-86, 206-211.

[9] Vieta, _Opera math._ (Leiden, 1646); Marie, _Hist. des sciences
math._ iii. 27 seq. (Paris, 1884).

[10] Kluegel, _Math. Woerterb._ ii. 606, 607.

[11] Kaestner, _Gesch. d. Math._ i. (Goettingen, 1796-1800).

[12] But see _Les Delices de Leide_ (Leiden, 1712); or de Haan,
_Mess. of Math._ iii. 24-26.

[13] For minute and lengthy details regarding the quadrature of the
circle in the Low Countries, see de Haan, "Bouwstoffen voor de
geschiedenis, &c.," in _Versl. en Mededeel. der K. Akad. van
Wetensch._ ix., x., xi., xii. (Amsterdam); also his "Notice sur
quelques quadrateurs, &c.," in _Bull. di bibliogr. e di storia delle
sci. mat. e fis._ vii. 99-144.

[14] It is thus manifest that by his first construction Snell gave
an approximate solution of two great problems of antiquity.

[15] _Elementa trigonometrica_ (Rome, 1630); Glaisher, _Messenger of
Math._ iii. 35 seq.

[16] See Kiessling's edition of the _De Circ. Magn. Inv._
(Flensburg, 1869); or Pirie's tract on _Geometrical Methods of
Approx. to the Value of [pi]_ (London, 1877).

[17] See Euler, "Annotationes in locum quendam Cartesii," in _Nov.
Comm. Acad. Petrop._ viii.

[18] Gergonne, _Annales de math._ vi.

[19] See _Vera Circuli et Hyperbolae Quadratura_ (Padua, 1667); and
the _Appendicula_ to the same in his _Exercitationes geometricae_
(London, 1668).

[20] _Penny Cyclop._ xix. 187.

[21] See Sherwin's _Math. Tables_ (London, 1705), p. 59.

[22] See W. Jones, _Synopsis Palmariorum Matheseos_ (London, 1706);
Maseres, _Scriptores Logarithmici_ (London, 1791-1796), iii. 159
seq.; Hutton, _Tracts_, i. 266.

[23] See _Hist. de l'Acad._ (Paris, 1719); 7 appears instead of 8 in
the 113th place.

[24] _Comment. Acad. Petrop._ ix., xi.; _Nov. Comm. Ac. Pet._ xvi.;
_Nova Acta Acad. Pet._ xi.

[25] _Introd. in Analysin Infin._ (Lausanne, 1748), chap. viii.

[26] _Mem. sur quelques proprietes remarquables des quantites
transcendantes, circulaires, et logarithmiques._

[27] See Legendre, _Elements de geometrie_ (Paris, 1794), note iv.;
Schloemilch, _Handbuch d. algeb. Analysis_ (Jena, 1851), chap. xiii.

[28] _Nova Acta Petrop._ ix. 41; _Thesaurus Logarithm. Completus_,
633.

[29] On the calculations made before Shanks, see Lehmann, "Beitrag
zur Berechnung der Zahl [pi]," in _Grunert's Archiv_, xxi. 121