The story of how Oxygen was discovered was super interesting and involved all of these methods.

Argon is an interesting one. A comparison between chemically synthesised nitrogen and ‘pure’ nitrogen extracted from the air (with the oxygen, carbon dioxide and water removed) revealed a discrepancy:

https://en.wikipedia.org/wiki/Argon#History

https://www.youtube.com/watch?v=loqudG71uBM (Chemistorian, noble gases)

Wow. Pre that discovery what did they think explained phonomenon like snuffing out a candle. Or blowing air on a fire.