nondiagnostic

The story

1. Proto-Indo-European*né
2. Proto-Germanic*ne
3. Proto-Indo-European*ís?
4. Proto-Indo-European*h₁óynos
5. Proto-Germanic*ainaz
6. Proto-Germanic*nainaz
7. Proto-West Germanic*nain
8. Old Englishnān
9. Middle Englishnon
10. Old Englishnān
11. Old Englishnān-
12. Middle Englishnon-
13. Englishnon-
14. Proto-Indo-European*dwóh₁
15. Proto-Indo-European*trísinflu.
16. Proto-Indo-European*dwís
17. Ancient Greekδιά (diá)
18. Ancient Greekδια- (dia-)
19. Proto-Indo-European*ǵneh₃-
20. Proto-Indo-European*ǵn̥h₃sḱéti
21. Proto-Hellenic*gignṓskō
22. Ancient Greekγῐγνώσκω (gĭgnṓskō)
23. Ancient Greekδῐαγῐγνώσκω (dĭagĭgnṓskō)
24. Ancient Greekδῐᾰ́γνωσῐς (dĭắgnōsĭs)
25. Ancient Greekδῐᾰ- (dĭă-)
26. Proto-Indo-European*ǵneh₃-
27. Proto-Indo-European*ǵneh₃tis
28. Ancient Greekγνῶσις (gnôsis)
29. Ancient Greekγνωστῐκός (gnōstĭkós)
30. Ancient Greekδῐαγνωστῐκός (dĭagnōstĭkós)
31. Englishdiagnostic
32. English todaynondiagnostic

From non- + diagnostic.