370 B.C.: The dogmatic school of medicine

While Hippocrates is credited with creating the humoral hypothesis, it was his sons, Thessalus and Draco, who are credited with creating the first school, or sect, of medicine: the Dogmatic School of Medicine. (1, page)

There were various names for this school, depending on the era it was being described, and who was describing it.

Since it was based on the writings of the Hippocratic writers and Hippocrates himself, it was sometimes called the Hippocratic school, and physicians called Hippocratici. 

Since it was based on philosophers who believed it was necessary to rationalize about medicine, it was sometimes called the Rationalist school, and physicians called rationalists.

Since it was based on the belief that health was determined by a balance of the four humors (blood, phlegm, black bile and yellow bile) of Hippocrates, and diseases caused by an imbalance thereof, it was often called the Humoral school, and physicians called humoralists.

And, finally, since it was based on the dogma of Hippocrates, it was also called the Dogmatic school, and physicians called dogmatists or dogmatici. 

Regardless of the name, the general idea here is best explained by medical historian Edward Withington in 1894:  (3, page 57)

The ancient Greeks loved talking; his mind was more philosophical than scientific, and he preferred to speculate on things in general rather than to investigate particular facts... A Hippocratic writer had said, 'The physician who is also a philosopher is godlike.' This became the motto of the dogmatic school, was made the excuse for an immense amount of useless speculation, and was finally taken as the text of a special treaties by Galen himself. (3, page 57)

The dogmatic school of medicine was generally taught at the School of Cos, and was based on the opinions of Hippocrates, yet it was also based on the Stoic philosophy. This led to much "useless speculation," (3, page 57)

Part of this "useless" speculation was that diseases were caused by imbalances of the four elements and humors, and remedies were a means to re-establish the balance.  Remedies may be as simple as a lifestyle change, and as harsh as bleeding and purging.  Any particular remedy did not require any specific evidence that it worked.

You can  also learn more about Hippocratic medicine by reading about the medical wisdom of Hippocrates.

Followers of this school believed in the importance of studying anatomy, and often performed autopsies on animals such as pigs, monkeys and apes.  They performed autopsies on humans if possible, although this was frowned upon and illegal in the ancient world.  Human autopsies were performed when permission was granted, and in such cases was usually performed upon stolen corpses or, worse, live prisoners.

They had a basic understanding of human anatomy: the layout of the main organs, the vessels that line the body.  They understood the importance of correlating medicine with physiology.  The obvious problem with their school was the reliance on opinions as opposed to observation, experience and science.  Of course when the school was formed there was no knowledge of any of those things.  (3, page 60)

By about 50 A.D., when most referred to it as the Humoral or Rational School, it was under fierce competition by four other schools that also formed in Greece. Despite this competition, the basic tenants of this school would be followed by physicians all the way to the middle of the 18th century.

References:

1. "Rationalism (philosophy), Encyclopedia Britannica.com, http://www.britannica.com/EBchecked/topic/492034/rationalism
2. Withington, Edward Theodore, "Medical History from the Earliest Times," 1894, London
3. Watson, John, "Medical Profession in Ancient Times, "
4. Magill, Frank N., editor, "Dictionary of World Biography," Volume I: The Ancient World, 1998, Salem Press Inc., California
5. Meryon, Edward, "History of Medicine: comprising a narrative of its progress from the earliest ages to the present and of the delusions incidental to its advance from empericism to the dignity of a science," volume I, London, 1861,
6. Adams, Charles, Kendall, editor, "Johnson's Universal Cyclopedia: A new edition," volume V, A. Johnson Company, New York, 1894
7. Garrison, Fielding Hudson, "An introduction to the history of medicine: with medical chronology, Bibliographic data and test questions," 1913, Philadelphia and London, W.B. Saunders company
8. Neuburger, Max, writer, "History of Medicine," 1910, translated by Ernest Playfair, Volume I, London, Oxford University Press