They were referred to as "four-cornered" 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.
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.
Triangular-shaped sails helped catch wind from the sides and rear.
"Square-riggers" have primarily square sails, but the jib sails are triangular.
Square sails are square
One type is the "lateen sail", but there are also jibs; Genoa & spinnaker.
The triangular sail was invented beginning in the 16th century. They were first seen in the Mediterranean as single yarded lateen sails.
Square sails (rectangular) were (are) called four-cornered sails.
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