Is 「～べくして」 related to 「～べき」 / 「～べく」?

Question

How I understand it, ～べく, meaning "for the purpose of..." / "In order to....", is the conjunctive form of ～べき, which indicates something that should be done.

• たくさん本を読む べき (you should read many books)

• エンジニアになる べく 一生懸命勉強した (I studied hard in order to become an engineer)

In the following example sentence, is the べくして related grammatically or semantically to ～べき or ～べく?

起こる べくして 起こった事故だった。 It was an accident waiting to happen.

Answer 1

Rikaichan writes べくして as 可くして and translates it as

(uk) as it is bound to (happen)/following the natural course

(uk) though possible as it may be

which is derived from べく / ～べき, which are written as 可く / ～可き, respectively.