'Under the Law' in the Bible

Moved by the Spirit, Simeon came into the Temple Courts, and, when the parents brought in the child Jesus, to do for him what was customary under the Law,

And that, in union with him, every one who believes in him is absolved from every sin from which under the Law of Moses you could not be absolved.

Indeed, under the Law, almost everything is purified with blood; and, unless blood is shed, no forgiveness is to be obtained.

First come the words-- 'Thou dost not desire, nor dost thou take pleasure in, sacrifices, offerings, burnt offerings, and sacrifices for sin' (offerings regularly made under the Law),