The Septuagint

[Spyridon]

This is Flavius Josephus in his preface to Antiquities of the Jews:

I found, therefore, that the second of the Ptolemies was a king who was extraordinarily diligent in what concerned learning, and the collection of books; that he was also peculiarly ambitious to procure a translation of our law, and of the constitution of our government therein contained, into the Greek tongue. Now Eleazar the high priest, one not inferior to any other of that dignity among us, did not envy the forenamed king the participation of that advantage, which otherwise he would for certain have denied him, but that he knew the custom of our nation was, to hinder nothing of what we esteemed ourselves from being communicated to others. Accordingly, I thought it became me both to imitate the generosity of our high priest, and to suppose there might even now be many lovers of learning like the king; for he did not obtain all our writings at that time; but those who were sent to Alexandria as interpreters, gave him only the books of the law, while there were a vast number of other matters in our sacred books. They, indeed, contain in them the history of five thousand years; in which time happened many strange accidents, many chances of war, and great actions of the commanders, and mutations of the form of our government. Upon the whole, a man that will peruse this history, may principally learn from it, that all events succeed well, even to an incredible degree, and the reward of felicity is proposed by G-d; but then it is to those that follow his will, and do not venture to break his excellent laws: and that so far as men any way apostatize from the accurate observation of them, what was practical before becomes impracticable and whatsoever they set about as a good thing, is converted into an incurable calamity.
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And this is from the Talmud:

???R. Judah said: When our teachers permitted Greek, they permitted it only for a scroll of the Torah???. This was on account of the incident related in connection with King Ptolemy, as it has been taught: ???It is related of King Ptolemy that he brought together seventy-two elders and placed them in seventy-two rooms, without telling them why he had brought them together, and he went in to each one of them and said to him, Translate for me the Torah of Moses your master.
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It would seem that the original Septuagint was only a translation of the Torah, rather than the Hebrew Scriptures in its entirety.

[Dawid]

Correct. This is also borne out by text critical examination of the text, as well as an ancient Samaritan tradition. (though, after that the Samaritan tradition gets really goofy. The seventy translators were put in seventy separate rooms, translating individually, and all came out with identical versions which reflected the Samaritan tradition, even though most of them were not Samaritans. Sounds like something I read in Eusebius. lol.)
But yeah, the other books were translated later by various translators, no one is really certain when or by whom. There are guesses based on morphology, but that's form criticism stuff that I don't really believe in. I think that the best way to tell would be by comparing the TN"K text with later books that were translated into Greek. The Apocrypha could really help here. We could see translation styles and maybe tell how it developed, etc. I'm sure this has been done somewhere, but I don't know where.