1: εὔχομαι
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(Strong's #2172 — Verb — euchomai — yoo'-khom-ahee )

is rendered "to wish" in Acts 27:29 (RV marg., "prayed"); so Romans 9:3; in 2—Corinthians 13:9; 3—John 1:2 , RV, "pray:" see PRAY.

2: βούλομαι
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(Strong's #1014 — Verb — boulomai — boo'-lom-ahee )

in Mark 15:15 , RV, is translated "wishing" (AV, "willing"); so 2—Peter 3:9; in Acts 25:22 , RV, could wish" (AV, "would"). See WILL , C, No. 2.

3: θέλω
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(Strong's #2309 — Verb — thelo — )

in 1—Corinthians 16:7 , RV, is translated "wish" (AV, "will"); Galatians 4:20 , "I could wish" (AV, "I desire"). See WILL , C, No. 1.