Astronomical Images : Calculating longitude using the parallax of the Moon

Daniel Santbech

Astronomical Images

<p style='text-align: justify;'>Daniel Santbech's <i>Problemata</i> is a miscellaneous work in mixed mathematics, including astronomy, gnomonics, perspective, surveying, gunnery and navigation. The unifying element in such a wide range of disciplines is the instrument called the geometric quadrant. According to Lynn Thorndike, Santbech showed appreciation both for specific aspects of Copernicus's work, such as lunar theory, and for the <i>Prutenic Tables</i>, but he ignored cosmological issues. Copernicus is mentioned many times. Virtually nothing is known about Santbech, apart from the fact that he published, in addition to this work, an edition of Regiomontanus's <i>De triangulis</i> (Basel, 1561). The title-page calls Santbech '<i>Noviomagus</i>', and this is generally interpreted as meaning 'of Nijmegen', but Andreas Kleinert reports that Santbech could be from Speyer of Neumagen, a small town near Trier. The volume included a dedicatory letter by Santbech to '<i>Domino Joanni Ludovico a Windeck</i>', dated 1561. The existence of a 1542 Basel edition is disputed by Ernst Zinner. The figures in this edition seem to have been copied from Oronce Fine's <i>Protomathesis</i>. Santbech uses these figures to explain the method of finding longitude by reference to lunar eclipses. The reader had to know the time at which an eclipse would happen at a given longitude ' information that was to be looked up in tables. This could then be compared with the time at which the eclipse was actually observed and the difference in time could be converted to the difference in longitude. The uppermost figure here shows the Earth on its own, while the lower figure shows the Earth in the context of the celestial sphere. Note that north is shown at the bottom of the uppermost figure. While this is perhaps unconventional, it did not interfere with the explanation that Santbech offered, and indeed he referred to the Arctic pole as being at point B, that is at the bottom of the figure, in the text.</p>