Abstract
The treatise «Preliminary Knowledge for Those Seeking the Quadrature and Rectification of the Circle» («Vorläufige Kenntnisse für die, so die Quadratur und Rectification des Circuls suchen») was written in 1766 and published in 1770 as part of the second of the three volumes entitled Contributions to the Use of Mathematics and Its Application (Beyträge zum Gebrauche der Mathematik und deren Anwendung).
Twenty-two years I have been trying to find the fixed point. [...] The same thing happens to me with the quadrature of the circle, which I have been so close to finding, that I do not know, nor can I conceive, how I do not already have it in my pocket.
—Miguel de Cervantes, The Dialogue of the Dogs.
[T]he pursuit of mathematics is a divine madness of the human spirit.
—Alfred North Whitehead, Science and the Modern World.
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Notes
- 1.
The original version can be consulted at http://www.kuttaka.org/~JHL/L1770a.html.
- 2.
Lambert (1770, p. [II]).
- 3.
Klein (1897, pp. 55, 78).
- 4.
Ferreirós (2015, p. 218).
- 5.
Arndt et al. (2001, p. 7).
- 6.
- 7.
- 8.
cf. Dunn et al. (2014).
- 9.
cf. Boistel (2016, pp. 66–67, 446). For a guide on how to use the quadrant, see http://www.meridienne.org/atelier/instruments/quartier-reduction/utilisation/ (accessed on 26 March 2024).
- 10.
- 11.
- 12.
- 13.
cf. Heath (1897, p. 93).
- 14.
cf. Knorr (1993, pp. 153–155).
- 15.
cf. Van Ceulen (1615, p. 163). Because of the accuracy of this approximation, \(\pi \) was for a long time known as the «Ludolphian number» (Ludolphsche Zahl), especially in German-speaking territories, and in fact there are still people today who know it by this designation, cf. Arndt et al. (2001, p. 183).
- 16.
The original version can be consulted at http://www.kuttaka.org/~JHL/L1770a_3.pdf (accessed on 26 March 2024).
- 17.
Lambert (1765–1766/1770, p. 82), cf. Bauer (2005).
- 18.
Unger (1829, pp. 326–327).
- 19.
- 20.
- 21.
- 22.
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Dorrego López, E., Fuentes Guillén, E. (2024). Lambert, the Circle-Squarers and \(\pi \): Introduction to Lambert’s Vorläufige Kenntnisse. In: Irrationality, Transcendence and the Circle-Squaring Problem. Logic, Epistemology, and the Unity of Science, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-031-52223-9_2
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