Arcing is a tool for following and documenting the flow of thought in the Biblical text. In brief, arcing involves dividing the text into its propositions and then noting the logical relationship between the propositions.
A proposition is an assertion, or statement, that affirms or denies something. For example, the sentence "I am not ashamed of the gospel, for it is the power of God unto salvation for all who believe" in Romans 1:16 has two propositions:
16a: I am not ashamed of the gospel,
16b: for it is the power of God unto salvation for all who believe
After dividing the text into its propositions, the next step is to record the relationship between them. There are about 16 different logical relationships that are possible. In this case, the "for" indicates that 16b is the ground of 16a: The reason Paul is not ashamed of the gospel is because it is the power of God.
Another type of relationship is that of inference, which we see exemplified in Galatians 5:1:
1a: It was for freedom that Christ set us free,
1b: therefore keep standing firm
In this example, 1b is an inference from 1a: Since Christ set us free "for freedom," we should consequently keep standing firm.
All of the various logical relationships, as well as the mechanics of how to do arcing, are covered very well in the following resources:
- Tom Schreiner, Interpreting the Pauline Epistles, chapter 6
- John Piper, "Biblical Exegesis: Discovering the Meaning of Scriptural Texts" (116KB PDF)