solvable

adj

Etymology: From solve + -able. Piecewise doublet of soluble. More information The mathematical senses derive from Galois theory: Galois discovered that one could determine whether a given polynomial could be solved by radicals by studying the properties of a particular group attached to a particular field extension deriving from the polynomial in question; if the group satisfies some conditions then polynomial can be solved by radicals. Any group meeting these conditions — whether or not it arises from this process — is thus called solvable, as is any field extension giving rise to such a group. The Lie-theoretic sense is by analogy, the study of Lie algebras deriving much of its terminology from group theory. In regular use by the late 19th century.

1. Capable of being solved.

   “a solvable problem”

   “1677, Matthew Hale, The Primitive Origination of Mankind, London: William Shrowsbery, “De homine,” Chapter 2, p. 56, Intellective Memory, which I call an act of the intellective faculty because it is wrought by it, though I do not inquire how or where, because it is not solvible:”

2. Capable of being solved.
3. Capable of being solved.
4. Capable of being solved.
5. Capable of being solved.
6. Capable of being dissolved or liquefied.

   “1664, John Chandler (translator), Van Helmont’s Works, London: Lodowick Lloyd, A Treatise of Fevers, Chapter 8, p. 971, […] they administer Pearles, and Corrals being beaten to dust or dissolved in distilled vinegar, or the juice of limons, and again dryed, and solvable in any potable liquour:”

7. Able to pay one's debts.

   “[…] although imprisonment was imposed by law on persons not solvable, yet officers were unwilling to cast them into goale,”

   “The Government is solvable in case of Loss, whereas private Men often fail;”

8. Capable of being paid and discharged.

   “solvable obligations”