Albert Barnes Commentary 1 Corinthians 10:18

"Behold Israel after the flesh: have not they that eat the sacrifices communion with the altar?" — 1 Corinthians 10:18 (ASV)

Behold Israel. Look at the Jews. The purpose here is to illustrate the point he was establishing, by referring to the fact that among the Jews those who partook of the same sacrifices were regarded as one people, and as worshipping one God. So, if they partook of the sacrifices offered to idols, they would also be regarded as fellow worshippers of idols with them.

After the flesh. See Romans 4:1. The phrase "after the flesh" denotes the Jews who were not converted to Christianity—the natural descendants of Israel, or Jacob.

Are not they which eat of the sacrifices? A portion of the sacrifices offered to God was eaten by the offerer, and another portion by the priests. Some portions of the animal, such as the fat, were burned; and the remainder, unless it was a holocaust (or whole burnt-offering), was then the property of the priests who had officiated, or of the persons who had brought it (Exodus 29:13, 22; Leviticus 3:4, 10, 15; 4:9; 7:3, 4; 8:26).

The right shoulder and the breast were the parts which were assigned to the priests; the remainder belonged to the offerer.

Partakers of the altar? Worshippers of the same God. They are united in their worship and are regarded as such. And in like manner, if you partake of the sacrifices offered to idols and join with their worshippers in their temples, you will be justly regarded as united with them in their worship and partaking with them in their abominations.