Who made the first documented parachute jump in a "frameless" parachute from a high altitude?

Leonardo da Vinci conceived the idea of the parachute in his writings (circa 1495) but did not convert the idea into action. Fauste Veranzio (Vrančić) built a device derived from da Vinci's drawings and safely jumped from a tower in Venice in 1617.

Louis-Sebastien Lenormand (May 25, 1757 – April 4, 1837) made a kind of parachute out of two umbrellas and jumped from a tree in 1783. Later that year he successfully jumped from the tower of the Montpellier observatory in front of a crowd that included Joseph Montgolfier, using a 14ft parachute with a rigid wooden frame. However, it was André-Jacques Garnerin (31 January, 1769 – 18 August, 1823) who was the first to design and test a frameless parachute capable of slowing a man’s fall from a high altitude.

On October 22, 1797, Garnerin attached his parachute to a balloon and ascended to an altitude of 3,200 feet. He was trusting his life to a canopy 23ft in diameter, that had no rigid frame, and was attached to a basket with suspension ropes which he would cut to separate the parachute from the balloon.

Without an air vent at the top of the prototype, Garnerin oscillated wildly in his descent, but he landed shaken but unhurt half a mile from the balloon’s take-off site. In 1799, Garnerin’s wife, Jeanne-Genevieve, became the first female parachutist. In 1802, Garnerin made a spectacular jump from 8,000 feet during an exhibition in England. He died in a balloon accident in 1823 while preparing to test a new parachute.