Does anyone know the language?
Joanni is the Latin dative case of Joannes (=John), and Nicolao is the Latin dative case of Nicolaus (=Nicholas), so if they're found together like this somewhere, then I'd guess Latin for the language with a very strong certainty.
The dative case is used for indirect objects, i.e. the recipient or beneficiary of an action. It is usually expressed in English using the preposition "to", so Joanni Nicolao is more specifically "to John Nicholas".
A link to the record would be helpful.
Would anyone know what "Mathildam Catharinam" translates into. I think these are the Catholic Church's religious names they are given as children when they are baptized, I think? Anyway a good guess by me would be Mathilda Catharine.
This is the Latin form. The records are from Roman Catholic parish registers.
Some priests were better at their Latin than others. Matilda Catharine for this one.
The Wiki has several Latin to English name lists. https://www.familysearch.org/en/wiki/England_Latin_Versions_of_Given_Names_(National_Institute)
Mathildam is the Latin accusative case of Mathilda, and Catharinam is the Latin accusative case of Catharina.
Accusative case marks the direct object of a verb. Modern English expresses this by the order of words within a sentence. (In "the cat sees the dog", the dog is the direct object, while in "the dog sees the cat", the cat is the direct object.) The only place where English still preserves an accusative case is in pronouns. (In "he sees her", she is the direct object; in "she sees him", he is the direct object.)
There's no easy way to express in English the difference between Latin Mathildam Catharinam and Mathilda Catharina; the latter would be the form used if she were doing something, while the former is the form used if something is being done to her. (In this case, the "something" is probably baptism.)
Catharinam could also be Katharina, Katherine, etc. Early Classical Latin had no letter K and it was not unusual for later church record makers to substitute C for K. Hence Karl could be written Carl or Carol among other variants.
I'm not completely sure but my guess would be that Johannis Engel was born on 3 Apr 1746 in Diemerstein, Kaiserslautern, Rheinland-Pfalz, Deutschland and he married on 10 Jan 1782 to Elisabetha Katherina Koch, born on 22 dec 1762 in Goddelau, Gross-Gerau, Hessen, Germany.
@Margreet, Johannis is the genitive case of Latin Johannes (=John). Genitive case is usually expressed in English as a possessive, so Johannis = "John's".
@dontiknowyou, all of those different spellings are still the same name. The concept of naming a child "Kate, not Katherine" is very, very modern; before the mid-20th century, if you told the parish priest that your name was Kate (or Cathy, or Kathryn, or ...), he'd automatically translate that into the language he was writing (i.e. Latin) and write down Kat(h)arina or Cat(h)arina, depending on how/where he learned his Latin. Even sticking to a single language -- especially if that was English -- didn't set anything in stone about the spelling of your name; if the census enumerator was in the habit of writing Catherine, then all of the Kates and so on in the district would get recorded as Catherine.
Thank you-all for your comments.
@Julia Szent-Györgyi There's also a set of baptisms in Gibraltar where the mother's name has been entered as Catalina, presumably from Kathleen, although the woman in question appears in most records as Katherine, so we presume she went by Kathy, Katy or Kate. The couple were Irish, which led me to learn that Yolande is (or was at the time) Spanish for Ireland, something I'd never considered before.