Isaiah - Hebrew
Isaiah 28:16
Therefore, thus said the Lord Jehovah: `Lo, I am laying a foundation in Zion, A stone -- a tried stone, a corner stone precious, a settled foundation, He who is believing doth not make haste. (YLT)
Assuredly, Thus says the Lord GOD: "Behold, I will found in Zion, stone by stone, [a]a tower of precious cornerstones[a] exceedingly firm; he who trusts will not fear. (NJPS)
[a-a] meaning of Hebrew uncertain
The meaning in the Hebrew is difficult. There is a repetition of words אבן אבן which the NJPS treats as stone by stone. The meaning of בּחן פּנּת יקרת, tried corner precious is uncertain, but implies a third stone. The words of YHVH after Behold and before he who trusts begin and end with the same word: מוּסּד... יסּד. This is a type of inclusio effectively setting this statement from what follows.
Isaiah - Greek LXX
Isaiah 28:16 (LXX)
Therefore thus say the Lord, See, I will lay for the foundations of Zion a precious, choice stone, a highly valued cornerstone for its foundations, and the one who believes in him will not be put to shame
διὰ τοῦτο οὕτως λέγει κύριος ἰδοὺ ἐγὼ ἐμβαλῶ εἰς τὰ θεμέλια Σιων λίθον πολυτελῆ ἐκλεκτὸν ἀκρογωνιαῖον ἔντιμον εἰς τὰ θεμέλια αὐτῆς
καὶ ὁ πιστεύων ἐπ᾽ αὐτῷ οὐ μὴ καταισχυνθῇ
The LXX understands the words stone by stone as a single stone, precious, choice, highly valued as a cornerstone. It makes the repetition of the singular foundation as plural and in doing so makes the stone plural by implication. A precious stone will be the cornerstone of each foundation.
The LXX deviates from the Hebrew in this approach, but there is a certain historical justification for this line of reasoning. The passage is admittedly difficult. One way to understand the meaning is to look at what actually happened. After the return from the Babylonian captivity the Temple had been rebuilt: one foundation had been laid. Nevertheless, the prophecy was not completely fulfilled. The glorious restoration described in 28:17-29 was still future and there must be another foundation to come.
Isaiah - NT
The LXX is a translation of the Hebrew. With respect to the position the Bible is from God, the inspired words were Hebrew, not Greek. When an OT passage is used in the NT, this falls in the category of inspired interpretation. That is, the Greek words interpret the meaning of the Hebrew. Passages where the Hebrew is uncertain are made clear by the use in the NT.
The primary sense of the Hebrew is one of stones plural not stone singular.
Peter and Paul both cite this passage from Isaiah.
1 Peter 2:6
For it stands in Scripture: “Behold, I am laying in Zion a stone, a cornerstone chosen and precious, and whoever believes in him will not be put to shame.”
διότι περιέχει ἐν γραφῇ ἰδοὺ τίθημι ἐν Σιὼν λίθον ἀκρογωνιαῖον ἐκλεκτὸν ἔντιμον καὶ ὁ πιστεύων ἐπ᾽ αὐτῷ οὐ μὴ καταισχυνθῇ
Romans 9:33
as it is written, “Behold, I am laying in Zion a stone of stumbling, and a rock of offense; and whoever believes in him will not be put to shame.”
καθὼς γέγραπται ἰδοὺ τίθημι ἐν Σιὼν λίθον προσκόμματος καὶ πέτραν σκανδάλου καὶ ὁ πιστεύων ἐπ᾽ αὐτῷ οὐ καταισχυνθήσεται
Both used the same passage; both agree verbatim in beginning and end; both place different emphasis what the stone accomplishes.
Agreement
Behold I am laying in Zion a stone
Included Omitted
Peter: a cornerstone chosen and precious of stumbling and a rock of offense
Paul: of stumbling and a rock of offense a cornerstone chosen and precious
Agreement
and whoever believes in him will not be put to shame
The fact neither used the entire passage does not mean misuse. Each only cited what was relevant to the point they were making. Paul, writing about those who did not believe, cited that aspect of the rock; Peter, writing to about those who believe, cited the other aspect of the rock.
Paul's identification of the stone is nothing like what is described in 28:16. Arguably, Paul understood one of the stones as that in Isaiah 8:14.
Isaiah 8
13 But the LORD of hosts, him you shall honor as holy. Let him be your fear, and let him be your dread. 14 And he will become a sanctuary and a stone of offense and a rock of stumbling to both houses of Israel, a trap and a snare to the inhabitants of Jerusalem. 15 And many shall stumble on it. They shall fall and be broken; they shall be snared and taken.”
Both Paul and Peter understand and interpret the Hebrew text which has reads אבן אבן literally stone stone. Each interpret Isaiah's repetition of the word by describing a different aspect of a stone. The same foundation which is a tested stone, a precious cornerstone is the stone Isaiah spoke of earlier, a stone of stumbling and a rock of offense.