It is well known that geometry had its origin in the valley of the Nile, that it arose to meet a practical need, and that it was in the first place, as its name implies, a measurement of the earth—a crude surveying, employed in the restoration of boundaries obliterated by the annual inundations of the river. Egyptian geometry cared little for theory. It addressed itself to actual problems, such as determining the area of a square or triangular field from the length of the sides. To find the area of a circular field, or floor, or vessel, from the length of the diameter was rather beyond the science of 2000 B.C. This was, however, a practical problem which had to be solved, even if the solution were not perfect. The practice was to square the diameter reduced by one ninth.
In all the Egyptian mathematics of which we have record there is to be observed a similar practical bent. In the construction of a temple or a pyramid not merely was it necessary to have regard to the points of the compass, but care must be taken to have the sides at right angles. This required the intervention of specialists, expert "rope-fasteners," who laid off a triangle by means of a rope divided into three parts, of three, four, and five units. The Babylonians followed much the same practice in fixing a right angle. In addition they learned how to bisect and trisect the angle. Hence we see in their designs and ornaments the division of the circle into twelve parts, a division which does not appear in Egyptian ornamentation till after the incursion of Babylonian influence.
There is no need, however, to multiply examples; the tendency of all Egyptian mathematics was, as already stated, concerned with the practical solution of concrete problems—mensuration, the cubical contents of barns and granaries, the distribution of bread, the amounts of food required by men and animals in given numbers and for given periods of time, the proportions and the angle of elevation (about 52°) of a pyramid, etc. Moreover, they worked simple equations involving one unknown, and had a hieroglyph for a million (the drawing of a man overcome with wonder), and another for ten million.
The Rhind mathematical papyrus in the British Museum is the main source of our present knowledge of early Egyptian arithmetic, geometry, and of what might be called their trigonometry and algebra. It describes itself as "Instructions for arriving at the knowledge of all things, and of things obscure, and of all mysteries." It was copied by a priest about 1600 B.C.—the classical period of Egyptian culture—from a document seven hundred years older.
Medicine, which is almost certain to develop in the early history of a people in response to their urgent needs, has been justly called the foster-mother of many sciences. In the records of Egyptian medical practice can be traced the origin of chemistry, anatomy, physiology, and botany. Our most definite information concerning Egyptian medicine belongs to the same general period as the mathematical document to which we have just referred. It is true something is known of remoter times. The first physician of whom history has preserved the name, I-em-hetep (He-who-cometh-in-peace), lived about 4500 B.C. Recent researches have also brought to light, near Memphis, pictures, not later than 2500 B.C., of surgical operations. They were found sculptured on the doorposts at the entrance to the tomb of a high official of one of the Pharaohs. The patients, as shown in the accompanying illustration, are suffering pain, and, according to the inscription, one cries out, "Do this [and] let me go," and the other, "Don't hurt me so!" Our most satisfactory data in reference to Egyptian medicine are derived, however, from the Ebers papyrus. This document displays some little knowledge of the pulse in different parts of the body, of a relation between the heart and the other organs, and of the passage of the breath to the lungs (and heart). It contains a list of diseases. In the main it is a collection of prescriptions for the eyes, ears, stomach, to reduce tumors, effect purgation, etc. There is no evidence of a tendency to homeopathy, but mental healing seems to have been called into play by the use of numerous spells and incantations. Each prescription, as in medical practice to-day, contains as a rule several ingredients. Among the seven hundred recognized remedies are to be noted poppy, castor-oil, gentian, colchicum, squills, and many other familiar medicinal plants, as well as bicarbonate of soda, antimony, and salts of lead and copper. The fat of the lion, hippopotamus, crocodile, goose, serpent, and wild goat, in equal parts, served as a prescription for baldness. In the interests of his art the medical practitioner ransacked the resources of organic and inorganic nature. The Ebers papyrus shows that the Egyptians knew of the development of the beetle from the egg, of the blow-fly from the larva, and of the frog from the tadpole. Moreover, for precision in the use of medicaments weights of very small denominations were employed.
The Egyptian embalmers relied on the preservative properties of common salt, wine, aromatics, myrrh, cassia, etc. By the use of linen smeared with gum they excluded all putrefactive agencies. They understood the virtue of extreme dryness in the exercise of their antiseptic art. Some knowledge of anatomy was involved in the removal of the viscera, and much more in a particular method they followed in removing the brain.
In their various industries the Egyptians made use of gold, silver, bronze (which on analysis is found to consist of copper, tin, and a trace of lead, etc.), metallic iron and copper and their oxides, manganese, cobalt, alum, cinnabar, indigo, madder, brass, white lead, lampblack. There is clear evidence that they smelted iron ore as early as 3400 B.C. maintaining a blast by means of leather tread-bellows. They also contrived to temper the metal, and to make helmets, swords, lance-points, ploughs, tools, and other implements of iron. Besides metallurgy they practiced the arts of weaving, dyeing, distillation. They produced soap (from soda and oil), transparent and colored glass, enamel, and ceramics. They were skilled in the preparation of leather. They showed aptitude for painting, and for the other fine arts. They were expert builders, and possessed the engineering skill to erect obelisks weighing hundreds of tons. They cultivated numerous vegetables, grains, fruits, and flowers. They had many domestic animals. In seeking the satisfaction of their practical needs they laid the foundation of geometry, botany, chemistry (named, as some think, from the Egyptian Khem, the god of medicinal herbs), and other sciences. But their practical achievements far transcended their theoretical formulations. To all time they will be known as an artistic, noble, and religious people, who cherished their dead and would not allow that the good and beautiful and great should altogether pass away.