The deuterocanonical books, treated as part of the Bible by the Orthodox and Catholic churches, are accepted because they appear in the Septuagint. However, they are excluded from the Jewish Bible, the Tanakh (and are therefore also excluded by most (all?) Protestant Christians). Given that the Septuagint was a Jewish publication, why does it contain books which are not part of the Tanakh?
In Judaism the final decision of which writings (Ketuvim, the third part of the Tanakh) were canonical did not happen until at least the end of the 1st century CE. This was after Christianity and Judaism had largely split, and so the two groups made different decisions about which writings were accepted as canonical.
In particular, nascent Rabbinic Judaism made the decision to only include writings which were originally written in Hebrew (possibly with parts in Aramaic), but not books which were originally written in Greek (or thought to have been originally written in Greek). The deutorocanonical books are roughly the books which were popular among the Greek speaking Jewish diaspora in the 1st century, but were excluded from the writings on the basis of their being written in Greek (and possibly also excluded for other reasons). Around the same time nascent Rabbinic Judaism also rejected using the Septuagint in favor of only using the original Hebrew texts.
(A key search term to find more to read on this topic is the "Council of Jamnia," which is the name of the hypothetical council which made the decision on canonizing the Ketuvim. The hypothesis that there was an actual council is no longer particularly popular, instead people tend to think it was a more gradual process, nonetheless the name is still useful for finding material on the topic.)
The Greek translation of Jewish scripture (the Septuagint) occurred between the 3rd and 1st centuries BCE. The canon of the Tanakh was finalized hundreds of years later. The Christian canon was debated from the 4th to the 16th centuries. We have a tendency of thinking of the Bible as written in stone, so to speak, but the canon has been the object of scholarly debate and change for millennia. Catholic and Orthodox Bibles are generally based on the Septuagint, whereas Protestant Bibles are based on the Masoretic (the authoritative Hebrew text of the Jewish Bible), which was developed between the 7th and 10th centuries CE.
The Tenakh was not a book but a collection of scrolls from which Jewish scribes translated into Greek. What most likely began with the Torah (original LXX: 5 Books of Moses) continued over 200 years. During this period of time additional scrolls were written in Hebrew (e.g. Books of Maccabees, Jesus Sirach, Judith, Tobith) and then translated. Some may have found more acceptance, others less. They were read, copied, translated, allowed by some, forbidden by others, valued and forgotten. One can assume (for the 1st century A.D.: The closer to Jerusalem, Temple and Saducees, the less prevalent these later (non-Torah) texts were. In Greek translation they had a longer lifespan and wider distribution (in the synagogues of diaspora), and even more so after the Greek-speaking churches grew more and more and the Rabbis emphasized on the Hebrew text to clearer separate Jewish from Christian beliefs (and followers).
The answer for the question what texts (scrolls) the Greek scriptures (later named Septuagint) comprised, depends largely on the time and location one asks for.
Obviously the Greek translation of the 7 books in question, means they had to be translated from something. The Greek wasn't translated from the Greek. These also were written in Hebrew. The dead sea scrolls prove this. Also the New Testament refers over 350 times to the Old Testament and 300 of those references are from the 7 books in question. So obviously the Jews in Israel at the time of Christ, used these 7 books. The truth is that there was an agenda in place by the Jews and later by the Protestants for not including these 7 books.
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