Natural product to modern discovery of their active ingredients and eventually to the development of new drugs. A large number of currently prescribed drugs have been either directly derived from or inspired by natural products. A few representative examples are listed below. Some of the oldest natural product based drugs are analgesics. The bark of the willow tree has been known from antiquity to have pain relieving properties. This is due to presence of the natural product salicin which in turn may be hydrolyzed into salicylic acid. A synthetic derivative acetylsalicylic acid better known as aspirin is a widely used pain reliever.
Hippocrates of Chios would be known too. Only much later was it proven (by Ferdinand von Lindemann, in 1882) that this approach had no chance of success, because the factor pi (π) is transcendental. The number π is the ratio of the circumference to the diameter of a circle, and also the ratio of the area to the square of the radius. In the century after Hippocrates at least four other mathematicians wrote their own "Elements", steadily improving terminology and logical structure. In this way Hippocrates' pioneering work laid the foundation for Euclid's "Elements" (c. 325 BC) that was to remain the standard