The Greeks and Romans described animals objectively and scientifically, with detailed descriptions of their size, shape and specific characteristics. Georges Cuvier remarked "The ancients knew the elephant very well . . . They were not ignorant even of some differences which distinguish African from Asian elephants."
  Unfortunately some things are difficult to convey in writing. This strange cloven-hoofed elephant dating from around 1380 forms part of the oak choir stalls of Chester Cathedral in England. The craftsman had obviously never seen the real thing.

Courtesy of Steve Howe. 

In the Middle Ages the study of animals was seen as an aspect of religion, as all animals were made by God. Medieval bestiaries included fabulous beasts, such as unicorns and griffins, and described animals in moralistic terms.  
  The Aberdeen Bestiary is a magnificent illuminated manuscript, produced in England around 1200. One image depicts a fanciful elephant being strangled by a dragon.
  This image is taken from the book Libellus de Natura Animalium, an Italian bestiary printed between 1508 and 1512 in Mondovi.

Courtesy of C.W. Mullen from The Illustrated Book: A digital library.

During the Renaissance people once more adopted a scientific approach to the study of animals.
  Conrad Gesner, a physician and professor of philosophy at the University of Zurich, is known as the "father of zoology" because of his defining work Historiae animalium, a systematic compilation of information on animals published in five volumes from 1551 onwards. This highly illustrated book contains descriptions of many animals from nature, and includes this delightful woodcut of an elephant.
  Since the time of Gesner detailed drawings have been a standard tool in zoology.

Reproduced with permission from Australian Museum Online.

In 1796, George Cuviers introduced the concept of comparison in zoological study stating "The studies of elephant bones published up until now contain so little detail that even today a scientist cannot say whether they belong to one or another of our living species, and of the enormous quantity of fossil bones about which so many writers have spoken, we have good drawings of only two or three." He went on to publish detailed studies of elephant anatomy that showed that African and Asian elephants and fossil mammoths all belong to separate species.
  This illustration compares the trunk tips of a mammoth (top), an African elephant (middle), and an Asian elephant (bottom). 

Adapted from a drawing by Hans van Essen in Mammoths, Dick Mol, Larry D. Agenbroad, and Jim I. Mead, The Mammoth Site of Hot Springs, South Dakota, Inc., Hot Springs, South Dakota, 1993, p. 9.

Courtesy of the Paleontological Research Institution.