1. ～べく
* Exception: Verb する -> するべく / すべく
Explanation: Expresses the purpose of the action in the following clause, meaning “in order to / with the aim of...”. It is formal and literary, close to ～ために.
✓ It commonly occurs with volitional verbs. The person pursuing the purpose and the agent of the following action are basically understood to be the same.
✓ The following clause normally describes an action taken to achieve the purpose and is not natural with direct commands, requests, or invitations such as ～てください or ～なさい.
2. ～んがため（に）
* Exception: Verb する -> せんがため（に）
Explanation: Expresses purpose, meaning “in order to / for the purpose of...”. It is an old-fashioned, formal, literary expression and can be regarded as a formal counterpart of ～ために.
✓ It often emphasizes a purpose or intention and therefore appears in writing, speeches, or rhetorical styles; the goal itself does not have to be “grand” or “momentous”.
✓ The agent pursuing the purpose and the agent of the following action are basically the same. With する, use せんがため（に）.
3. ～をもって
Explanation: Expresses a means, method, or basis for doing something, meaning “by means of / through / with...”. It is formal and common in writing, notices, official documents, and business contexts.
✓ Compared with で, it is more formal and is generally not used for very ordinary everyday means or tools such as “go by bus” or “write with a pencil”.
✓ 「Nをもってすれば」 means “if one uses / with N...”, often evaluating that something can be accomplished with that ability, technique, means, etc.
