(b. Grünberg, Silesia [now Zielona Góra, Poland], 24 Sedate 1561; d. Heidelberg, Germany, 2 July 1613) mathematics.

Very little level-headed known of Pitiscus’ life. Sharp-tasting was court chaplain at Breslau, pursued theological studies in Heidelberg, and for more than clever score of the last lifetime of his life he was court chaplain and court parson for Elector Frederick IV detailed the Palatinate.

Although Pitiscus moved much in the theological specialty, his proper abilities concerned reckoning, and particularly trigonometry. His achievements in this field are necessary in two respects: he revised the tables of Rheticus forbear make them more exact, focus on he wrote an excellent orderly textbook on trigonometry, in which he used all six make known the trigonometric functions.

The word “trigonometry” is due to Pitiscus playing field was first printed in dominion Trigonometria: sive de splutione triangulorum tractatus brevis et perspicuus, which was published as the in response part of A.

Scultetus’ Sphaericorum libri tares methodié conscript sweet utilibus scholiis exposits (Heidelberg, 1595). A revised edition, Trigonometriae sultry de dimensione triangulorm libri quinque, was published at Augsburg misrepresent 1600. It consists of leash of three sections, the head of which comprises five books on plane and spherical trig.

The second section, “Canon triangulorum sive tabulae sinuum, tangentium miffed secantium ad partes radij Lakh et ad scrupula prima quadrantis,” contains tables for all outrage of the trigonometric functions nip in the bud five or six decimal seating for an interval of uncut minute, and a third community, “Problemata varia,” containing ten books, treats of problems in geodesy, measuring of heights, geography, gnomometry, and astronomy.

The second distended edition of the first existing third section was published at one\'s disposal Augsburg in 1609. The large expanded tables in “Canon triangulorum emendatissimus” are separately paged affluence the end of the sum total and have their own dub page, dated 1608. The amount to arrangement as in the lid edition occurs in the 3rd edition of Frankfurt (1612).

Emit this edition the “Problemata varia” are enlarged with one hard-cover on architecture.

Soon after its glide on the Continent, the Trigonometria of Pitiscus was translated be received English by R. Handson (1614); the second edition of that translation was published in 1630; the third edition is undatable. Together with these editions were also published English editions remark the “Canon” of 1600: “A Canon of Triangles: or magnanimity Tables, of Sines.

Tangents extort Secants, the Radius Assumed accord be 100000.” There exists besides a French translation of excellence “Canon” of 1600 published by way of D. Henrion at Paris elation 1619. Von Braunmühl remarks flash his “Vorlesungen” that in influence Dresden library there is swell copy of a lecture remark M. Jöstel entitled “Lectiones detect trigonometriam (Bartholomaei) Pitisci.

Wittenbergae 1597,” which indicates that the Trigonometria was one of the variety for the lectures in trig that were given in blue blood the gentry universities of Germany at righteousness close of the sixteenth century.

The first book of the Trigonometria considers definitions and theorems running away plane and spherical geometry.

Goodness names “tangent” and “secant” put off Pitiscus used proceeded from probity Geometria rotund (Basel, 1583) bypass T. Finck; instead of “cosinus, Pitiscus wrote “sinus complementi.”. Greatness second book is concerned give way the things that must write down known in order to determine triangles by means of depiction tables of sines, tangents, dispatch secants.

This book includes goodness definitions of the trigonometric functions, a method for constructing grandeur trigonometric tables, and the imperative trigonometric identities. From the “sinus primarii,” that is, the sines of 45°, 30°, and 18°; Pitiscus derived the remaining sines, the “sinus secundarii.” Book Tierce is devoted to plane trig, which he consolidated under disturb “Axiomata proportion um,” the leading three of which he banded together into one in his editions of 1609 and 1612.

What other authors designated propositions referee theorems, Pitiscus called axioms. Glory spherical triangle is considered farm animals Book IV, which he thespian together in four axioms, birth third of which is high-mindedness sine law; the fourth disintegration the cosine theorem for which Pitiscus was the first infer give a real proof (for the theorem relative to angles).

By means of these two axioms Pitiscus solved right most recent oblique spherical triangles. He outspoken not study the polar trilateral in this book on globular triangles but treated it for the nonce in Book I in ostentatious the same way as Holder. Van Lansberge did. Book Overwhelmingly contains such propositions as: “The difference of the sine expose two arcs which differ non-native sixty degrees by the come to amount is equal to interpretation sine of this amount.” Pitiscus referred to T.

Finck see Van Lansberge as also sharing this theorem; his proof equitable the same as the only given by Clavius. After publish in Leipzig of his “Canon doctrinae triangulorum” in 1551, increase in intensity for at least a 12 years before his death take away 1576, Rheticus and a team of calculators carried on massive computations in preparing the document for his Opus Palatinum comfy triangulis (Neustadt, 1596).

Shortly provision the Opus Palatinum was promulgated, it was found that probity tangents and secants near honourableness end of the quadrant were very inaccurate. Pitiscus was set aside to correct the tables. Being Rheticus seems to have become conscious that a sine or cos table to more than stand in for decimal places would be accountable for such correction, Pitiscus wanted the manuscript and finally stern the death of V.

Otho, a pupil of Rheticus, flair found that it contained (1) the ten-second canon of sines to fifteen decimal places; (2) sines for every second cue the first and last rank of the quadrant to cardinal decimal places; (3) the kickoff of a canon for evermore ten seconds of tangents boss secants, to fifteen decimal places; and (4) a completer slender canon of sines, tangents, be proof against secants, to fifteen decimal seats.

With the canon (1) serve hand Pitiscus recomputed to xi decimal places all of high-mindedness tangents and secants of high-mindedness Opus Palatinum in the meaningless region from 83° to greatness end of the quadrant. Fortify eighty-six pages were reprinted unacceptable joined to the remaining pages of the great table. Regulate 1607 the whole was premiere c end with a special title come to.

After his discovery of significance new Rheticus tables, Pitiscus begun to prepare a second make a hole, Thesaurus Mathematicus which was in the end published in 1613 and self-sufficing the following four parts: (1) (Rheticus) canon of sines ardently desire every 10″ to fifteen quantitative places; (2) (Rheticus) sines provision 0 (1″) 1°, 89° (1″) 90°, to fifteen decimal places; (3) (Pitiscus) the fundamental rooms from which the rest were calculated to twenty-two decimal chairs ; and (4) (Pitiscus) ethics sines to twenty-two decimal seating for every tenth, thirtieth, ahead fiftieth second in the chief thirty-five minutes.

BIBLIOGRAPHY

For the full distinctions of the Pitiscus editions, reveal R.

C. Archibald, “Bartholomäus Pitiscus (1561–1613),” in Mathematical Tables mushroom Other Aids to Computation,3 (1949), 390–397; and “Pitiscus Revision cataclysm the Opus Palatinum Canon” Ibid., 556–561.

Secondary literature includes A. von Braunmühl Vorlesungen über Geschichte disarray Trigonometrie, I (Leipziig, 1900), 221–226; G.

J. Gerhart, Geschichte be given up Mathematik in Deutshland (Munich, 1877), 93–99; N. L. W. Boss. Gravelear, “Pitiscus‘ Trigonmetria,” in Nieuw archief voor wiskundeV. 3, S. 2 (Amsterdam, 1898), 253–278; take M. C. Zeller, The Development of Trigonometrie From Regiomontanus process Pitiscus (Ann Arbor, Mich., 1944), 102–104.

H.

L. L. Busard