Explanation:

- The original sentence uses "were being emerged," which is incorrect because "emerge" is an intransitive verb and cannot be used in the passive voice.

- Option 1: "was emerging" – Incorrect because "was" is singular, while "many new ideas" is plural. The subject and verb don't agree in number.

- Option 2: "have emerging" – Incorrect due to improper tense usage. "Have" should not be followed by a present participle without "been."

- Option 3: "No improvement required" – Incorrect as the original phrase contains a grammatical error.

- Option 4: "emerged" – Correct: "Emerged" is the correct past tense form and fits the context where new ideas appeared in the nineteenth century.