The period of the Quest before Strauss is driven by the question of the miraculous/supernatural.
Strauss equated miracle with the mythic elements of the gospel materials; not historical.
Scholars in the period after Strauss bracket miracle, ruling it out of the realm of history.
E.g., Karl August Hase (1800-1890), in his The Life of Jesus (1829), is a rationalist but skeptical. He leaves open the possibility of miracle. Also, he tries to grasp the inner connection of the events of Jesus' ministry and, in so doing, "Hase created the modern historico-psychological picture of Jesus."(1) He shows a development iin Jesus' consciousness. E.g., Jesus began with Jewish messianism, but his practical experience showed this to be erroneous. Thus, he developed his own ideas. This notion of two periods of Jesus' life became the plan of all Lives of Jesus down to Johannes Weiss.
E.g., Friedrich Ernst Daniel Schleiermacher (The Life of Jesus, 1864, based on student notes from his 1832 lectures) dealt with Christology, not history. He is rationalist in the sense that he:
1. sees restoration from a trance state or supernatural restoration to life as equally valid conceptions of the resurrection
2. sees the Baptismal miracle as a subjective experience on Jesus' part (following Jn)
3. rejects the gospel reports of miracles at Jesus' birth, death, and in childhood
but, 4. he emphasizes the 4th gospel as a source v. the synoptics
Strauss, a Hegelian, sees the mythological explanation of the gospel as the synthesis of its (thesis) supernaturalistic explanation and the (antithesis) rationalistic interpretation. In his two volume work, The Life of Jesus (1835-1836):
Also by Strauss: The Christ of Faith and the Jesus of History. A Criticism of Schleiermacher's Life of Jesus (1865)
1. Albert Schweitzer, The Quest of the Historical Jesus: A Critical Study of Its Progress from Reimarus to Wrede, tr. W. Montgomery from the first German Edition, Von Reimarus zu Wrede, 1906 (A. & C. Black, 1910; New York: Macmillan, 1959), 61.