A number of written works on mathematics, geometry in particular, and physics have been attributed to Hero of Alexandria. Hero developed the formula for calculating the area of a triangle from its three sides, now known as Hero’s formula, and invented the aeolipile, the first steam-powered engine. Metrica, Hero’s most significant work on geometry, was lost until 1896.
Besides his works, which were written in Greek, nothing is known about the life of Hero. The earliest written mention of Hero appeared in a work by pappus of Alexandria around a.d. 300, which quoted from Hero’s book, Mechanics. The tentative date of a.d. 62 for Hero’s life was derived from the description of an eclipse in one of Hero’s works, found to correspond undeniably to the eclipse of a.d. 62. Because of the nature of the books written by Hero, it was believed that he taught at the University of Alexandria in such disciplines as mathematics, physics, pneumatics, and mechanics.
The treatise Metrica dealt with geometry and comprised three books. Metrica introduced his formula for finding the area of a triangle. The first book encompassed plane figures and surfaces of common solids. Hero explained how to calculate the area of quadrilaterals, circles, regular polygons, and ellipses. He also described how to find the surface area of cylinders, cones, spheres, and segments of spheres. Also in Book I was a method for estimating the square root of a number, a method later used in computers. Book II provided methods for determining the volume of such figures as the cone, pyramid, cylinder, prism, and sphere. The third book discussed procedures for dividing certain areas and volumes into parts of given ratios.
Hero’s longest work was Pneumatics, considered to be a collection of notes for a textbook.
The treatise tackled a number of mechanical problems and included discussion of the aeolipile, the steam-powered engine designed and built by Hero. The engine was made of a sphere with two nozzles positioned so that steam jets produced from the inside would cause the device to turn. Pneumatics also discussed the pressure of air and water, as well as the occurrence of a vacuum in nature. Treatment of siphons, coin-operated machines, a fire pump, and a water organ also appeared in the work. Hero also described a number of toys and playthings, such as puppet shows and trick jars that released wine or water separately.
Another important work by Hero was Mechanics, which was a textbook for engineers, builders, and architects that dealt with the mechanical problems of everyday life. The theory of the wheel and the theory of motion were covered in the work, and Hero also explained how to construct plane and solid figures in a given proportion to a given figure. He presented the theory of the center of gravity and equilibrium and the theory of the balance, using the ideas of archimedes. Mechanics also discussed the five simple machines—the lever, the pulley, the winch, the wedge, and the screw. The work described cranes, devices for transport, winepresses, and screw-cutters, believed to have been invented by Hero.
Dioptra was about land surveying and contained a description of a diopter, a surveying instrument most likely developed by Hero. The work also described an odometer, another Hero invention, and dealt with astronomy, offering a method for calculating the distance between Alexandria and Rome through the simultaneous observation of a lunar eclipse in both cities. Yet another work, Catoptrica, offered the theory of reflection and provided instructions on how to make mirrors.
Hero’s works have been widely studied, and evidence exists to suggest his texts enjoyed a large audience. Pneumatics was read by many during the Middle Ages and the Renaissance, and more than 100 copies have surfaced. His writings indicate that Hero was a man of great scientific knowledge and creativity.
