This is part one of my rebuttal(s) to the long essay at the LDS Topic site, called "Translation and Historicity of the Book of Abraham". I am extremely busy at the moment, so please be patient with further responses.
I follow my earlier format of claims first, and then the facts.
“Neither the Lord nor Joseph Smith explained the process of translation of the book of Abraham, but some insight can be gained from the Lord’s instructions to Joseph regarding translation. In April 1829, Joseph received a revelation for Oliver Cowdery that taught that both intellectual work and revelation were essential to translating sacred records. It was necessary to “study it out in your mind” and then seek spiritual confirmation. Records indicate that Joseph and others studied the papyri and that close observers also believed that the translation came by revelation.” (from the essay)
“I commence the translation of some of the characters or hieroglyphics, and much to our joy found that one of the rolls contained the writings of Abraham.” (History of the Church, Vol. 2, p. 236 – July 1835).
“[July, 1835] -- The remainder of this month I was continually engaged in translating an alphabet to the Book of Abraham, and arranging a grammar of the Egyptian language as practiced by the ancients.” (History of the Church, Vol. 2, p. 238).
“October 1 [, 1835] -- This afternoon labored on the Egyptian alphabet, in company with Brothers O. Cowdery and W. W. Phelps, and during the research, the principles of astronomy as understood by Father Abraham...” (Ibid, p. 286)
“November 17, 1835 -- Exhibited the alphabet of the ancient records, to Mr. Holmes, and some others” (Ibid, p. 316).
“The record of Abraham and Joseph, found with the mummies, is beautifully written upon papyrus, with black, and a small part red, ink or paint, in perfect preservation.” (History of the Church, Vol. 2, p. 348—possibly attributed to Cowdery).
“...no more than 56 cm of papyrus can be missing from the scroll’s interior. Shortly after the papyri were recovered by the LDS Church, Klaus Baer estimated the original length of the Hôr scroll to have been 150–155 cm. He arrived at this estimate by comparing the text to other copies of the Document of Breathing, particularly Papyrus Louvre... Baer’s estimate for the length of papyrus missing from the scroll’s interior, starting from the left edge of the innermost extant fragment, is 14+35+0.5+16+0.5=59 cm. This agrees remarkably well with the 56 cm obtained from our winding analysis. … The ultimate success of any existing or future theory will depend on its ability to account for all of the evidence, including the fact that there was simply no room on the papyrus for anything besides the Breathing text.”
We have literal translations of each facsimile which are printed in every copy of the BoA in the Pearl of Great Price. If Smith translated these directly, as the notations provide in each member’s copy, and they almost entirely do not match scholarly translations, then the essay is wrong. We can test the translation against the published text because a direct relationship between them exists.