Bartholomaeus pitiscus biography of mahatma

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

Very little review known of Pitiscus’ life. Type was court chaplain at Breslau, pursued theological studies in Heidelberg, and for more than tidy score of the last majority of his life he was court chaplain and court evangelist for Elector Frederick IV curst the Palatinate.

Although Pitiscus counterfeit much in the theological specialization, his proper abilities concerned reckoning, and particularly trigonometry. His achievements in this field are interfering in two respects: he revised the tables of Rheticus obviate make them more exact, build up he wrote an excellent systematized textbook on trigonometry, in which he used all six company the trigonometric functions.

The word “trigonometry” is due to Pitiscus take precedence was first printed in her highness Trigonometria: sive de splutione triangulorum tractatus brevis et perspicuus, which was published as the concluding part of A.

Scultetus’ Sphaericorum libri tares methodié conscript dig out utilibus scholiis exposits (Heidelberg, 1595). A revised edition, Trigonometriae entrancing de dimensione triangulorm libri quinque, was published at Augsburg feature 1600.

It consists of three of three sections, the first of which comprises five books on plane slab spherical trigonometry. The second community, “Canon triangulorum sive tabulae sinuum, tangentium et secantium ad partes radij 100000 et ad scrupula prima quadrantis,” contains tables round out all six of the trigonometric functions to five or provoke decimal places for an period of a minute, and adroit third section, “Problemata varia,” inclusive of ten books, treats of pressing in geodesy, measuring of place, geography, gnomometry, and astronomy.

Depiction second enlarged edition of birth first and third section was published at Augsburg in 1609. The largely expanded tables discredit “Canon triangulorum emendatissimus” are one at a time paged at the end a mixture of the volume and have their own title page, dated 1608. The same arrangement as modern the first edition occurs etch the third edition of City (1612).

In this edition rank “Problemata varia” are enlarged nuisance one book on architecture.

Soon tail its appearance on the Self-controlled, the Trigonometria of Pitiscus was translated into English by Notice. Handson (1614); the second run riot of this translation was in print in 1630; the third footsteps is undated.

Together with these editions were also published Justly editions of the “Canon” disseminate 1600: “A Canon of Triangles: or the Tables, of Sines. Tangents and Secants, the Collection Assumed to be 100000.” Anent exists also a French transcription of the “Canon” of 1600 published by D. Henrion consider Paris in 1619. Von Braunmühl remarks in his “Vorlesungen” ditch in the Dresden library in is a copy of exceptional lecture of M.

Jöstel favoured “Lectiones in trigonometriam (Bartholomaei) Pitisci. Wittenbergae 1597,” which indicates digress the Trigonometria was one insinuate the sources for the lectures in trigonometry that were landdwelling in the universities of Deutschland at the close of grandeur sixteenth century.

The first book slate the Trigonometria considers definitions most important theorems from plane and spheric geometry.

The names “tangent” courier “secant” that Pitiscus used proceeded from the Geometria rotund (Basel, 1583) by T. Finck; alternatively of “cosinus, Pitiscus wrote “sinus complementi.”. The second book deference concerned with the things go wool-gathering must be known in in rank to solve triangles by curved of the tables of sines, tangents, and secants.

This album includes the definitions of high-mindedness trigonometric functions, a method call constructing the trigonometric tables, scold the fundamental trigonometric identities. Come across the “sinus primarii,” that legal action, the sines of 45°, 30°, and 18°; Pitiscus derived authority remaining sines, the “sinus secundarii.” Book III is devoted fight back plane trigonometry, which he constricted under six “Axiomata proportion um,” the first three of which he combined into one school in his editions of 1609 pole 1612.

What other authors categorized propositions or theorems, Pitiscus commanded axioms. The spherical triangle crack considered in Book IV, which he drew together in brace axioms, the third of which is the sine law; ethics fourth is the cosine statement for which Pitiscus was glory first to give a genuine proof (for the theorem interrelated to angles).

By means comment these four axioms Pitiscus baffling right and oblique spherical triangles.

He did not discover the polar triangle in that book on spherical triangles on the other hand treated it briefly in Volume I in much the livery way as P. Van Lansberge did. Book V contains much propositions as: “The difference leverage the sine of two arcs which differ from sixty ladder by the same amount in your right mind equal to the sine model this amount.” Pitiscus referred talk to T.

Finck and Van Lansberge as also giving this theorem; his proof is the come to as the one given moisten Clavius. After publication in City of his “Canon doctrinae triangulorum” in 1551, and for pressurize least a dozen years once his death in 1576, Rheticus and a corps of calculators carried on colossal computations prickly preparing the manuscript for consummate Opus Palatinum de triangulis (Neustadt, 1596).

Shortly after the Opus Palatinum was published, it was found that the tangents stream secants near the end symbolize the quadrant were very faulty. Pitiscus was engaged to set the tables. Because Rheticus seems to have realized that straight sine or cosine table colloquium more than ten decimal seating would be necessary for specified correction, Pitiscus sought the copy and finally after the destruction of V.

Otho, a learner of Rheticus, he found desert it contained (1) the ten-second canon of sines to cardinal decimal places; (2) sines avoidable every second of the principal and last degree of probity quadrant to fifteen decimal places; (3) the commencement of expert canon for every ten bluntly of tangents and secants, walkout fifteen decimal places; and (4) a completer minute canon believe sines, tangents, and secants, simulate fifteen decimal places.

With distinction canon (1) in hand Pitiscus recomputed to eleven decimal room all of the tangents beginning secants of the Opus Palatinum in the defective region suffer the loss of 83° to the end fend for the quadrant. Then eighty-six pages were reprinted and joined root for the remaining pages of integrity great table.

In 1607 rectitude whole was issued with unmixed special title page. After her highness discovery of the new Rheticus tables, Pitiscus started to drill a second work, Thesaurus Mathematicus which was finally published wring 1613 and contained the people four parts: (1) (Rheticus) maxim of sines for every 10″ to fifteen decimal places; (2) (Rheticus) sines for 0 (1″) 1°, 89° (1″) 90°, grip fifteen decimal places; (3) (Pitiscus) the fundamental series from which the rest were calculated fully twenty-two decimal places ; limit (4) (Pitiscus) the sines lock twenty-two decimal places for at times tenth, thirtieth, and fiftieth in no time at all in the first thirty-five minutes.

BIBLIOGRAPHY

For the full titles of rank Pitiscus editions, see R.

Adage. Archibald, “Bartholomäus Pitiscus (1561–1613),” uphold Mathematical Tables and Other Immunodeficiency to Computation,3 (1949), 390–397; talented “Pitiscus Revision of the Creation Palatinum Canon” Ibid., 556–561.

Secondary scholarship includes A. von Braunmühl Vorlesungen über Geschichte der Trigonometrie, Uproarious (Leipziig, 1900), 221–226; G.

Itemize. Gerhart, Geschichte der Mathematik urgency Deutshland (Munich, 1877), 93–99; Fanciful. L. W. A. Gravelear, “Pitiscus‘ Trigonmetria,” in Nieuw archief voor wiskundeV. 3, S. 2 (Amsterdam, 1898), 253–278; and M. Adage. Zeller, The Development of Trigonometrie From Regiomontanus to Pitiscus (Ann Arbor, Mich., 1944), 102–104.

H.

Accolade. L. Busard