This can mean that Paul wants to emphasize 1) the statements that follow or 2) that this letter came from him.
## in my own handwriting ##
This can mean 1) Paul probably had a helper who wrote most of this letter as Paul told him what to write, but Paul himself wrote this last part of the letter or 2) Paul wrote the whole letter himself.
## make a good impression ##
"cause others to think well of them" or "cause others to think that they are good people"
## in the flesh ##
"with visible evidence" or "by their own efforts"
## compel ##
"force" or "strongly influence"
## so that they may not be persecuted for the cross of Christ ##
"so that the Jews will not persecute them for claiming that the cross alone is what saves"
## the cross ##
"the work Jesus did on the cross" or "the death and resurrection of Jesus." The physical cross is not meant here.
## they want ##
"those people who are urging you to be circumcised want"
## that they may boast ##
"so those who are urging you to be circumcised will have reason to boast"
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