Was born after the flesh - Ishmael was born according to the course of nature, his parents being both of a proper age, so that there was nothing uncommon or supernatural in his birth: this is the proper meaning of the apostle's κατα σαρκα, after or according to the flesh, and answers to the Hebrew phrase, על דרך בשר al derec basar, according to the manner of the flesh, i.e. naturally, according to the common process of nature.

By promise - Both Abraham and Sarah had passed that age in which the procreation of children was possible on natural principles. The birth, therefore, of Isaac was supernatural; it was the effect of an especial promise of God; and it was only on the ground of that promise that it was either credible or possible.

born.

Romans 9:7,8 Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall your seed be called...

but.

Genesis 17:15-19 And God said to Abraham, As for Sarai your wife, you shall not call her name Sarai, but Sarah shall her name be...

Genesis 18:10-14 And he said, I will certainly return to you according to the time of life; and, see, Sarah your wife shall have a son...

Genesis 21:1,2 And the LORD visited Sarah as he had said, and the LORD did to Sarah as he had spoken...

Romans 4:18-21 Who against hope believed in hope, that he might become the father of many nations, according to that which was spoken...

Romans 10:8 But what said it? The word is near you, even in your mouth, and in your heart: that is, the word of faith, which we preach;

Hebrews 11:11 Through faith also Sara herself received strength to conceive seed, and was delivered of a child when she was past age...

Adoption --The Spirit and the Cry
The divinity of each of these sacred persons is also to be gathered from the text and its connection. We do not doubt tee the loving union of all in the work of deliverance. We reverence the Father, without whom we had not been chosen or adopted: the Father who hath begotten us again unto a lively hope by the resurrection of Jesus Christ from the dead. We love and reverence the Son by whose most precious blood we have been redeemed, and with whom we are one in a mystic and everlasting union: and …
Charles Haddon Spurgeon—Spurgeon's Sermons Volume 24: 1878

The Gospel Message, Good Tidings
[As it is written] How beautiful are the feet of them that preach the Gospel of peace, and bring glad tidings of good things! T he account which the Apostle Paul gives of his first reception among the Galatians (Galatians 4:15) , exemplifies the truth of this passage. He found them in a state of ignorance and misery; alienated from God, and enslaved to the blind and comfortless superstitions of idolatry. His preaching, accompanied with the power of the Holy Spirit, had a great and marvellous effect. …
John Newton—Messiah Vol. 2

How Can I Obtain Faith?
May the Spirit of God assist us while we meditate upon the way by which faith cometh. This shall be followed by a brief indication of certain obstructions which often lie in that way; and then we will conclude by dwelling upon the importance that faith should come to us by that appointed road. I. First, then, THE WAY BY WHICH FAITH COMES TO MEN. "Faith cometh by hearing." It may help to set the truth out more clearly, if we say, negatively, that it does not come by any other process than by hearing;--not …
Charles Haddon Spurgeon—Spurgeon's Sermons Volume 18: 1872