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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Math. Comp. 3 (1949), 549-561 Request permission
    J. Stirling, Methodus Differentiate, London, 1730, p. 58; English transl, by F. Holliday, London, 1749, p. 51. K. F. Gauss, Werke, v. 3, Göttingen, 1866, p. 413. John Chapman, the publisher, at whose home George Eliot resided Jan. 8 to March 24, 1851. Adriaan van Roomen (or Adrianus Romanus), Ideae mathematicae pars prima, sive methodus polygonorum. Louvain and Antwerp, 1593. In preliminary material Roomen has (i) “lectori philomathi” in which he has words of praise for 15 of the principal mathematicians of his time (including Rheticus and Valentin Otho), and (ii) a letter written by Rheticus in 1568 to Petrus Ramus (1515-1572), telling not only of his great tabular calculations but also of such works as the following which he planned to publish: (a) Observation of Phenomena; (b) German astronomy; (c) Natural Philosophy; (d) Foundations of Chemistry. See H. Bosmans, “Romain (Adrien),” Biogr. Nationale . . . de Belgique. Brussels, v. 19, 1907, col. 855; also A. Müller,$^{23}$ p. 40. J. J. C. F. de LaLande, “Lettre sur tables de sinus extrêmement rares,” Jn. des Sçavans, Paris, Sept., 1771, p. 579-584. The Rheticus-Pitiscus Thesavrvs Mathematicvs, 1613. A. G. Kästner, Geschichte der Mathematik. Göttingen, v. 1, 1796, p. 561f, 590f; v. 2, 1797, p. 368. C. Hutton, Mathematical Tables: containing Common, Hyperbolic, and Logistic Logarithms. . . . To which is prefixed a large and original history of the discoveries and writings relating to those subjects. . . . London, 1785, p. 9-11; also in his Tracts on Mathematical and Philosophical Subjects. V. 1, London, 1812, p. 290-293. Jean Bernoulli, “Analyse de l’Opus palatinum de Rheticus & du Thesaurus mathematicus de Pitiscus,” Akad. d. Wissen., Berlin, Nouveaux Mémoires, 1786, p. 10-33. J. B. Delambre, “Rapport sur les grandes tables trigonométriques décimales du cadastre,” Acad. d. Sci., Paris, Mémoires, Sci. Math, et Phys., v. 5, 1804, p. 56-66. G. C. F. Riche de Prony, “Éclaircissemens sur un point de l’histoire des tables trigonométriques,” Acad. d. Sci., Mémoires, Sci. Math. et Phys., v. 5, 1804, p. 67-93. J. B. Delambre, Histoire de l’Astronomie Moderne, v. 2, Paris, 1820, p. 1-127: “Grandes tables trigonométriques en nombres naturels—Rheticus." A. DeMorgan, “Rheticus,” Penny Cycl., v. 19, 1841, also The English Cycl., Biography, v. 5, London, 1857. A. DeMorgan, “On the almost total disappearance of the earliest trigonometrical canon,” RAS, Mo. Not., v. 6, 1845, p. 221-228; reprinted with an addition in Phil. Mag., s. 3, v. 26, 1845, p. 517-526. A. DeMorgan, (i) “Table” in Supplement to the Penny Cycl., v. 2, London, 1846, p. 596-597, 599-600. (ii) “Table,” English Cycl., Arts and Sci. Sect., v. 7, 1861, cols. 984, 988-989. J. C. Poggendorff, Biogr.-Literar. Handwörterbuch, v. 2, Leipzig, 1863. J. W. L. Glaisher, Report of the Committee on Mathematical Tables, London, 1873, p. 43-45. F. Hipler, “Die chorographie des Joachim Rheticus. Aus dem Autographon des Verfassers mit einer Einleitung herausgegeben,” Z. Math. Phys., Hist.-literar. Abth., v. 21, 1876, p. 125-150. R. Wolf, Geschichte der Astronomie. Munich, 1877, p. 204f, 236f, 242f, 296, 343f. Allgemeine deutsche Biographie, Leipzig, v. 14, 1881, p. 93-94: “Joachim, G.” by K. C. Bruhns; v. 28, 1889, p. 388-390; “Rheticus, G. J.” by S. Günther. Leopold Prowe, Nicolaus Coppernicus. Berlin, 2 v., 1883-1884; v. 1, Das Leben, v. 2, Urkunden. “For the biography of Copernicus and the social history of his times the book is extremely valuable, but Prowe’s judgment in scientific matters was unreliable” (E. Rosen). M. Curtze, 1. “Zur Biographie des Rheticus,” Altpreussische Monatsschrift, v. 31, 1894, p. 491-496. This article contains an extract from a Munich library ms., Codex latinus Monacensis no. 24101, written by Johannes Prätorius (1537-1616), inventor of the plane table used in surveying, who was professor of mathematics at the University of Wittenberg 1571-1576, and professor at the University of Altdorf from 1576 until his death. In this ms. we are told that in Aug. 1573 Otho, then mathematician for the landgrave of Hesse, came to his patron Prätorius with two notable approximations for $\pi$: (a) $3.1415926537 > \pi > 3.14159265365$, published by Vieta 20 years later, in 1593; (b) 355/113, which is correct to 6D. The latter he had derived from the approximations 377/120, found by Ptolemy, and 22/7 given by Archimedes, by subtractions of numerators and denominators. This is the earliest sure date for discovery of this approximation. This statement is made with full knowledge of the attribution of this result to: (a) the fifth Century Chinese astronomer Tsu Ch’ung-Chih by Y. Mikami, The Development of Mathematics in China and Japan (Abh. z. Gesch. d. math. Wissen., Heft 30). Leipzig, 1913, p. 50; and (b) Adriaen Anthonisz (1527-1607) about 1583 by his son Adriaen Metius in his Arithmeticae libri duo et geometriae VI, 1626, p. 51. 2. “Die abgekürzte Multiplication,” Z. Math. Phys., hist.-literar. Abt., v. 40, 1895, p. 7-13. Abridged multiplication and mss. of Rheticus are here discussed. The names of Otho, Pitiscus and Werner, among others, also come up. K. Hunrath, “Des Rheticus Canon doctrinae triangulorum und Vieta’s canon mathematicus,” Abh. z. Gesch. d. Math., v. 9, 1899, p. 211-240. M. Cantor, Vorlesungen über Geschichte der Mathematik. V. 2, second ed., Leipzig, 1900, p. 472-475, 600-603, etc. A. von Braunmühl, Vorlesungen über Geschichte der Trigonometrie. Leipzig, v. 1, 1901, p. 140-149, 158-160, 212-226. (Das Opus Palatinum and Pitiscus), etc.; v. 2, 1903, 7 index references. Johann Werner (1468-1528) of Nuremberg, astronomer and meteorologist, De triangulis sphaericis libri quatuor. Edited by A. A. Björnbo; De Meteoroscopiis libri sex, cum prooemio G. J. Rhetici. Cracow 1557. Edited by J. Würschmidt. Abh. z. Gesch. d. Math. Wissen., v. 24, 1907, 1913. Adolf Müller, “Der Astronom und Mathematiker Georg Joachim Rheticus,” Vierteljahrsschrift für Geschichte und Landeskunde Vorarlbergs, n. s., v. 2, 1918, p. 5-46. Valuable collection and study of material about the life of Rheticus. “Vorarlberger an in- und ausländischen Hochschulen vom Ausgange des XIII. bis zur Mitte des XVII. Jahrhunderts,” Forschungen zur Geschichte Vorarlbergs und Liechtensteins, v. 1, 1920, p. 58, 128-130. Franz Haefele, “Zur Frage der Herkunft des Astronomen Georg Joachim de Porris,” Schriften des Vereines für Geschichte des Bodensees und seiner Umgebung, Heft 55, Friedrichshafen a.B., 1927, p. 122-137. Some new material. Martin Bilgeri, Das Vorarlberger Schrifttum, und der Anteil des Landes am deutschen Geistesleben. Vienna and Leipzig, 1936. “Georg Joachim, genannt Rheticus, der grosse Astronom und Mathematiker,” p. 64-70. Nothing original. Johannes Kepler, Gesammelte Werke, herausgegeben von Max Caspar, v. 1, Munich, 1938; Rheticus, Narratio prima, tenth edition, p. 88-131. Edward Rosen, Three Copernican Treatises: The Commentariolus of Copernicus, The Letter against Werner, The Narratio prima of Rheticus, translated with Introduction and Notes. New York, Columbia Univ. Press, 1939. Admirable work. Introduction: “Georg Joachim Rheticus,” p. 4-6; “The Narratio Prima,” p. 9-11. Text of “Narratio Prima,” p. 107-196, eleventh ed. Ernst Zinner, Entstehung und Ausbreitung der Coppernicanischen Lehre. Zum 200-jährigen Jubiläum der Friedrich-Alexander-Universität zu Erlangen. Phys.-medizin. Soz. z. Erlangen, Sitz., v. 74, 1943. Very many references to Rheticus in the index.
  • R. C. Archibald, Bartholomäus Pitiscus (1561–1613), Math. Tables Aids Comput. 3 (1949), 390–397. MR 28245, DOI 10.1090/S0025-5718-1949-0028245-1
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  • © Copyright 1949 American Mathematical Society
  • Journal: Math. Comp. 3 (1949), 549-561
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