I'm going over the derivation of the catenary presented in Hugh Neill's Teach Yourself Calculus, Ex. 21.3.2, p. 287 (See scanned pages below).
Could anyone confirm that the below line is correct, and if so how it works?
(P. 288, second image below)
It seems to be implying that T/δs = T, but shouldn't T/δs be closer to ∞?
(T + δT)sin(Ψ+δΨ)-TsinΨ=wδs
Expanding the left hand side and dividing by δs,
(T + δT/δs)sinΨcosδΨ+(T+δT)cosΨ(sinδΨ/δs)-TsinΨ=w