Quadratic equations were employed by them. The problem of finding x and y, when x2 + y2 = 100 and x:y = 1:¾, one of the earliest problems of this character known, was found in a papyrus at Kahun. The problem was stated as follows: "A given surface of, say, 100 units of area, shall be represented as the sum of two squares, whose sides are to each other as 1:¾."
The papyrus gave the working out of the solution. Many similar problems are given in mathematical works and papyri. They show the proficiency in mathematics that Egyptian scientists had attained at a remote period. But their methods of expressing mathematical problems were crude and, consequently, involved much tedious labor in finding solutions. There can be little doubt that if effective mathematical symbols had been devised the abstract sciences would have made even greater progress than they did in early Egypt. When we study the complicated solutions of algebraic problems made by the Egyptians, owing to the lack of simple symbols, we can appreciate how greatly modern mathematical science is benefited by the devices now employed for expressing quantities, variations, and operations.
The Egyptians were expert in applying the discoveries of science to the arts. The Nile made their country potentially rich in agriculture, and they devoted much attention to inventing such things as single and double plows, rakes, and other agricultural machines, many of which were drawn by oxen, donkeys, and other animals. Reaping was done with sickles and scythes. Not only was irrigation understood and widely practiced, but the importance of fertilization was recognized.
The farmers understood the preservation of meat, vegetables, and foodstuffs generally, by drying or pickling. They also brewed beer and made wines, vegetable and seed oils, and alcohol. The selection of breeding animals and the principles of variation were understood and employed for developing particular breeds of cattle and farm stocks.
The papyrus reed grew luxuriantly in Egypt and this resulted in the discovery of paper making, weaving, thread making and many textile methods. These industries led to the invention of looms, rope and twine twisting appliances, flax weaving and other machinery. The linens and cloths made by these machines have never been excelled.
Dyeing was developed with the textile industries. As the skies of Egypt are bright, the people in all ages have had a fondness for brilliant colors. The call for bright textile colors led to a considerable development in the chemistry of dyes and dyeing. Vegetable and mineral dyes were used. Dyes were not always applied to the whole pieces of goods, but stenciling and other methods of patterning were used. The highly organized artistic skill of the people demanded art-designed textiles and the manufacturers responded with beautiful and rich materials.
The fur and feather industries became important at an early period. The Egyptians were fond of beautiful ornamental skins like those of the panther or gazelle. Such skins were manufactured into numerous domestic articles, made into clothing or used as rugs, mats, and seat coverings.
Skins not valuable for art purposes were sent to the tanners to be converted into various kinds of leather. Tanning was highly developed, and the tanners turned out leathers which are to-day admired for their excellence. The tanners carried on their industries by chemical processes similar to those in use to-day.
The scarcity of wood in Egypt led to the invention of various substitutes. One common substitute was a kind of papier mâché. This was manufactured out of linen, wood or vegetable pulp and various kinds of paste. When it was used for art work the molded forms were covered with lacquer or various kinds of stucco. Very beautiful objects were manufactured from these substances, which indicate that the artists possessed a wide practical knowledge of physical and chemical principles.
Chemical knowledge was also well shown in their manufacture of glass. They excelled in this industry. All kinds of glass were made and decorated by staining and glazing. The glassmakers were able to imitate precious stones in glass and their glass-bead and enamel work has never been excelled. Some modern chemists express the opinion that glass making was carried to a greater degree of perfection in Egypt than any modern nation has attained.