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References
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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).
Samata Sakamoto, Tables of Gudermannian Angles and Hyperbolic Functions, Tokyo, 1934, p. 14-94.
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.
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.
M. Boll, Tables Numériques Universelles, Paris, 1947, p. 487.
L. Potin, Formules et Tables Numériques . . . Paris, 1925, p. 450-494.
V. Vassal, Nouvelles Tables donnant avec cinq Décimales . . . Paris, 1872, p. [67]-[111].
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.
K. Hayashi, Fünfstellige Funktionentafeln . . . Berlin, 1930, p. 2-19.
J. B. Dale, Five-Figure Tables of Mathematical Functions, London, 1903, p. 67.
G. Greenhill, The Applications of Elliptic Functions, London, 1892, p. 16. French ed., Paris, 1895, p. 569.
L. M. Milne-Thomson & L. J. Comrie, Standard Four-Figure Mathematical Tables, London, 1931, p. 208.
W. Hall, Tables and Constants to Four Figures, Cambridge, 1905, p. 48-49.
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.
L. Potin, Formules et Tables Numériques, Paris, 1925, p. 496-595.
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.
G. H. Chandler, Elements of the Infinitesimal Calculus. Third ed. rewritten, New York, 1907, p. 298.
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
- © Copyright 1948 American Mathematical Society
- Journal: Math. Comp. 3 (1948), 222-225
- DOI: https://doi.org/10.1090/S0025-5718-48-99538-6