different between pertinacity vs firmness

English

From Middle French pertinacité, from Old French pertinace (“obstinate, stubborn”).

pertinacity (usually uncountable, plural pertinacities)

The state or characteristic of being pertinacious.
- 1846, E.A.Poe, The Black Cat
  With my aversion to this cat, however, its partiality for myself seemed to increase. It followed my footsteps with a pertinacity which it would be difficult to make the reader comprehend.
- 1851, Nathaniel Hawthorne, The House of Seven Gables, ch. 19:
  Again and again, however, and half a dozen other agains, with the inexorable pertinacity of a child intent upon some object important to itself, did he renew his efforts for admittance.

firm +? -ness

firmness (countable and uncountable, plural firmnesses)

The state of being firm
1. security; steadfastness; good grip
2. strictness; mental strength
  - France, for the first time since the death of Charlemagne, was governed by a prince of great firmness and ability.
3. physical durability; rigidness (of material)

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