Galen as experimenter
In ancient history the Greek physician Galen (c. 129-c. 200) was the first to show that veins were connected to the heart and that arteries contained blood. Galen was an experimenter performing animal dissections and thoroughly describing anatomical details. The interpretation of his findings remained within the Greek tradition going back to Hippocrates and Aristotle.
He regarded blood to be produced in the liver where it received its "natural spirit" and from which it flowed out to the periphery of the body due to a pulling or attractive force. Transported to the heart, the blood obtained "vital spirits" moved from the right to left side of the heart (Galen supposed both halfs were separated by a permeable membrane) and finally received its "animal spirits" from the brain*.
Galen embraced by the Church
Galen's medical authority lasted for almost 1500 years. His writings on human physiology, anatomy, the use of medication etc. were embraced by the church and achieved dogmatic status. It was hard for his successors to propose new ideas on the physiology of blood and blood flow.