There are two distinct words here:
- The noun vertebra.
- The adjective vertebralis, "related to vertebra".
The adjective is derived from the noun, and both the noun and the adjective have various different forms.
This is an important starting point and helps make sense of such Latin terms.
Adding the prefix inter- to the adjective turns it into a new adjective intervertebralis, "between vertebrae" or "inter-vertebral".
The two cases you seem to need are nominative and genitive.
There are more cases, but they seem less relevant here.
The noun vertebra is always a feminine, but the adjective takes a different form depending on the gender of the noun it modifies.
The words facies, pars, columna are feminine, canalis is masculine, and foramen is neuter.
You can check the gender of a noun in any good online Latin dictionary.
Here are the relevant singular forms:
| Type |
Nominative |
Genitive |
| Noun |
vertebra |
vertebrae |
Adjective (masculine or feminine) |
vertebralis |
vertebralis |
Adjective (neuter) |
vertebrale |
vertebralis |
And here are the plural ones for comparison:
| Type |
Nominative |
Genitive |
| Noun |
vertebrae |
vertebrarum |
Adjective (masculine or feminine) |
vertebrales |
vertebralium |
Adjective (neuter) |
vertebralia |
vertebralium |
The only possible plural is the nominative of the noun, and all singular instances you have listed are either the genitive case of the noun ("of vertebra"), the nominative case of the noun ("vertebra") or the nominative case of the adjective in any gender.
These are bold in the table above.
I listed the other ones to remind that these are an excerpt from a much bigger system.
When two forms look alike (e.g. "of a vertebra" and "many vertebrae"), context helps.
If you can infer the meaning, it helps a lot.
In vertebrae thoracicae there seems to be an adjective in the same form and they are unlikely to be both genitive if they stand alone, so they are almost certainly plural nominative.
The word order also contains hints, as typically an adjective will follow the noun.
I am not sure if this is hard rule in anatomy, but it is not in Latin in general.
For some adjectives all three genders look different, but for this one the masculine and feminine look alike.
The adjective vertebratus ("vertebrate") looks different in the three genders (m/f/n) in nominative (vertebratus/vertebrata/vertebratum) and genitive (vertebrati/vertebratae/vertebrati).
You might notice that the feminine version has the same endings as vertebra.
The same or similar endings also occur elsewhere.
For example, vertebrae is not only the singular genitive and the plural nominative but also the singular dative.
I have refrained from giving complete paradigms here.