This may not seem to mean very much. Yet what it illustrates is just this. These men wanted a certain development of mathematics. They needed it for the work that they were engaged at. They set themselves to the solution of certain problems and in doing so evolved a theorem in pure mathematics and an application of it which greatly simplified construction and gave an impetus to mechanics. In so doing they anticipated the work of a long after time. This is what I would insist is always true with regard to man. When he needs some intellectual development he makes it. When he requires an application of it he succeeds in working it out. Later ages may go farther, but had he needed further developments he evidently had the power to make them and probably would have made them.
The old Greeks had a much better opportunity to study Egyptian remains than we have, and especially was this true after the foundation of [{42}] Alexandria. There must have been a lively interest in things Egyptian aroused in the Greek minds by this Greek settlement in old Egypt. It is not surprising, then, to find some magnificent compliments to the old Egyptians in the mouths of some of the writers about the time of the foundation of Alexandria. Eudemus, for instance, the pupil of Aristotle, wrote the history of Geometry in which he traces its invention to the Egyptians, and states that the reason for its invention was its necessity in the remeasurement of land demanded after the removal of landmarks by the annual rise of the Nile. Always does one find this, that when there is a serious demand for an invention in theory or practice men make it. It is not a change or development in man that brings about inventions, but a change in his environment which causes new necessities to arise, and then he proceeds with an ability always the same to respond properly to those necessities.
Eudemus says: "Geometry is said by many to have been invented among the Egyptians, its origin being due to the measurement of plots of land. This was necessary there because of the rising of the Nile, which obliterated the boundaries appertaining to separate owners. Nor is it marvellous that the discovery of this and other sciences should have arisen from such an occasion, since everything which moves in development will advance from the imperfect to the [{43}] perfect. From mere sense-perception to calculation, and from this to reasoning, is a natural transition."
The old Egyptians made some fine developments of arithmetic. These were afterwards lost and were reinvented probably several times. I have already quoted from Cantor the opinion that the Egyptians were familiar with the properties of the right triangle whose sides were in the ratio 3:4:5 over 4,000 years ago. In the Papyrus of Ahmes, whose contents probably come from before 2400 B.C., there are the solutions of many problems which show how far the Egyptians had gone in arithmetical calculations. For instance, there are methods of calculating the solid contents of barns. The solutions are not absolute but are very closely approximate. Ahmes has problems that were solved in connection with the pyramids, which make it very clear that the old Egyptians had more than a little knowledge of the principles of proportion, of certain geometrical figures and probably were familiar also with the simpler phases at least of trigonometry. The area of a circle is found in Ahmes by deducting from the diameter one-ninth and squaring the remainder, which gives a value for the ratio of the circumference to the diameter of a circle much more nearly correct than that used by most writers until comparatively recent times.
As a teacher of the history of medicine with certain administrative functions in a medical [{44}] school, I have been very much interested in the old-time medicine and above all the details of medical education that we find among the Egyptians. Ordinarily it would be assumed that there was so little of anything like medical education that it could be scarcely worth while talking about it. On the contrary, we find so much that is being constantly added to by discoverers, that it is a never-ending source of surprise. There is a well-grounded tradition founded on inscriptions that Athothis, the son of Menes, one of the early kings, wrote a work on anatomy. This king is said to have died about 4150 B.C. There are traces of the existence of hospitals at that time in which diseases were studied and medical attendants trained. Even earlier than this there was a great physician, the first physician of whom we have record in history, whose name was I-Em-Hetep, which means "the Bringer of Peace." He had two other titles, one of which was "the Master of Secrets," partly because he possessed the secrets of health and disease, very probably also because so many things had to be confided to him as a physician. Another of his titles was that of "The Scribe of Numbers," in reference, doubtless, to the fact that he had to use numbers so carefully in making out his prescriptions.
His first title, that of the bringer of peace, shows that very early in the history of medicine it was recognized that the physician's first duty was to bring peace of mind to his patients. A [{45}] distinguished French physician (Director) of the department of physiology of the University of Paris, Professor Richet, said not long since, that physicians can seldom cure, they can often relieve, but they can always console, and evidently this oldest physician took his duty of consolation seriously and successfully. He lived in the reign of King Tehser, a monarch of the Third Dynasty in Egypt, who reigned about 4500 B.C. or a little later. How much this first physician was thought of will be best appreciated from the fact that the well-known step pyramid at Sakkara, the old cemetery near Memphis, is called by his name. So great indeed was the honor paid to him that after his death he was worshipped as a god, and so we have statues of him seated with a scroll on his knees, with an air of benignant knowledge, a placid-looking man with a certain divine expression of sympathy well suited to his name, the bringer of peace. While they raised him to their altars he does not wear a beard as did all their gods and their kings when they were raised to the godly dignity, but evidently they felt that his humanity was of supreme interest to them.
There is another monument at Sakkara that is of special interest to us in its consideration of old-time medicine. I discussed it and its inscriptions in the Journal of the American Medical Association (Nov. 8, 1907). It is the tomb of a surgeon, decorated within with pictures of surgical operations. The grandeur of the tomb and its [{46}] location show us that the surgeon must have held a very prominent place in the community of that time. The date of this tomb is not later than 2500 B.C. Certain of the surgical operations resembled those done at the present time. There is the opening of a carbuncle at the back of the neck which shows how old are men's diseases and the modes of their treatment. After this the oldest monument in the history of medicine is documentary, the Ebers Papyrus, the writing of which is probably not much later than 1700 B.C. This consists, moreover, of a collection of older texts and suggestions in medicine, and some of the idioms are said to belong to several distant periods. It is probable that certain portions of this papyrus were composed not much later than the oldest book in the world, and that they date from nearly 3000 B.C. This papyrus is as interesting and as startling in its anticipation of some of our modern medical wisdom as is the Instruction of Ptah Hotep in the practical wisdom of life. This seems a good deal to say, but there is ample evidence for it.
According to Dr. Carl von Klein, who discussed the "Medical Features of the Ebers Papyrus" in some detail in the Journal of the American Medical Association about five years ago, over 700 different substances are mentioned as of remedial value in this old-time medical work. There is scarcely a disease of any important organ with which we are familiar in the modern [{47}] time that is not mentioned here. While the significance of diseases of such organs as the spleen, the ductless glands, and the appendix was of course missed, nearly every other pathological condition was either expressly named or at least hinted at. The papyrus insists very much on the value of history-taking in medicine, and hints that the reason why physicians fail to cure is often because they have not studied their cases sufficiently. While the treatment was mainly symptomatic, it was not more so than is a great deal of therapeutics at the present time, even in the regular school of medicine. The number and variety of their remedies and of their modes of administering them is so marvellous, that I prefer to quote Dr. von Klein's enumeration of them for you:
"In this papyrus are mentioned over 700 different substances from the animal, vegetable and mineral kingdoms which act as stimulants, sedatives, motor excitants, motor depressants, narcotics, hypnotics, analgesics, anodynes, antispasmodics, mydriatics, myotics, expectorants, tonics, dentifrices, sialogogues, antisialics, refrigerants, emetics, antiemetics, carminatives, cathartics, purgatives, astringents, cholagogues, anthelmintics, restoratives, haematics, alteratives, antipyretics, antiphlogistics, antiperiodics, diuretics, diluents, diaphoretics, sudorifics, anhydrotics, emmenagogues, oxytocics, ecbolics, galactagogues, irritants, escharotics, caustics, styptics, haemostatics, emollients, demulcents, protectives, antizymotics, [{48}] disinfectants, deodorants, parasiticides, antidotes and antagonists."
Scarcely less interesting than the variety of remedies were their methods of administration: