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First finds

Pterosaur fossils are very rare, due to their light bone construction. Complete skeletons can generally only be found in geological layers with exceptional preservation conditions, the so-called Lagerstätten. The pieces from one such Lagerstätte, the Late Jurassic Solnhofen Limestone in Bavaria, became much sought after by rich collectors. In 1784, Italian naturalist Cosimo Alessandro Collini was the first scientist to describe a pterosaur fossil. At that time the concepts of evolution and extinction were imperfectly developed. The bizarre build of the pterosaur was shocking, as it could not clearly be assigned to any existing animal group. The discovery of pterosaurs would thus play an important role in the progress of modern paleontology and geology. Scientific opinion at the time was that if such creatures were still alive, only the sea was a credible habitat; Collini suggested it might be a swimming animal that used its long front limbs as paddles. A few scientists continued to support the aquatic interpretation even until 1830, when German zoologist Johann Georg Wagler suggested that Pterodactylus used its wings as flippers and was affiliated with Ichthyosauria and Plesiosauria.

In 1800, Johann Hermann first suggested that it represented a flying creature in a letter to Georges Cuvier. Cuvier agreed in 1801, understanding it was an extinct flying reptile. In 1809, he coined the name Ptéro-Dactyle, "wing-finger". This was in 1815 Latinised to Pterodactylus. At first most species were assigned to this genus and ultimately "pterodactyl" was popularly and incorrectly applied to all members of Pterosauria. Today, paleontologists limit the term to the genus Pterodactylus or members of the Pterodactyloidea.

In 1812 and 1817, Samuel Thomas von Soemmerring redescribed the original specimen and an additional one. He saw them as affiliated to birds and bats. Although he was mistaken in this, his "bat model" would be influential during the 19th century. In 1843, Edward Newman thought pterosaurs were flying marsupials. Ironically, as the "bat model" depicted pterosaurs as warm-blooded and furred, it would turn out to be more correct in certain aspects than Cuvier's "reptile model" in the long run. In 1834, Johann Jakob Kaup coined the term Pterosauria.