This survey traces the history of the astronomer's cross staff on the Continent from Levi ben Gerson to Gemma Frisius, in England from John Dee to John Greaves, and again on the Continent from Tycho Brahe to Adrian Metius. The emphasis throughout is on sources and influences, on distinguishing the various kinds of cross staff, and on clarifying terminology.

SummaryThis paper is an account of Kepler's explicit awareness of the problem of experimental error. As a study of the Astronomia nova shows, Kepler exploited his awareness of the occurrences of experimental errors to guide him to the right conclusion. Errors were thus employed, so to speak, perhaps for the first time, to bring about a major physical discovery: Kepler's laws of planetary motion. ‘Know then’, to use Kepler's own words, ‘that errors show us the way to truth.’ With a (...) survey of Kepler's revolutionary contribution to optics, the paper demonstrates that Kepler's awareness of the problem of experimental error extended beyond discrepancies between calculations and observations to types of error which pertain to observations and instruments. It emerges that Kepler's belief in the unity of knowledge and physical realism, facilitated—indeed created—the right philosophical posture for comprehending the problem of error in an entirely novel way. (shrink)

Summary In his Theoremata de lumine, et umbre (1521), Francesco Maurolyco (1494–1575) discussed, inter alia, the problem of the pinhole camera. Maurolyco outlined a framework based on Euclidean geometry in which he applied the rectilinear propagation of light to the casting of shadow on a screen behind a pinhole. We limit our discussion to the problem of how the image behind an aperture is formed, and follow the way Maurolyco combined theory with instrument to solve the problem of the projection (...) of light through small apertures. We show that Maurolyco not only reformed the classical sources which, he thought, were no longer the authoritative code of textual knowledge, but also established with the dioptra a novel linkage of method, theory, and instrument. He thereby demonstrated the importance of optics to the science of astronomy. (shrink)

Precision measurements have been made of the scales on a group of European astrolabes manufactured between c. 1450 and 1659. Little is known from documentary sources of the construction and scale-dividing methods used by late-medieval craftsmen. The measurements of the present group of twenty-four scales have been analysed statistically, so that the parameters of accuracy expected of them can be deduced. Scribing marks and other features give clear indications of how the scales were constructed.

We will examine Kepler's use of a relation between velocity and distance from a centre of circular motion. This relation plays an essential role, through a derivation in chapter 40 of the Astronomia Nova, in the presentation of the Area Law of planetary motion. Kepler transcends ancient and contemporary applications of the distance-velocity relation by connecting it with his metaphysical commitment to the causal role of the Sun. His second main innovation is to replace the astronomical models of his predecessors (...) with an account that derives trajectories from physical principles. In this paper we restrict our attention primarily to the first 40 chapters of Kepler's Astronomia Nova. Hence, we do not discuss Kepler's discovery of elliptical planetary orbits. (shrink)