<p style='text-align: justify;'>Having lost the favour of the Danish court in the latter years of the sixteenth century, Tycho Brahe published his <i>Astronomiae instauratae mechanica</i> in 1598 as part of a strategy to procure royal patronage elsewhere. Addressed to his eventual patron, Holy Roman Emperor Rudolph II, the work lavishly described and illustrated the innovative astronomical instruments that Tycho had designed and constructed on the island of Hven, the site of his astronomical programme under the patronage of the Danish court. Though primarily focused on his instruments, the work also included an appendix on 'architectonic structures suitable for astronomical observations', which offered descriptions and illustrations of his two observatory buildings, as well as a map of Hven based on his own observational data. As such, the <i>Mechanica</i> offered not simply an overview of Tycho's instruments, but rather a presentation of his whole astronomical programme for which he was seeking financial support. This is an image of Tycho's medium-sized brass quadrant. Altitude measurements could be made by sighting the celestial phenomenon through a pair of pinnules at either end of the alidade, DE, and recording the respective altitude value on the circumference, BC. Furthermore, the horizon ring upon which the quadrant proper was fixed enabled azimuth measurements to be obtained as the quadrant was rotated to the vertical plane of the relevant star. The circumference of the quadrant was divided both according to Tycho's usual method of transversal points, and that described by the Portuguese mathematician, Petrus Nonnius (1492-1577). This latter method involved a series of concentric arcs, divided into a progressively smaller number of divisions (such that the outer circumference was divided into ninety parts, the next into eighty-nine, the third into eighty-eight, and so on until the innermost arc, which was divided into forty-six). During observation, the row and division intersected by the alidade would be recorded and then compared to a computational table engraved on the reverse of the quadrant, which would then give a value for degrees and minutes. Despite including this alternative method of division on several of his instruments, Tycho was unconvinced by its practical use. In his description of this instrument, Tycho also reveals a little of the process of instrument construction on Hven. He emphasises the need to employ skilled craftsmen in order that the instruments will be 'as nearly perfect as is possible in every respect'. In order to achieve this, he suggests that instruments may need to be repeatedly reconstructed in order to remove defects; as a consequence, 'we have remade most of the instruments described in this book more than once, not without great expense'. This is suggestive of a continual process of instrument development, supported by the inclusion in the <i>Mechanica</i> of a section on instruments yet to be constructed.</p>
