'appeasably' ultimately derives from English adjective 'appeasable', which itself comes from the verb 'appease' (from Old French 'apaissier'), the latter ultimately related to Vulgar Latin *pacāre and Latin 'pax' meaning 'peace'.

'appease' entered Middle English as 'appesen'/'appeisen' from Old French 'apaissier'; the adjective 'appeasable' formed in English with the suffix '-able', and the adverb 'appeasably' formed by adding '-ly' to the adjective.

Originally related to making or restoring 'peace' (Latin root), the sense shifted to 'pacify, placate, or satisfy' and the adverb now conveys 'in a manner that appeases or can be appeased'.