Tycho Brahe · 1591 (date on the manuscript; first issued 1886 — see Edition)
Read the translation (PDF) · Editorial footnotes (PDF)
The Triangulorum planorum et sphaericorum praxis arithmetica is Tycho Brahe’s working manual of trigonometry. Tycho never printed it; it survives in a single known manuscript at Prague, bound with a copy of Rheticus’s table of trigonometric functions.
Sixteen numbered rules, seven for plane triangles and nine for spherical, each showing how to find a triangle’s unknown sides and angles by arithmetic, with worked examples and figures.
The manual shows the computing that lay behind the reductions of the Uraniborg observations: the everyday trigonometry by which raw measurements of altitude and distance became the positions recorded in the Thesaurus Observationum.
The manuscript first appeared in 1886 as a photolithographic facsimile edited by F. J. Studnička in Prague, and this translation follows that facsimile, in the Bavarian State Library copy. Studnička took the manuscript for Tycho’s autograph; J. L. E. Dreyer, in his 1913 edition of Tycho’s works, argued that the hand is not Tycho’s.