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The tensile strength of ropes used on a boat are much more h'gher than the loads. 12.5 mm rope has a tensile stregth of at least 10.000 lbs. This value can decrease as much as 50% depend'ng on the knot used. The expected load on any corner of a sail is not more than 2000 lbs. This means you have at least a safety factor of two including knotting.
The main factor for rope diameter is the handling properties. A thin ropewill be difficult to handle.