According to The Wikipedia website "The earliest known writings on the circulatory system are found in the Ebers Papyrus (16th century BCE), an ancient Egyptian medical papyrus containing over 700 prescriptions and remedies, both physical and spiritual."
Though written about in great lengths throughout history, the circulatory system was rarely understood. With regular occurrence, separate and distinct parts of the circulatory system would be discovered, identified and recorded long before they would be functionally understood. For example, most early Greek physicians attributed the arteries for delivering air, and nothing else, directly to body parts. It would be twelve centuries later before veins and arteries would be credited with the transportation of the vital substance we call blood. Even as late as the fourth century BC, when heart valves were discovered by a physician of the Hippocratean order, true understanding of their function would elude physicians for another thirteen hundred years.
The father of anatomical research, a greek physician Herophilus (335-280 BCE) discovered a clear difference between veins and arteries. Many of Herophilis' discoveries were made either through scientific dissection of a dead corpse or a systematic vivisection of a live human being. Shortly after his death, dissection was outlawed and it would be almost eighteen hundred years later, with Leonardo Da Vinci's work, that internal anatomical studies would advance once again. It was Herophilus' apprentice, the unconfirmed grandson of Aristotle, named Erasistratus that discovered that when arteries were cut, while the patient was still alive, they would actually spill blood.
Five hundred years after the death of Herophilus, Claudius Galunus, (AD 129 200/217), made a definite separation between the venous sytem and the arterial system. He concluded that the venous system carried the blood that held nutrition while the arterial system carried "the body heat". In addition, Galen also supposed that these systems carried a dual spirit called the Pneuma which was made up of an "animal spirit" and a "natural spirit". Many of Galen's theories were taught in highly respected medical schools as late as the nineteenth century.
Time would continue to beat on until, as stated in the New World Encyclopedia, William Harvey, "a pupil of Hieronymus Fabricius (who had earlier described the valves of the veins without recognizing their function), performed a sequence of experiments and announced, in 1628, the discovery of the human circulatory system as his own." While Harvey may have believed his own discovery was complete, it would take Marcello Malpighi, an Italian doctor to identify the capillary system connecting arteries and veins, nearly thirty years later.
While anatomically, the circulatory system had finally been mapped, true understanding of the function of the circulatory system would not be achieved until the 20th century. For even as late as the early 1900's, physicians were still actively prescribing leeches and bloodletting. These practices, used and relied on for many thousands of years, involved the draining of blood from patients, many times with fatal results.
Three thousand five hundred years later, the question begs to be asked. With the advent of nuclear medicine and the MRI, it would seem that physicians would be able to study the circulatory system in greater detail and with greater accuracy, but, one still has to wonder, will the medical community ever really understand the circulatory system?