The "Luff".
Try roach
When a sail fills out because of wind blowing in it, the curved, concave part is called its 'belly'.
The first sail on a ship is typically called the "fore sail" or "main sail," depending on the type of vessel. In traditional sailing ships, the fore sail is the first sail set at the front of the ship, while the main sail is the largest and is usually rigged on the main mast. These sails are crucial for catching wind and propelling the ship forward.
The mast is the upright mailsail holder. A sprit is a pole that extends diagonally across a fore-and-aft sail from the lower part of the mast to the peak of the sail. Also see bowsprit. All are called sail holders. Tks, Sina.
The lowest fore-and-aft sail on the main mast is called the mainsail, while that on the mizzen is called the mizzen sail. These may be any type of fore-and-aft sail, in any combination. The Scots Zulu, for example, had a dipping lug main with a standing lug mizzen.
If you mean the one that is often fixed to a foreward boom, that would be a Lateen sail.
It is a jib or fore sail that has a slot cut into it.
The definition of a sprit is a long pole that extends diagonally across a fore and aft sail quadrilateral from the lower part of the mast to the peak of the sail.
A lanteen sail
Lateen
yacht this was the original answer but this can refer to a powered vessel too. As in motor yacht. A one masted fore and aft rigged vessel is called a sloop and can have various sail plans e.g. Gaff rigged, bermudian rigged
The most forward sail is normally called a jib.On vessels with more than one jib, the names of the jibs (from forward to aft) are: Flying jib, Outer jib, Inner jib and Fore (topmast) staysail.