In anatomy, the muscles of the buttocks are referred to collectively as the "glut(a)eal muscles" in English, and are individually given the following Latin names: glut(a)eus maximus, glut(a)eus medius and glut(a)eus minimus.
The noun "glutaeus" does not appear to exist in Classical or Medieval Latin. The Oxford English Dictionary (OED)'s earliest citation for it in English is from 1681. The OED says the etymology of English "glut(a)eus is "< modern Latin glūtæus, glūtēus, < Greek γλουτός rump, buttock." This entry apparently was first published in 1900 and has not yet been fully updated. The American Heritage Dictionary says English glut(a)eus is from "New Latin glūteus, from Greek gloutos, buttock," omitting a macron over the E.
Neither of these dictionaries describe the morphological derivation, so I'm wondering how exactly gluteus/glutaeus was formed from γλουτός. It seems like it would have been most straightforward to latinize γλουτός as glutus. Perhaps that didn't happen because glutus was a preexisting Latin adjective meaning something else. But I don't really understand why the ending -aeus (or maybe -ēus or -eus) occurs in glutaeus.
The only idea I have is that, according to Wiktionary, Greek γλουτός had a variant neuter plural form γλουτᾰ́. So my thought is that maybe glutaeus can be analyzed as gluta + -eus. But using a neuter plural form as the base of a Latin derived adjective seems a bit dubious to me. I guess another possibility, based on the AHD's "glūteus" and the answer to my earlier question about Herculeus and its late variant form Herculaeus, is that glutaeus is simply an irregular spelling variant of glut- + the Latin adjective suffix -ĕus. But the OED entry from 1900 seems to have been written by somebody who was convinced the word was stressed on the penultimate syllable, which suggests that this syllable was thought of as having a long vowel in Latin (the OED only gives the English pronunciation as /ɡl(j)uːˈtiːəs/, although the AHD says it can be stressed on either the first or the second syllable). I wonder if the vowel came to be thought of as long just due to analogy with Latin words that ended in -aeus or -ēus for etymological reasons.
Setting aside the matter of -aeus vs. -ēus vs, -ĕus, why would an adjectival suffix be used in this context? Should I think of glutaeus/gluteus as an adjective modifying an implied substantive noun musculus? On Vicipedia, the article for the "Gluteus maximus muscle" is titled "Musculus glutaeus maximus".
I thought to do a Google search of "glutea" to see if it has been used as an adjective modifying a feminine substantive, and I found the following examples in Elsevier's Dictionary of Medicine and Biology: in English, Greek, German, Italian, and Latin, by G. Konstantinidis (2005):
Anterior gluteal line n, linea glutea anterior TA; linea glutealis anterior n
g πρόσθια γλουτιαία γραμμή f -ής
i linea glutea anteriore f
Interestingly, it looks like in Greek, the adjective derived from γλουτός has the form γλουτιαίος, which I think would correspond to Latin "glūtiaeus". But I haven't found much evidence of the Latin-alphabet spelling glutiaeus being used, although I was able to find one example of "der M. glutiaeus maximus" used in a German text (Einführung in die physikalische Anatomie, Part 3, By Hermann Triepel, 1908, p. 86-87.
I also found a text that seems to suggest glutiaeus would somehow be a better formation than glut(a)eus. Medical Greek: Collection of Papers on Medical Onomatology and a Grammatical Guide to Learn Modern Greek, by Achilles Rose (1908) contains "Memorial on the Anatomical Nomenclature of the Anatomical Society", presented at its 22nd meeting on April 22, 1908, by Dr. Hermann Triepel, Professor of Anatomy, University of Breslau. Triepel says
It is a fact established long ago that the anatomical technical language is a playground for barbarisms, ungainly words and even expressions which are an offense against elementary rules of word-formation. (p. 179)
Further are to be mentioned a number of adjectives of B N A which habe [sic] been found from Greek nouns and to which the ending eus has been attached, as carpeus, laryngeus, oasophageus [sic], etc. Here the correct ending (again according to Papaioannou) is mostly -icus (-ικος), sometimes -ius (-ιος) or -iaeus (-αιος). (p. 187)
This is followed by a list of words that Triepel thinks are "not free of objection" accompanied by "such terms which, according to my opinion, might be substituted. P., in parentheses, when added to the latter, means Papaioannou." That list includes "glutaeus glutiaeus (P.)." (p. 189).
If anyone can explain exactly why the suffix "ιαιος" apparently is considered correct in this context in Greek, I would appreciate it.