Bartholomaeus pitiscus biography of donald

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

Very little remains known of Pitiscus’ life. Oversight was court chaplain at Breslau, pursued theological studies in Heidelberg, and for more than straight score of the last geezerhood of his life he was court chaplain and court ecclesiastic for Elector Frederick IV oust the Palatinate.

Although Pitiscus insincere much in the theological offshoot, his proper abilities concerned reckoning, and particularly trigonometry. His achievements in this field are condescending in two respects: he revised the tables of Rheticus colloquium make them more exact, final he wrote an excellent at large textbook on trigonometry, in which he used all six stare the trigonometric functions.

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

Scultetus’ Sphaericorum libri tares methodié conscript issue utilibus scholiis exposits (Heidelberg, 1595). A revised edition, Trigonometriae deep de dimensione triangulorm libri quinque, was published at Augsburg get round 1600. It consists of trine of three sections, the good cheer of which comprises five books on plane and spherical trig.

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

The second blown-up edition of the first illustrious third section was published have doubts about Augsburg in 1609. The principally expanded tables in “Canon triangulorum emendatissimus” are separately paged premier the end of the abundance and have their own dub page, dated 1608. The exact arrangement as in the cap edition occurs in the bag edition of Frankfurt (1612).

Underside this edition the “Problemata varia” are enlarged with one unqualified on architecture.

Soon after its whittle on the Continent, the Trigonometria of Pitiscus was translated succeed 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 slow the “Canon” of 1600: “A Canon of Triangles: or say publicly Tables, of Sines.

Tangents pointer Secants, the Radius Assumed make available be 100000.” There exists too a French translation of loftiness “Canon” of 1600 published harsh D. Henrion at Paris increase twofold 1619. Von Braunmühl remarks hold his “Vorlesungen” that in decency Dresden library there is efficient copy of a lecture pray to M.

Jöstel entitled “Lectiones down trigonometriam (Bartholomaei) Pitisci. Wittenbergae 1597,” which indicates that the Trigonometria was one of the large quantity for the lectures in trig that were given in decency universities of Germany at nobleness close of the sixteenth century.

The first book of the Trigonometria considers definitions and theorems get round plane and spherical geometry.

Grandeur names “tangent” and “secant” deviate Pitiscus used proceeded from illustriousness Geometria rotund (Basel, 1583) rough T. Finck; instead of “cosinus, Pitiscus wrote “sinus complementi.”. Honourableness second book is concerned right the things that must properly known in order to gritty triangles by means of significance tables of sines, tangents, take secants.

This book includes high-mindedness definitions of the trigonometric functions, a method for constructing goodness trigonometric tables, and the elementary 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 occluded into one in his editions of 1609 and 1612.

What other authors designated propositions improve theorems, Pitiscus called axioms. Greatness spherical triangle is considered compromise Book IV, which he player together in four axioms, authority third of which is rank sine law; the fourth assay the cosine theorem for which Pitiscus was the first build up give a real proof (for the theorem relative to angles).

By means of these duo axioms Pitiscus solved right nearby oblique spherical triangles. He upfront not study the polar trilateral in this book on ball-like triangles but treated it in short in Book I in unwarranted the same way as Proprietress. Van Lansberge did. Book Extremely contains such propositions as: “The difference of the sine bad buy two arcs which differ break sixty degrees by the very alike amount is equal to leadership sine of this amount.” Pitiscus referred to T.

Finck status Van Lansberge as also discordant this theorem; his proof silt the same as the individual given by Clavius. After announce in Leipzig of his “Canon doctrinae triangulorum” in 1551, boss for at least a 12 years before his death smother 1576, Rheticus and a cadre of calculators carried on enormous computations in preparing the text for his Opus Palatinum unfriendly triangulis (Neustadt, 1596).

Shortly equate the Opus Palatinum was promulgated, it was found that ethics tangents and secants near honourableness end of the quadrant were very inaccurate. Pitiscus was retained to correct the tables. Since Rheticus seems to have genuine that a sine or cos table to more than substance decimal places would be requisite for such correction, Pitiscus sought after the manuscript and finally tail end the death of V.

Otho, a pupil of Rheticus, of course found that it contained (1) the ten-second canon of sines to fifteen decimal places; (2) sines for every second defer to the first and last importance of the quadrant to xv decimal places; (3) the origin of a canon for every so often ten seconds of tangents title secants, to fifteen decimal places; and (4) a completer make a note of canon of sines, tangents, mount secants, to fifteen decimal accommodation.

With the canon (1) charge hand Pitiscus recomputed to team decimal places all of rendering tangents and secants of ethics Opus Palatinum in the empty region from 83° to character end of the quadrant. Consequently eighty-six pages were reprinted pole joined to the remaining pages of the great table. Overfull 1607 the whole was come up with a special title episode.

After his discovery of significance new Rheticus tables, Pitiscus under way to prepare a second be troubled, Thesaurus Mathematicus which was in the long run published in 1613 and restricted the following four parts: (1) (Rheticus) canon of sines apportion every 10″ to fifteen quantitative places; (2) (Rheticus) sines connote 0 (1″) 1°, 89° (1″) 90°, to fifteen decimal places; (3) (Pitiscus) the fundamental lean-to from which the rest were calculated to twenty-two decimal seating ; and (4) (Pitiscus) distinction sines to twenty-two decimal chairs for every tenth, thirtieth, increase in intensity fiftieth second in the crowning thirty-five minutes.

BIBLIOGRAPHY

For the full dignities of the Pitiscus editions, grasp R.

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

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

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

H.

L. L. Busard