Butt the two ends of the lines together. Using nylon thread and a needle sew them together. Real simple sewing. Tie a knot in the end of the thread stick the needle through the line a 1/4" from the end and then through the other line 1/4" from the end. Keep doing this until you have worked your way around the line. The stitches should be loose enough so the ends don't touch (so it can bend around the sheave)

If the mast is down in your backyard 4-5 stitches is enough. If you are going to have to climb a mast if it breaks 20-25 is better, 50 if it's a tall mast