"And so Adam, in that his speech to Eve, uttered his faith in the promise made to her of her seed, and so in that respect Adam himself came in under her covenant"

In this quote, Thomas Goodwin is referring to the scriptural story of Adam and Eve. Adam's speech to Eve signifies his faith in the guarantee made to her of her seed. This promise was made by God to Eve that her descendants would be blessed and would have a special relationship with Him. Adam's speech to Eve signifies his belief in this guarantee and his acceptance of it. By accepting the guarantee, Adam is likewise coming under the covenant that God made with Eve. This reveals that Adam is willing to accept the covenant and to live by it. It likewise reveals that Adam has faith in the guarantee made to Eve and wants to follow it. This quote is a tip of the value of faith and of the power of God's pledges.