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Abstract
Jacob Bernoulli's entries about mechanics in his scientific notebook, the ‘Meditationes’, reveal new facts about the history of the catenary curve. Bernoulli's analyses show that the catenaria, velaria, lintearia and elastica curves together form a family of curves, which I will refer to as the funicularia family. Attending to the history of the whole family of these curves provides remarkable insights into the origin of the catenary problem and the process of its discovery. Studying the ‘Meditationes’ together with Bernoulli's correspondence and publications shows how analysis of one curve led him to the discovery of the others. As a result, this study shows that – although Leonhard Euler is known to be the one who unified the catenary problem and the elastica problem in 1728 – Jacob Bernoulli had in fact proven the same more than thirty years earlier, providing in his notebook a general differential equation for this family of curves. Furthermore, I demonstrate Jacob Bernoulli's priority over his brother Johann in finding the velaria curve.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Correction Statement
This article has been corrected with minor changes. These changes do not impact the academic content of the article.
Notes
1 Johann reported his recollection of the discovery of the catenary curve in a letter to de Montmort on 29 September 1718 (Spiess Citation1955, 98; Peiffer Citation2006, 8). See the letter in http://ark.dasch.swiss/ark:/72163/1/0801/avS1iF1SRUKyLcmXglkrmQ9.
2 See Galilei 1638; Heß and Babin Citation2011, 100, n 17.
3 Ms UB Basel L Ia 3. The notebook consists of 367 pages; more than of the 286 entries deal with questions of mathematics and physics. The editors of Die Werke von Jacob Bernoulli decided to distribute its 286 articles among the individual volumes according to their subject matter; most of them have appeared in five different volumes over the past decades, although the mechanical notes which were supposed to appear in the sixth volume were not edited until recently. The entire ‘Meditationes’ is now integrated into the Bernoulli–Euler Online (BEOL) platform, together with normalized and diplomatic transcriptions and translations. Entries discussed in this article are available online on the BEOL platform, https://beol.dasch.swiss/; I quote them as Med. ###. Although most entries in the ‘Meditationes’ are not dated, it is possible to estimate their dates with the help of Bernoulli's publications as well as the citations they contain and the topics they address.
4 http://ark.dasch.swiss/ark:/72163/1/0801/KEHd_i=3SG2fCKMUduYdTQO, http://ark.dasch.swiss/ark:/72163/1/0801/sobTv3=LT4m_Q5MBtFA8Xwl.
9 See letter N(2,3) (Spiess Citation1955, 107).
12 See Bos' description of the choice of the progression of variables in the seventeenth-century Leibnizian calculus: (Bos Citation1974, 42–47).
17 See the note in http://ark.dasch.swiss/ark:/72163/1/0801/KL1EJfbWSCuf6_n5GlIVnwT.
27 See the equations in http://ark.dasch.swiss/ark:/72163/1/0801/a=SXQBgXRw2f0=HqBJkDxQG.
32 The manuscript is conserved at the Basel University Library: Ms UB Basel L Ia 1.
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