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In DOI: 10.4236/ahs.2020.94019 235 Advances in Historical Studies, p.234 D’Alembert and the Wave Equation: Its Disputes and Controversies, or https://www.scirp.org/pdf/ahs_2020112716312281.pdf p.6 of 11

A. R. E. Oliveira states

Euler criticized d’Alembert’s work pointing out that the two arbitrary functions ϕ and ψ are determined by the initial conditions of the problem: ... which represent the initial form of the curve and the distributions of initial velocities

but he does not give a specific reference. He does list 5 Euler references--only 1 in English. My questions are: Which is the source which contains this assertion by Euler and is there an English translation?

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  • $\begingroup$ See if this is it (ref. to English translation given in the question): hsm.stackexchange.com/questions/7214/… $\endgroup$
    – Michael E2
    Nov 21, 2023 at 16:00
  • $\begingroup$ On p. 3 of the english translation Euler states "will not be necessary to consider the velocities of each point of the chord, which simplifies the solution tremendously." so ??? $\endgroup$
    – user45664
    Nov 21, 2023 at 18:04
  • $\begingroup$ Sorry, I just realized you asked the question I linked. The reference to Euler is from Riemann (1867) fn. 3. @Ziegler answered your earlier question, that it was D'Alembert (1747) para. XIII, not Euler, who incorporated the integral term. Isn't that correct? $\endgroup$
    – Michael E2
    Nov 21, 2023 at 19:07
  • $\begingroup$ since in the english translation p.3 Euler states "will not be necessary to consider the velocities of each point of the chord, which simplifies the solution tremendously." I am confused. $\endgroup$
    – user45664
    Nov 23, 2023 at 19:03
  • $\begingroup$ My motivation: The velocity IC is the key to removal of the backward wave in Huygens Principle (see my nature.com/articles/s41598-021-99049-7 ) so it is very important. $\endgroup$
    – user45664
    Nov 23, 2023 at 19:12

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