would hold that the scientific revolution started in the seventeenth century and that it covered the period from Galileo to Newton. Sometimes a second scientific revolution is said to have occurred in the first quarter of the twentieth century , a revolution which should be considered as great as the first one. (shrink)

This paper examines the discrepancy between the attitudes of many historians of mathematics to sixteenth-century geometry and those of museum curators and others interested in practical mathematics and in instruments. It argues for the need to treat past mathematical practice, not in relation to timeless criteria of mathematical worth, but according to the agenda of the period. Three examples of geometrical activity are used to illustrate this, and two particular contexts are presented in which mathematical practice localised in the sixteenth (...) century takes on a special historical significance. (shrink)

Like it or not, a big picture of the history of science is something which we cannot avoid. Big pictures are, of course, thoroughly out of fashion at the moment; those committed to specialist research find them simplistic and insufficiently complex and nuanced, while postmodernists regard them as simply impossible. But however specialist we may be in our research, however scornful of the immaturity of grand narratives, it is not so easy to escape from dependence – acknowledged or not – (...) on a big picture. When we define our research as part of the history of science, we implicitly invoke a big picture of that history to give identity and meaning to our specialism. When we teach the history of science, even if we do not present a big picture explicitly, our students already have a big picture of that history which they bring to our classes and into which they fit whatever we say, no matter how many complications and refinements and contradictions we put before them – unless we offer them an alternative big picture. (shrink)

In the late sixteenth century a number of mathematicians tried to introduce geometrical methods into surveying practice, to be based on simplified astronomical instruments, angle measurement, and triangulation. A measure of success is indicated by the acceptance of the simple theodolite, but the surveyors resisted such complex instruments as the altazimuth theodolite, recipiangle, and trigonometer. Counter-proposals, in particular the plane table, threatened to undermine the geometrical programme, but by the mid-seventeenth century a stable compromise had evolved. Among other things, the (...) demise of the shadow square indicates that angle measurement was then part of surveying practice. (shrink)