The first equations

[Daniel Bernoulli]
[Hermann von Helmholtz]
[John William Strutt]
[Artur H. Benades]

There is nothing here at the moment,
you can consult the following chapter:
Peter L. Hoekje’s spreadsheet

Links

Arthur H. Benade: Acoustical evolution of wind instruments.
CCRMA, Stanford University: The Arthur H. Benade Archive.
Wikipedia: Arthur H. Benade.