Richter, Lehrbuch der Harmonie

Ernst Friedrich Richter was a composer who taught music theory in the Leipzig Conservatory, where his Lehrbuch der Harmonie was used for instruction. His views on the extended chords were conservative, even though his attitude toward practical harmonic theory was progressive, even radical, for the early 1850s, in that he not only adopted Weber's Roman numeral labels but specifically rejected figured bass symbols as chord labels, using them only as adjuncts to the Roman numerals (in other words, in the manner still widely used today). In the Preface (I am citing from the third edition [1860], Richter says that the study of music theory by means of thorough bass "has long since been replaced by a more rational method" (ix-x), but that he still finds them useful for instruction in voice leading.

Richter strongly emphasizes practical harmony, which works to the disadvantage of the extended tertian chords. He does not acknowledge the Ramellian heritage of these chords but instead associates them with thorough bass: "The ninth chord . . . is a vestige of the old so-called general-bass, which taught every vertical formation of tones, no matter how accidental they were, as individual chords, without bringing all these accidental formations into an orderly system, and thereby made instruction in harmony much harder and quite complex" (1860, p. 77; my translation).

He divides chords into two groups: in Part 1, basic harmonies (Grundharmonien) , in Part 2, accidental chords (Zufällige Akkordbildungen), to which are added notes foreign to the harmony (that is, passing tones and the various accented and unaccented neighbor notes). The basic harmonies are the usual triads and seventh chords of the key, and he does include a short chapter on the 9th, 11th, and 13th chords in Part 1, but like many other authors, he does so only by way of explaining that they don't really belong there. He allows the dominant ninth chord only (no ninth chords on other scale degrees) and only with preparation (see below, his Figure 157). Otherwise he places it, along with the eleventh and thirteenth chords, among suspensions and the category of "accidental chords" (these are largely the same as Kirnberger's non-essential chords—Richter even includes passing chords (Durchgehende Akkorde) in Part 2).

The views which may be entertained of the above chords are various, but they all tend to one practical result. It may be taken for granted that these are either real chords, such as the chord of seventh, in which case they must be considered and treated as such, or that they belong to the list of suspensions, [that is] occur accidentally when one or more parts remain stationary. In the first case their explanation, and especially that of their inversions, would be extremely prolix, and moreover the chords themselves would often be difficult to recognize, inasmuch as in four-part harmony one or more of their intervals must always be omitted. If, however, considered as suspensions or accidental chords, their explanation becomes very simple. In order to obtain a clear insight into their nature, we will now proceed to examine their construction, &e. 

In pure harmonic progression it is necessary that either the ninth or the root should be prepared the following example, therefore, in which both root and ninth enter freely, is objectionable on account of its [stiffness (Steifheit)] and want of connection [Verbindungslosigkeit].  (1864, p. 62) 

Finally, from Part 2, here are three suspensions involving the ninth. The first and third of these form the dominant ninth chord (1860, p. 99, from Fig. 198):

Reference:
Ernst Friedrich Richter, Lehrbuch der Harmonie (1853). The third edition (1860) was available to me. Source: IMSLP; digital facsimile of a copy in the Sibley Library, Eastman School of Music.
Ernst Friedrich Richter, Treatise on Harmony, trans. Franklin Taylor (1864). Source: Internet Archive; digital facsimile of a copy in the National Library of Scotland.