Background

Bartholomaeus Pitiscus was born on August 24, 1561, in Grunberg, Silesia (now Zielona Gora, Poland), then a part of the Austrian-ruled Duchy of Glogau (Głogów). He was born into a poor family, no further details of which are known.

Education

Pitiscus studied theology, first at Zerbst, then at Heidelberg.

Career

Pitiscus was a court chaplain at Breslau, pursued theological studies in Heidelberg, and for more than a score of the last years of his life he was court chaplain and court preacher for Elector Frederick IV of the Palatinate. Although Pitiscus worked much in the theological field, his proper abilities concerned mathematics, and particularly trigonometry.

The word “trigonometry” is due to Pitiscus and was first printed in his Trigonometria: sine de solutione triangulorum tractatus brevis et perspicuus, which was published as the final part of A. Scultetus’ Sphaericontm libri tres methodice conscripti et utilibus scholiis expositi (Heidelberg, 1595). A revised edition, Trigonometriae sive de dimensiorte triangulorum libri quinque, was published at Augsburg in 1600. It consists of three sections, the first of which comprises five books on plane and spherical trigonometry.

The second section, “Canon triangulorum sive tabulae sinuum, tangentium et secantium ad partes radij 100000 et ad scrupula prima quadrantis,” contains tables for all six of the trigonometric functions to five or six decimal places for an interval of a minute, and a third section, “Problemata varia,” containing ten books, treats of problems in geodesy, measuring of heights, geography, gnomometry, and astronomy. The second enlarged edition of the first and third section was published at Augsburg in 1609. The largely expanded tables in "Canon triangulorum emendatissimus” are separately paged at the end of the volume and have their own title page, dated 1608. The same arrangement as in the first edition occurs in the third edition of Frankfurt (1612). In this edition the “Problemata varia" are enlarged with one book on architecture.

Soon after its appearance on the Continent, the Trigonometria of Pitiscus was translated into English by R. Handson (1614); the second edition of this translation was published in 1630; the third edition is undated. Together with these editions were also published English editions of the “Canon” of 1600: “A Canon of Triangles: or the Tables, of Sines, Tangents and Secants, the Radius Assumed to be 100000.” There exists also a French translation of the “Canon” of 1600 published by D. Henrion at Paris in 1619. Von Braunmiihl remarks in his “Vorlesungen” that in the Dresden library there is a copy of a lecture of M. Jostel entitled “Lectiones in trigonometriam (Bartholomaei) Pitisci. Wittenbergae 1597,” which indicates that the Trigonometria was one of the sources for the lectures in trigonometry that were given in the universities of Germany at the close of the sixteenth century.

After his discovery of the new Rheticus tables, Pitiscus started to prepare a second work. Thesaurus Mathematicus, which was finally published in 1613.

Achievements

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  Pitiscus' achievements in the field of mathematics are important in two respects. First, he revised the tables of Rheticus to make them more exact, and second, he wrote an excellent systematic textbook on trigonometry, in which he used all six of the trigonometric functions.
  
  Also, Pitiscus achieved recognition with his influential work written in Latin, called Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus (1595, first edition printed in Heidelberg), which introduced the word "trigonometry" to the English and French languages, translations into which had appeared in 1614 and 1619, respectively.
  
  The lunar crater Pitiscus is named in his honor.

Works

More photos

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  • Bartholomaei Pitisci Grunbergensis Silesij Trigonometriae siue, De dimensione triangulorum libri quinque 1612
  • Iohannis Rosini Antiquitatum romanarum corpus absolutissimum 1743
  • Sinuum, tangentium et secantium canon manualis accomodatum ad trigonometriam 1613
  • Lexicon latinobelgicum novum 1771
  • Canon triangulorum emendatissimus, et ad usum accomodatissimus pertinens ad trigonometriam Bartholomaei Pitisci Grunbergensis Silesii 1612
  • Trigonometriae siue. De dimensione triangulorum libri quinque. Problematum variorum. ... libri decem. trigonometriae sub iuncti, ad, vsum eius demonstrandum 1600

Religion

In his religious affiliation, Pitiscus was a Calvinist, studying Calvinist theology, and he remained a staunch proponent of this form of Christianity throughout his life.

Views

The first book of the Pitiscus’ Trigonometria considers definitions and theorems from plane and spherical geometry. The names “tangent” and “secant” that Pitiscus used proceeded from the Geometria rotundi (Basel, 1583) by T. Finck; instead of “cosinus,” Pitiscus wrote “sinus complementi.”

The second book is concerned with the things that must be known in order to solve triangles by means of the tables of sines, tangents, and secants. This book includes the definitions of the trigonometric functions, a method for constructing the trigonometric tables, and the fundamental trigonometric identities. From the “sinus primarii,” that is, the sines of 45°, 30°, and 18°; Pitiscus derived the remaining sines, the “sinus secundarii.”

Book III is devoted to plane trigonometry, which he consolidated under six “Axiomata proportionum,” the first three of which he combined into one in his editions of 1609 and 1612.

What other authors designated propositions or theorems, Pitiscus called axioms. The spherical triangle is considered in Book IV, which he drew together in four axioms, the third of which is the sine law; the fourth is the cosine theorem for which Pitiscus was the first to give a real proof (for the theorem relative to angles). By means of these four axioms, Pitiscus solved right and oblique spherical triangles.

He did not study the polar triangle in this book on spherical triangles but treated it briefly in Book I in much the same way as P. Van Lansberge did. Book V contains such propositions as: “The difference of the sine of two arcs which differ from sixty degrees by the same amount is equal to the sine of this amount.” Pitiscus referred to T. Finck and Van Lansberge as also giving this theorem; his proof is the same as the one given by Clavius.

Because Rheticus seems to have realized that a sine or cosine table to more than ten decimal places would be necessary for such correction, Pitiscus sought the manuscript and finally after the death of V. Otho, a pupil of Rheticus, he found that it contained (1) the ten-second canon of sines to fifteen decimal places; (2) sines for every second of the first and last degree of the quadrant to fifteen decimal places; (3) the commencement of a canon for every ten seconds of tangents and secants, to fifteen decimal places; and (4) a complete minute canon of sines, tangents, and secants, to fifteen decimal places. With the canon (1) in hand, Pitiscus recomputed to eleven decimal places all of the tangents and secants of the Opus Palatinum in the defective region from 83° to the end of the quadrant. Then eighty-six pages were reprinted and joined to the remaining pages of the great table.

Quotations: "And how admirable and rare an ornament, O good God, is mildenesse in a divine? And how much is it to be wished in this age, that all divines were mathematicians? that is men gentle and meeke."

References

• LEXIKON BEDEUTENDER MATHEMATIKER
  1990
• Dictionary of Scientific Biography
  1975
• The development of trigonometry from Regiomontanus to Pitiscus
  1946