Trapezoidal, actually. But the square sails were called square sails. Lateen or square could be referred to as yards.
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They were referred to as "four-cornered" sails.
The triangular sail was invented beginning in the 16th century. They were first seen in the Mediterranean as single yarded lateen sails.
I'm not an expert, but I believe you can sail closer to the wind with a lateen-rigged sail than with square sails.
Lateen Sails
The lateen sail was invented around 100.
Triangular-shaped sails helped catch wind from the sides and rear.
It cannot be known for sure -probably in many place at roughly the same time. They have been known for more than 5,000 years.
Square sails are not truly square but rectangular with a longer long side on the bottom perimeter of the sail. They were and are referred to as "four-cornered" sails.
One type is the "lateen sail", but there are also jibs; Genoa & spinnaker.
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