When Hebrews 8:10 and Hebrews 10:16 were originally written, did they say:
“my laws… write them”?
“my law… write it”?

Hebrews 8:10
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(Young’s Literal)
because this is the covenant that I will make with the house of Israel,
after those days, saith the Lord,
giving My laws into their mind,
and upon their hearts I will write them,
and I will be to them for a God,
and they shall be to Me for a people;

(Aramaic Bible in Plain English)
“But this is The Covenant that I shall give to the family of the house of Israel:
After those days, says THE LORD JEHOVAH,
I shall put my law in their minds
and upon their hearts I shall write it,
and I shall be to them a God,
and they shall be to me a people.”

Hebrews 10:16
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(NIV)
“This is the covenant I will make with them after that time, says the Lord.
I will put my laws in their hearts,
and I will write them on their minds.”
(Aramaic Bible in Plain English)
“This is the covenant that I shall give them after those days, says THE LORD JEHOVAH:
I shall put my law into their minds,
and I shall write it upon their hearts,

dukhrana.com, Peshitta tool, EBV with footnotes:
Hebrews 10:16 – “Dit is het Verbond dat Ik na die dagen aan hen geven zal, zegt de HEERE! ‘Ik zal mijn Wet in hun verstand leggen en die op hun harten schrijven,
Ik zal mijn Wet … schrijven – dit is de lezing van de Aramese Peshitta. De lezing van de Griekse NA28, MHT en TR luidt: ‘Ik zal mijn wetten in hun harten geven en Ik zal ze in hun verstand schrijven”.

translate.google.com:
Hebrews 10:16 – “This is the Covenant that I will give them after those days, says the LORD!
‘I will put my Law in their minds
and write it on their hearts,
I will write my Law … – this is the reading of the Aramaic Peshitta.
The reading of the Greek NA28, MHT, and TR reads:
‘I will put my laws in their hearts and I will write them on their minds’.

Andrew Xian Nyhärt, _The One Law Covenant: Recovering the Heart of the New Covenant_ (2025), 186pp., on 57, 61

In Hebrews 8 and 10, the writer quotes Jeremiah 31– the new covenant promise– not from the Hebrew wording but from the Greek Septuagint.
The LXX renders Jeremiah’s “_my law [torati]_” in the singular as “_my laws [tous nomous mou]_” in the plural.
Hebrews cites that Greek wording faithfully.
…
Also worth noting: Hebrews itself, outside the quotation, prefers “law” in the singular when stating the theological shift (Heb. 7:12).

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snips
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Hebrews 7:5 N-AMS
INT: according to the law this is

Hebrews 7:12 N-GMS
NAS: a change of law also.

Hebrews 7:16 N-AMS
NAS: [such] not on the basis of a law of physical

Hebrews 7:19 N-NMS
KJV: For the law made nothing

Hebrews 7:28 N-NMS
NAS: For the Law appoints men

Hebrews 7:28 N-AMS
NAS: which came after the Law, [appoints] a Son,

Hebrews 8:4 N-AMS
KJV: gifts according to the law:

Hebrews 8:10 N-AMP
GRK: Κύριος διδοὺς νόμους μου εἰς
NAS: I WILL PUT MY LAWS INTO THEIR MINDS,

Hebrews 9:19 N-AMS
INT: according to the law by Moses

Hebrews 9:22 N-AMS
INT: according to the law and apart from

Hebrews 10:1 N-NMS
KJV: For the law having a shadow

Hebrews 10:8 N-AMS
NAS: are offered according to the Law),

Hebrews 10:16 N-AMP
GRK: Κύριος διδοὺς νόμους μου ἐπὶ
NAS: I WILL PUT MY LAWS UPON THEIR HEART,
KJV: I will put my laws into their

Hebrews 10:28 N-AMS
NAS: who has set aside the Law of Moses

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“Paul, in early writings (e.g., 1 Corinthians 15:3), states he ‘received’ and passed on the doctrine that Christ died for sins”

Is 1 Cor 15:3 best rendered with:
“Christ died for our sins”?
“Christ died on account of our sins”?

1Corinthians 15:3
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(Etheridge) For I delivered to you from the first, according as I had received:
That the Meshiha died for our sins, as it is written;
(Murdock) For I delivered to you from the first, as I had received it;
that the Messiah died on account of our sins, as it is written:
(KJV) For I delivered unto you first of all that which I also received,
how that Christ died for our sins according to the scriptures;