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According to [[Hermine Hartleben]], who wrote the most extensive biography of Champollion in 1906, the breakthrough came on 14 September 1822, a few days before the ''Lettre'' was written, when Champollion was examining Huyot's copies.{{sfn|Buchwald|Josefowicz|2020|p=385}} One cartouche from [[Abu Simbel]] contained four hieroglyphic signs. Champollion guessed, or drew on the same guess found in Young's ''Britannica'' article, that the circular first sign represented the sun. The Coptic word for "sun" was ''re''. The sign that appeared twice at the end of the cartouche stood for "s" in the cartouche of Ptolemy. If the name in the cartouche began with ''Re'' and ended with ''ss'', it might thus match "Ramesses", suggesting the sign in the middle stood for ''m''. Further confirmation came from the Rosetta Stone, where the ''m'' and ''s'' signs appeared together at a point corresponding to the word for "birth" in the Greek text, and from Coptic, in which the word for "birth" was ''mise''. Another cartouche contained three signs, two of them the same as in the Ramesses cartouche. The first sign, an [[ibis]], was a known symbol of the god [[Thoth]]. If the latter two signs had the same values as in the Ramesses cartouche, the name in the second cartouche would be ''Thothmes'', corresponding to the royal name "[[Tuthmosis]]" mentioned by Manetho. These were native Egyptian kings, long predating Greek rule in Egypt, yet the writing of their names was partially phonetic. Now Champollion turned to the title of Ptolemy found in the longer cartouches in the Rosetta Stone. Champollion knew the Coptic words that would translate the Greek text and could tell that phonetic hieroglyphs such as ''p'' and ''t'' would fit these words. From there he could guess the phonetic meanings of several more signs. By Hartleben's account, upon making these discoveries Champollion raced to his brother's office at the Académie des Inscriptions, flung down a collection of copied inscriptions, cried "''Je tiens mon affaire!''" ("I've done it!") and collapsed in a days-long faint.{{sfn|Adkins|Adkins|2000|pp=180–181}}{{sfn|Robinson|2012|pp=140–142}}{{refn|The earliest version of the story of Champollion's exclamation and fainting comes from an account written by an author named Adolphe Rochas in 1856, according to which Champollion was working on notes for the ''Lettre'' when it took place. Hartleben's account is the earliest to connect the event to Huyot's inscription copies.{{sfn|Buchwald|Josefowicz|2020|pp=372, 385}}|group="Note"}}
[[File:Tableau Général des signes et groupes hieroglyphiques No 125 (color).jpg|thumb|right|Hieroglyphic and [[cuneiform]] spellings of the name of [[Xerxes I]] on the [[Caylus vase]], copied in ''Précis du système hiéroglyphique'']]
Over the next few months Champollion applied his hieroglyphic alphabet to many Egyptian inscriptions, identifying dozens of royal names and titles. During this period Champollion and the orientalist [[Antoine-Jean Saint-Martin]] examined the [[Caylus vase]], which bore a hieroglyphic cartouche as well as text in [[Persian cuneiform]]. Saint-Martin, based on the earlier work of [[Georg Friedrich Grotefend]] believed the cuneiform text to bear the name of [[Xerxes I]], a king of the [[Achaemenid Empire]] in the fifth century BC—before whose realm included Egypt. Champollion confirmed that the identifiable signs in the cartouche matched Xerxes's name, strengthening the evidence that phonetic hieroglyphs were used long before Greek rule in Egypt and supporting Saint-Martin's reading of the cuneiform text. This was a major step in the [[decipherment of cuneiform]].{{sfn|Pope|1999|pp=72–74, 100–101}}
Around this time Champollion made a second breakthrough.{{sfn|Robinson|2012|pp=148–149}} Although he counted about 860 hieroglyphic signs, a handful of those signs made up a large proportion of any given text. He also came upon a recent study of Chinese by [[Abel Rémusat]], which showed that even Chinese writing used phonetic characters extensively, and that its ideographic signs had to be combined into many [[Orthographic ligature|ligatures]] to form a full vocabulary. Few hieroglyphs seemed to be ligatures. And Champollion had identified the name of [[Antinous]], a non-royal Roman, written in hieroglyphs with no cartouche, next to characters that seemed to be ideographic. Phonetic signs were thus not limited to cartouches. To test his suspicions, Champollion compared hieroglyphic texts that seemed to contain the same content and noted discrepancies in spelling, which indicated the presence of homophones. He compared the resulting list of homophones with the table of phonetic signs from his work on the cartouches and found they matched.{{sfn|Pope|1999|pp=75–78}}{{refn|Hartleben said that according to an established "tradition" Champollion came to this realisation on his birthday, 23 December 1821. [[W. Andrew Robinson|Andrew Robinson]], author of a more recent biography, argues that this date is too early, given that the ''Lettre à M. Dacier'', written the following September, gives no indication that hieroglyphs were used phonetically outside the cartouches. Robinson suggests Champollion might instead have realised the extent of phoneticism in December 1822, when his work was more advanced.{{sfn|Robinson|2012|pp=148–149}} [[Jed Z. Buchwald]] and Diance Greco Josefowicz argue that there is no sign in the primary documents that the breakthrough came earlier than March 1823.{{sfn|Buchwald|Josefowicz|2020|p=422}}|group="Note"}}
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