What comes after (Primary,unary),(secondary,binary),(tertiary,ternary),...?

Solution 1:

Logically it should be "quartary" because the Latin is "third" = "tertius"; "fourth" = "quartus"

In the first, we deleted the "us," hence "quartary."

I can see a 1773 publication in the search results for "quartary" that uses the word: https://books.google.com/books?id=1-UEAAAAQAAJ

Solution 2:

Here is something I was able to discover on the internet the prime time I confronted the same predicament as you.

• 1st = primary
• 2nd = secondary
• 3rd = tertiary
• 4th = quaternary
• 5th = quinary
• 6th = senary
• 7th = septenary
• 8th = octonary
• 9th = nonary
• 10th = denary
• 12th = duodenary
• 20th = vigenary.

These come from the Latin roots. The -n- ones come as well from Latin but this time are distributive adjectives, "one each, two each, etc."; they are always used in plural. They were sometimes also used in a sense roughly similar to the ordinals, which is probably why English uses them in an odd way.

1. (Singuli — single "one each")
2. Bini — binary "two each"
3. Terni/trini — ternary/*trinary
4. Quaterni — quaternary
5. Quini — quinary
6. Seni — senary
7. Septeni — septenary
8. Octoni — octonary
9. Noveni — *novenary
10. Deni — denary
11. Undeni — *undenary
12. Duodeni — duodenary
13. Terni/trini deni — *ternidenary/*tridenary