Died: 2 July 1613 in Heidelberg, Germany

**Bartholomeo Pitiscus** was born into a poor family, no further details of which are known. He studied theology, first at Zerbst, then at Heidelberg. He was a Calvinist, studying Calvinist theology, and he remained a staunch proponent of this form of Christianity throughout his life.

Pitiscus's future was much tied to Friedrich der Aufrichtige, known as Frederick IV, elector of the Palatine of the Rhine. Frederick's father died in 1583 and John Casimir, his uncle, became guardian to the ten year old Frederick. John Casimir was an ardent Calvinist and appointed Pitiscus to teach Frederick in 1584. Later Pitiscus was appointed court chaplain at Breslau and court preacher to Frederick IV. When John Casimir died in 1592, Frederick undertook the government of the Palatinate continuing his uncle's policies of hostility to the Catholic Church. Pitiscus strongly supported the Calvinist policies from a major position of influence. On 8 April 1603 Pitiscus was appointed professor of mathematics at the University of Heidelberg, succeeding Valentinus Otho who had been a pupil of Rheticus (see [6]).

H L L Bustard writes in [1]:-

Although Pitiscus worked much in the theological field, his proper abilities concerned mathematics, and particularly trigonometry.

The word 'trigonometry' is due to Pitiscus and first occurs in the title of his work *Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus* first published in Heidelberg in 1595 as the final section of A Scultetus's *Sphaericorum libri tres methodicé conscripti et utilibus scholiis expositi.* In 1600 a revised version of Pitiscus's work was published in Augsburg as *Trigonometriae sive de dimensione triangulorum libri quinque.* This work is in three sections.

The first section, divided into five books, covers plane and spherical trigonometry. In the first book he introduced the main definitions and theorems of plane and spherical trigonometry. In the second book he defined the six trigonometric functions, gave results concerning which properties of a triangle must be known in order to solve it using these trigonometric functions, and also gave techniques to construct tables of the functions. For example he shows how to construct sine tables based on a knowledge of the values of sin 45°, sin 30°, and sin 18°. The third of the five books is devoted to plane trigonometry and it consists of six fundamental theorems. Perhaps we should note that Pitiscus actually calls these 'axioms' rather than 'theorems' but they are theorems in the usual sense given with proofs. The fourth book consists of four fundamental theorems on spherical trigonometry, while the fifth book proves a number of propositions on the trigonometric functions.

The second section of the 1600 work consists of tables for all six trigonometric functions. This section has the title *Canon triangulorum sive tabulae sinuum, tangentium et secantium ad partes radii 100000* (A canon of triangles: or, the tables, of sines, tangents, and secants, the radius assumed to be 100000). The tables give the values to five or six decimal places. The third section of the work contains ten books discussing [1]:-

... problems of geodesy, measuring of heights, geography, gnomometry, and astronomy.

It was translated into English by Ralph Handson and published in 1614, and into French in 1619. A second edition of the English publication appeared in 1630, with a third edition in 1642. This edition is described as follows:-

Trigonometry: or, the doctrine of triangles. First written in Latin, by Bartholomew Pitiscus of Grunberg in Silesia, and now translated into English by Ralph Handson. Whereunto is added(for the mariners use)certain nautical questions, together with the finding of the variation of the compass. All performed arithmetically, without map, sphere, globe, or astrolabe, by the said Ralph Handson, London ...[Bound with, as issued:]A canon of triangles: or, the tables, of sines, tangents, and secants, the radius assumed to be100000.

Pitiscus was not the first to publish tables of all six trigonometric functions. Rheticus, with the help of six assistants who were funded by Emperor Maximilian II, had computed tables of all these six functions in *Opus Palatinum de triangulis* which was completed and published in 1596 by Valentinus Otho many years after Rheticus's death [1]:-

Shortly after the Opus Palatinum was published, it was found that the tangents and secants near the end of the quadrant were very inaccurate. Pitiscus was engaged to correct the tables.

First Pitiscus had to find a manuscript copy of Rheticus's tables which he did after the death of Valentinus Otho (in 1603). He recomputed all the tangents and secants between 83° and 90° to eleven decimal places and 86 pages of *Opus Palatinum de triangulis* was reprinted incorporating Pitiscus' corrections. A new edition, with new title page, was reissued in 1607. Pitiscus then began to work on a new project incorporating his own work with that of Rheticus. The *Thesaurus mathematicus* was eventually published in 1613 and contained a table of sines by Rheticus calculated for every 10'' to fifteen decimal places; a calculation of the sine at 1'' intervals for the first and last degree of the quadrant, again by Rheticus to fifteen decimal places; values for the basic sines from which the others were calculated to 22 decimal places by Pitiscus; and sines to 22 decimal places by Pitiscus for each tenth, thirtieth, and fiftieth second in the first 35 minutes.

**Article by:** *J J O'Connor* and *E F Robertson*

**August 2006**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Pitiscus.html]