Several theories posit ways in which the Book of Abraham text relates to the papyri. The Church of Jesus Christ of Latter-day Saints maintains that Joseph Smith translated the Book of Abraham from papyri, but they do not specify which papyri. Theories about the relationship may be categorized under three heads: Joseph Smith produced the Book of Abraham (1) from the fragments of papyri that we still have, (2) from papyri that we no longer have, or (3) without the aid of any of the Joseph Smith Papyri.
Some, both inside but more commonly outside the Church, believe that Joseph Smith produced the Book of Abraham from the remaining fragments of the Joseph Smith Papyri, specifically from the Document of Breathings Made by Isis found in Joseph Smith Papyrus XI, a different text altogether from the Book of Abraham. Proponents of this theory have yet to provide a cogent account of the connection between the two. Failure to produce a coherent explanation for the production of the Book of Abraham usually forces proponents of this theory into some version of the theory that the Book of Abraham was produced solely by inspiration.
Others have noticed that the Book of Abraham does not match any of the preserved papyri and have posited that it was translated from a portion of the papyri that has been lost. Nineteenth-century eyewitnesses, both Latter-day Saint and non-Latter-day Saint, support this theory, because they said that Joseph Smith translated the Book of Abraham from the long scroll, which does not match any of the current fragments that came from the glazed slides. Any theory, such as this one, that has Joseph Smith translating an authentic ancient text assumes that he had to have done so by divine inspiration. This theory is common in the Church.
Still others, both Latter-day Saint and non-Latter-day Saint, have thought that the Book of Abraham was not connected in any way with the Joseph Smith Papyri but was received by inspiration. The source of that inspiration differs depending on the religious preferences of the individual who holds this theory. Within the Church this seems to be the most popular of the theories.
Each theory has its proponents, but not all of the theories account equally for the historical evidence. It is worth knowing some of the problems associated with the various theories. Whichever theory one chooses to follow, one must be prepared to deal with the problems posed by the evidence that the theory cannot account for.
The theory that holds that Joseph Smith translated the Book of Abraham from the existing fragments of the Joseph Smith Papyri runs into the obvious problem that the current Joseph Smith Papyri come from either a Document of Breathings Made by Isis belonging to Horos, the son of Osoroeris, or a Book of the Dead belonging to Semminis, daughter of Eschons. It also does not match the historical evidence. The nineteenth-century eyewitnesses, both Mormon and non-Mormon, favorable and hostile to the Church, agree that the Book of Abraham was translated from a long roll of papyrus that was still a long roll in the 1840s and 1850s. The current fragments of the Joseph Smith Papyri, however, were all mounted on heavy paper and placed in glass frames in 1837. None of them can be the long roll described in the 1840s and 1850s. So these fragments are specifically not the source of the Book of Abraham according to the eyewitnesses. This poses a problem for this particular theory.
The theory that holds that Joseph Smith translated the Book of Abraham from papyri in his possession has certain advantages and difficulties. It is clear that Joseph Smith had papyri that we no longer have. Some, at least, were destroyed in the Chicago Fire of 1871. Facsimiles 2 and 3, for example, are no longer extant. It is clear from the descriptions of nineteenth-century eyewitnesses that the papyrus from which Joseph Smith translated the Book of Abraham does not match any of the existing fragments. This theory accounts for that evidence but is frustrating to many people. Because the papyri are no longer extant, there is no possible way to check Joseph Smith’s translation of the Book of Abraham.
The theory that holds that Joseph Smith received the Book of Abraham directly through revelation and not from the Joseph Smith papyri also has certain advantages and disadvantages. One advantage is that in Doctrine and Covenants section 7, Joseph Smith translated an ancient papyrus that he never had in his possession; hence, there is a precedent for Joseph Smith translating a papyrus that was not in his possession, and so there is no reason to suppose that he had to have the papyrus of the Book of Abraham in his possession either. The theory, however, also has some problems. In a discourse given on 16 June 1844, just before his death, Joseph Smith said, “I want to reason—I learned it by translating the papyrus now in my house—I learned a test. concerning Abraham & he reasoned concerng. the God of Heaven—in order to do that sd. he—suppose we have two facts that supposes that anotr. fact may exist two men on the earth—one wiser than the other—wod. shew that antr. who is wiser than the wisest may exist—intelligences exist one above anotr. that there is no end to it—if Abra. reasoned thus.” Joseph Smith prefaces a paraphrase of Abraham 3:16–19 with a statement that he “learned it by translating the papyrus now in my house,” and ends by saying that it is Abraham’s reasoning. This quotation supports the theories that he translated the Book of Abraham from papyri that he had in his possession, but seems to be the only statement from Joseph Smith on the subject other than the preface to the published Book of Abraham that it was “A Translation of some ancient Records that have fallen into our hands from the catacombs of Egypt” that presumably Joseph Smith authored. The quotation, however, comes from fragmentary and incomplete notes of a sermon Joseph Smith gave and thus the evidence is not as solid as might be desired.
Given our current state of knowledge, the theory that Joseph Smith translated the Book of Abraham from papyri that we no longer have accounts for the most evidence with the fewest problems. Even so, for none of the theories is the evidence as neat or as compelling as one might wish.
But while it is impossible to directly compare the Book of Abraham with the papyri from which Joseph Smith translated it, another way of testing the Book of Abraham is available. One can compare the Book of Abraham with what is known of Abraham’s time and place, and thereby situate the book in its ancient historical context.
 Joseph Smith, discourse 16 June 1844, in Words of Joseph Smith, 380 (Thomas Bullock version).