In the Greek and Roman section of the British Museum I saw many instruments of daily life, including a bronze bleeding cup. I saw a similar item carved into the marble tombstone of a second century A.D. Athenian physician. In the first century A.D., the physician Celsus described the use of such vessels. A burning lint was placed inside the cup which was then inverted over an incision on the patient's skin. A vacuum was thereby created and as a result of it, blood flowed into the cup. The purpose of the bloodletting was to get rid of an imbalance in the humors -- to get rid of the excessive pneuma. Bloodletting has continued into modern times. See Four Humors.
Bleeding cups were generally of bronze, horn, or glass, if measurement was necessary. The Latin name is cucurbitula, suggesting the original ones were made of a gourd. The Greek name for them is siku'a or ku'athos.
11 Now there are two kinds of cups, one made of bronze, the other of horn. The bronze cup is open at one end, closed at the other; the horn one, likewise[p. 167] at one end open, has at the other a small hole. Into the bronze cup is put burning lint, and in this state the mouth is applied and pressed to the body until it adheres. The horn cup is applied as it is to the body, and when the air is withdrawn by the mouth through the small hole at the end, and after the hole has been closed by applying wax over it, the horn cup likewise adheres. Either form of cup may be made, not only of the above materials, but also of anything else suitable; when others are lacking, a small drinking-cup or porridge bowl with a narrowish mouth may be adapted conveniently for the purpose. If the skin upon which the cup is to be stuck is cut beforehand with a scalpel, the cup extracts blood; when the skin is intact, wind. Therefore when it is some matter inside which is doing the harm, the former method of cupping should be employed, when it is flatulency, then the latter. Now the use of a cup is the rule for a disease, not of the body as a whole, but of some part, the sucking out of which suffices for the re-establishment of health. And this same fact is a proof that with a scalpel, when a part is being relieved, blood must be let from that very part where the injury already exists; since unless it be to divert haemorrhage in that direction, nobody applies a cup to a part distant from the disease, but to that which is actually affected and has to be relieved. Further there may be need for cupping in chronic maladies, although already of somewhat long duration, if there is corrupted material or an unhealthy condition of wind; in certain acute cases also, if the body ought to be depleted and at the same time the patient's strength does not admit of cutting a vein; and cupping, as it is a less severe remedy, so it is a safer[p. 169] one; nor is it ever dangerous, even if adopted in the midst of the attack of a fever, or even with food undigested. Therefore, when blood-letting is needed, if cutting a vein is an instant danger, or if the mischief is still localised, recourse is to be had rather to cupping, not forgetting that whilst we recognize the absence of danger, its efficacy is thus the less, and it is impossible to remedy a severe malady unless by a remedy likewise severe.
De Medicina. Celsus. W. G. Spencer. Cambridge, Massachusetts. Harvard University Press. 1971 (Republication of the 1935 edition).
Reference: Surgical Instruments in Ancient Times, by John Stewart Milne (1907).