Where does “mise” come from?

I can't write this etymology because the chain provided is circular and doesn't establish a clear path from older to newer languages—it repeats "French mise" and "Latin -are" without showing progression through different languages or forms, making it impossible to construct an accurate etymology sentence. Could you provide a corrected etymological chain that shows the actual progression (for example, from Latin through Old French to Middle English to Modern English)?

mise (English): The issue in a writ of right; Expense; cost;...

Definitions

  1. The issue in a writ of right; Expense; cost;...

Ancestry of “mise”, step by step

StepLanguageWordMeaning
1Frenchmisefeminine singular of the past participle of...
2Frenchmiserto bet
3French-erForms infinitives of first-conjugation verbs
4English-erA person or thing that does an action indicated...
5Middle English-eragentive suffix; agent noun suffix
6Old French-erAlternative form of -ier, verbal suffix;...
7Latin-ārefirst conjugation
8Proto-Italic-āōForms primarily denominative verbs
9Proto-Indo-European-eh₂yétiCreates iterative/ frequentative/ intensive...
10Proto-Indo-European-yétiCreates intransitive, often deponent,...
11Proto-Indo-Europeanyé-
12Chichewaiyehe, she
Every word from Chichewa iyeEvery word from English -erEvery word from French -er