Question: The "ninth chord" that Rameau, Kirnberger, Marpurg or Koch (inter alia) discuss during the 18th century is the chord formed by a triad and an added ninth, and its explanation is always through a "chord of supposition", i.e., the supposed root is a third above the lowest note of the chord, since chords that spanned more than an octave were not "acceptable"

70-80 years laters, in harmony treatises like Reber or Richter (around 1850) the dominant ninth chord has earned its status as dissonant chord along with the seventh, and it is considered as a dominant 7 plus a third, its root being the root of the dominant seventh. Furthermore, diminished and half diminished seventh chords are now considered as a dominant ninth without its fundamental.

My question is: who was the first theoretician that considered this chord as an acceptable entity, and placed it side by side with the triad and the seventh chords? Who started thinking about chords as a stack of thirds that could exceed the octave? Who was the first to propose that diminished and halfdim chords are rootless dominant ninths?

Any help would be much appreciated.

Answer: 
In addition to Reber and Richter that you mention, I know that Fétis (1844), Durand (1881), and Dubois (1889, 1921) also discussed ninth chords.

But the earliest theorist that I know of, not including theorists like Sorge that fall into the fundamental-bass camp with Rameau and Marpurg (it was this group, by the way, that claimed that diminished chords were incomplete dominant ninths), would be Charles-Simon Catel (1773–1830). His *Traité d'harmonie* of 1804 was actually the official harmony textbook of the Paris Conservatory (of which Catel was a founding member).

Believe it or not, Catel actually claimed that a single ninth chord was the source of all harmony (!). He vaguely justifies it with the opening pitches of the harmonic series, but mostly it's just a pedagogical tool that he uses: chords that are a part of this ninth chord are "natural," and chords that are not found within the ninth chord are "artificial."

[![enter image description here](https://i.stack.imgur.com/cMMbH.png)](https://i.stack.imgur.com/cMMbH.png)

And Catel's work is especially important because it was really the forerunner to Fétis's own treaty, which would be the single most influential French text on harmony in the nineteenth century.

Lastly, it should be noted that many viewed Catel's work as a bastardization of Rameau's treatise; they felt that Catel was too invested in "third-stacking" to be musically helpful.
It first gained common usage in the late baroque, its origin was through intervallic supposition and accidental harmonic forms.