Longomontanus · 1640
Read the translation (PDF) · Editorial footnotes (PDF)
A comprehensive textbook of astronomy and the definitive technical account of the Tychonic system — Earth at rest, the Sun circling it, the planets circling the Sun. It is the fullest pre-Newtonian exposition of that system, written by the man who had computed at Tycho’s side.
The book begins with the mathematics before it reaches the sky. Part One opens on the compendious analysis of plane and spherical triangles by numbers, supplying general theorems for their solution, and then sets out the prosthaphaeretic doctrine — the technique of turning multiplication into addition by trigonometric identity, which is how large astronomical computations were made tractable before logarithms. A long sequence of numbered doctrines applies this to plane and then spherical triangles in worked numeric form.
With the computational apparatus in hand, the work proceeds systematically through the structure of the cosmos, the motions of the Sun and Moon, eclipses, the planets, the fixed stars, and precession, with working tables and geometric diagrams throughout. An appendix treats the new stars of 1572 and 1604 and the comets of 1607 and 1618 — the phenomena that had broken the old cosmology and that the Tychonic system was built to accommodate.
Longomontanus had been Tycho’s assistant, and Astronomia Danica is the system’s technical case as its own camp would have made it: not a sketch of an arrangement, but a full working astronomy with the tables an observer needs to predict positions. It is the book to read to understand why the Tychonic compromise was taken seriously for as long as it was — it did the job, on data that could not yet distinguish it from the alternatives.
The translated source is the 1640 printing, which opens with a dedicatory epistle and a set of commendatory addresses to the author as professor in the Royal Danish Academy.