800 B.C: Homer was first to use the term asthma

Bust of Homer (British Museum, London). By using the term
asthma in his epic poem The Illiad, he became the first to
use the term in written literature.  

As a child Homer (800 or 850 B.C.) listened to poems recited by his dad about a war that occurred almost 400 years before he was born.  He was so impressed that as a young man he many spent hours in the open courtyard writing them down.

He couldn't remember word per word the stories his dad told.  What made it even more confusing was that his uncle sang the same stories, only the twists and turns were different. The names used, the plot, the ending, and the morals learned, however, were the same no matter who told the story.

So as he was jotting down the stories from memory, he realized it was okay to exaggerate and to expound at times in order to make his story more complete.  The important thing was to have the story in writing so future fathers could tell the same story every time it was told.  

As the years passed Homer became so rapt in his task that he became the slightly obese middle-aged, bearded man that is represented in the various busts of him. He would go down in history as one of the first and greatest story tellers of all time.

Whether or not he was actually the first to tell these stories may never be known, although what is known is he is often given credit.  This was because, unlike the ancient Egyptians and Mediterraneans, the ancient Greeks liked to associate works of writing to either the author or some famous person.  While Homer may not have been the creator of the Iliad, since he wrote it down he is given credit by history as the author.  (1, page 19-20)

It was a story of a siege at Troy estimated to have occurred between 1194-1184 B.C. (4, page 46)  After writing this story, Homer would write many more.  As eluded to above, he probably obtained most of his stories from those told by his ancestors by word of mouth, mainly through poems and songs that were easy to remember.  (1, pages 19-20)

Another thing Homer did, as his father and uncle did earlier, was add into the story modern events.  This made the story more interesting to the modern audience. While he may not have known it at the time, this would give future historians a better idea of what life was like in ancient Greece.  (1, page 19-20)

The story would also become significant to medical historians, because Homer made allusions to the state of medicine at the time.  While he described the battles, he also described battle wounds, and the symptoms that resulted from these wounds, sometimes in the process of dying.  So various medical historians have made reference to these allusions as some of the earliest knowledge of medicine. (1, page 19-20)

Homer was also the first, or so it is thought, to use the term asthma (άσθμα) in an actual piece of literature. (2, pages 10-11)

The term asthma is referenced in the Iliad, book XV, line 10:

"He saw Hector lying on the plain, his companions
sitting round him. Hector was gagging painfully,
dazed and vomiting blood." 

In this scene Zeus wakes up as the Greeks are trying to push a line of Trojans back, and he finds the Trojan leader Hector breathing painfully and vomiting blood. The above is the English translation, although the word Homer used for "gagging painfully" was asthma or asthmati.

Homer later made another reference to asthma in the Iliad, book XV, line 290:

"He was just starting to recover,
to recognize his comrades round him. He'd stopped
gasping and sweating, for aegis-bearing Zeushad revived his mind"

In this scene Homer described Hector as just starting to catch his breath.

Homer used the term asthma to refer to being winded as from fighting in battle, or as from wounds obtained in battle.  It made sense to use the term asthma this way, because it was a term meaning short, gasping breaths.  It was a vague term used simply to describe the symptom of dyspnea, or shortness of breath, regardless of t cause.

Another term that was sometimes used by the Greeks was panos, which meant panting.  Homer apparently preferred the term asthma.

Another early description of asthma was the sacred disease.  Actually, epilepsy was the sacred disease because the seizures were thought to be caused by divine intervention.  Those with the disease were thought to be rewarded with happiness in the next world.

Asthma was also referred to as the sacred disease simply because it was thought to be epilepsy of the lungs.  Perhaps the gasping efforts of the asthmatic made the chest appear as though it were seizing.  So if you had asthma you were blessed with eternal happiness.

While asthma was considered a divine blessing, this does not mean that the gods didn't cause all other diseases too, because they did.  This is confirmed, perhaps, by homer in his Odyssey (ix. 411):

 "the blinded and howling Cyclops is told by his friend that, if he is ill, he should remember that sickness comes from Zeus and is unavoidable." (3, page 38)  

Homer did not, however, refer to the disease asthma. His use of the term was simply to describe the symptom of dyspnea.

References:

1. Sigerist, Henry E, "A History of Medicine," Volume II, 1961, Oxford University Press, New York, pages 19-20
2. Jackson, Mark, "Asthma: The Biography," 2009, Oxford University Press, pages 10-11.  Note:  While Mark Jackson is not the only person to acknowledge the Iliad as the first reference to the term asthma, I still want to give him credit here.  
3. Withington, Edward, "Medical History from the earliest times," 1894, London, page 38
4. Buck, Albert Henry, Williams Memorial Public Funds, "The growth of medicine from the earliest times to about 1800," 1917, London, Oxford University Press