Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 

 

Notes


Journal: Math. Comp. 3 (1948), 222-225
DOI: https://doi.org/10.1090/S0025-5718-48-99538-6
Full-text PDF Free Access

References | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] A. E. Kennelly, ``Gudermannians and Lambertians with their respective addition theorems,'' Amer. Phil. Soc., Proc., v. 68, 1929, p. 179. The well-known formula given here on p. 183, namely: $ \operatorname{lam} 2\omega = 2{\tanh ^{ - 1}}(\tan \omega )$, was intended in the 1909 edition of G. F. Becker & C. E. Van Orstrand, Smithsonian Mathematical Tables. Hyperbolic Functions, with $ g{d^{ - 1}}2\omega $ for $ \operatorname{lam} 2\omega $, p. xv (see MTAC, v. 2, p. 311).
  • [2] Samata Sakamoto, Tables of Gudermannian Angles and Hyperbolic Functions, Tokyo, 1934, p. 14-94.
  • [3] A. Cayley, ``On the orthomorphosis of the circle into the parabola,'' Quart. Jn. Math., v. 20, 1885, p. 220; also in Coll. Math. Papers, v. 12, 1897, p. 336.
  • [4] E. W. Hobson, A Treatise on Plane Trigonometry. Cambridge, 1891, and second ed., 1897, p. 316; third ed., 1911, fourth ed., 1918, and fifth ed., 1921, p. 336.
  • [5] M. Boll, Tables Numériques Universelles, Paris, 1947, p. 487.
  • [6] L. Potin, Formules et Tables Numériques . . . Paris, 1925, p. 450-494.
  • [7] V. Vassal, Nouvelles Tables donnant avec cinq Décimales . . . Paris, 1872, p. [67]-[111].
  • [8] A. Forti & O. F. Mossotti, ``Tavole dei logaritmi delle funzioni circolari ed iperboliche,'' filling the whole of Annali delle Università Toscane, Pisa, v. 6, 1863, 4to; Forti's part of the work consists of the tables on [228] unnumbered pages, and the introduction, p.27-48; table of $ u$, p. [183-228]. This is preceded by Mossotti's ``Teoria ed applicazioni delle funzioni circolari ed iperboliche,'' p. 7-26 + plate. In 1863 this work seems to have been published separately at Pisa with the following title: Tavole dei Logaritmi delle Funzioni Circolari ed Iperboliche, precedute dalla Storia e Teoria delle Funzioni stesse e da Applicazioni. Second ed., Tavole di Logaritmi dei Numeri e delle Funzioni Circolari ed Iperboliche, precedute dalla Storia e Teoria delle Iperboliche, da Applicazioni, e da altre Tavole di Uso Frequente. Turin, Florence, Milan, Paravia & Co., 2 v., 1870; third ed., Turin and Rome, 1877, 584 p.
  • [9] K. Hayashi, Fünfstellige Funktionentafeln . . . Berlin, 1930, p. 2-19.
  • [10] J. B. Dale, Five-Figure Tables of Mathematical Functions, London, 1903, p. 67.
  • [11] G. Greenhill, The Applications of Elliptic Functions, London, 1892, p. 16. French ed., Paris, 1895, p. 569.
  • [12] L. M. Milne-Thomson & L. J. Comrie, Standard Four-Figure Mathematical Tables, London, 1931, p. 208.
  • [13] W. Hall, Tables and Constants to Four Figures, Cambridge, 1905, p. 48-49.
  • [14] C. Gudermann, ``Potenzial- oder cyklisch-hyperbolische Functionen,'' Jn. f. d. reine u. angew. Math., v. 7, 1831, p. 72-96, 176-200; v. 8, 1832, p. 64-116; v. 9, 1832, p. 362-378. Reprinted in Theorie der Potenzial- oder cyklisch-hyperbolischen Functionen, Berlin, 1833, p. 159-260, 337-350.
  • [15] L. Potin, Formules et Tables Numériques, Paris, 1925, p. 496-595.
  • [16] The Société d. Sciences Physiques et Naturelles de Bordeaux, Mémoires, v. 4; Cahier 2, 1866, contains the first edition complete, lxxi, [64], 2 p. of J. Hoüel, Recueil de Formules et de Tables Numériques, printed at Paris by Gauthier-Villars. On the title page of this first edition appears also ``Extrait des Mémoires de la Soc. d. Sci. phys. et nat. de Bordeaux.'' The table in which we are interested occurs on p. [36]-[55]. Second ed., a reprint, Paris, 1868; third ed., 1885; third ed. reprinted, 1901; third ed. rev. and corrected, 1927.
  • [17] G. H. Chandler, Elements of the Infinitesimal Calculus. Third ed. rewritten, New York, 1907, p. 298.
  • [18] E. Halley, ``An easie demonstration of the analogy of the logarithmick tangents to the meridian line or sum of the secants: with various methods for computing the same to the utmost exactness,'' R. Soc. London, Phil. Trans., v. 19, no. 219, Jan.-Feb. 1695/6, p. 202-214; the v. is dated 1698. Also in his Miscellanea Curiosa, second ed., v. 2, 1708, p. 20-36; and third ed., v. 2, 1723, p. 20-36.


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-48-99538-6
Article copyright: © Copyright 1948 American Mathematical Society