Best way
Do not use duct tape, paperclips or thread.Use fishing line. Square up each end of the old and new lines and sew the fishing line by crisscrossing back and forth. This will give you flexibility to go over the sheaves but strength not to come apart. When sewing, try to pull snug so the line doesn't foul as it bends. Try it at home first by experimenting. Your boat will look 100% better with new lines, trust me. When people ask why things look better, tell them, "I lost 20 pounds, thanks for asking."