Heron of Alexandria

Heron (or Hero) of Alexandria who lived around 10–85 AD was a mathematician, physicist and engineer who lived in the Hellenistic times in Alexandria, Egypt, at that time part of the Roman empire. Heron of Alexandria was an important geometer and worker in mechanics.

Heron was a teacher and researcher at the Musaeum of Alexandria, the famous library and university in Alexandria. Some of his writings are elaborate textbooks, others are lecture manuscripts in style.

The complete works of Heron represent something like an encyclopedia of applied mathematics and engineering sciences of the Greco-Roman era. His best known mathematical work is the formula for the area of a triangle in terms of the lengths of its sides. One of his most famous inventions was an experiment done as part of the earliest instance of harnessing wind energy on land.

He is said to have philosophies related to atomists, which he discussed in his work Mechanics. He also described pantographs.

Many scholars believe that not only he taught at the Musaeum of Alexandria, but that in addition he served as its Director and that he developed it as the first Polytechnic School, or Technical Institute.

He was made famous for documenting the first steam turbine, the aelolipile. He also invented many mechanisms for temples and theaters while he advanced or improved inventions by others, for example the hydraulis, originally invented by Ktesibius.

His most important invention was the Aeolipile, the first steam turbine. Other inventions include automated machines for temples and theaters, surveying instruments, and military machines and weapons.
Heron of Alexandria

Philo Byzantius (ca. 280 BC – ca. 220 BC) – Greek engineer and physicist

Philo Byzantius also known as Philo Mechanicus, was a Greek engineer, physicist, and writer on mechanics, who lived during the latter half of the 3rd century BC. Philo was a student of the famed engineer Ctesibius.

He descended from the city of Byzantium, lived in Rhodes and eventually settled in Alexandria. He was probably younger than Ctesibius, though some place him a century earlier. He compiled numerous treatises on applied mechanics, the most important of which is Michaniki Syntaxis (Mechanical Syntax).

Philo was one of the greatest engineers of the Hellenistic period, a pioneer in mechanics and the construction of automata. He was one alongside many illustrious scholars who worked in Alexandria, the most highly advanced spiritual center in the Western World at the time.

He constructed pneumatics, machines which functioned with the use of compressed air, levers, tools and hourglasses. In Alexandria, Philo invented the chain pump. This comprised a set of pots attached to a chain or belt that was moved by a rotating wheel.

Philo also described the force pump which was invented by the engineer Ctesibius of Alexandria. This pump is composed of two cylinders with pistons that were moved by means of connecting rods attached to opposite ends of a single lever.

In the field of mathematics, Philo formulated an alternative proof to the proposition of Euclid 1.8 and also devised an approximate solution to the problem of doubling the cube using the so-called Philo line.
Philon Byzantius (ca. 280 BC – ca. 220 BC) – Greek engineer and physicist

Ctesibius of Alexandria

Ctesibius of Alexandria or Ktesibios or Tesibius (285–222 BC) was a Greek inventor and mathematician in Alexandria, Ptolemaic Egypt. He was the son of a barber in Alexandria, and employed by Ptolemy II.

He was probably the first head of the Museum of Alexandria. He wrote the first survived to the present treatises on the science of compressed air and its uses in pumps. This, in combination with his work on the elasticity of air—Pneumatica, earned him the title of father of pneumatics.

Ctesibius of Alexandria is credited with inventing the pipe organ in the 3rd century B.C. In a pipe organ air is compressed in a chamber to which multiple pipes are attached. The water pipe organ, or hydraulis, reentered Europe in AD 757 as a gift to Pepin the Short (Charlemagne’s father) by the Byzantine Emperor Constantine Copronymus.

While most of his work was based on using compressed air as a control substance and he is known as the Father of Pneumatics, his most famous control system was the feedback he added to the already existing water clocks of the day.

Unlike the version of the clocks that was reliant upon two pots and the flow of water aided only by gravity, Ctesibius’s water clock used a system of gears and a water wheel to track the passage of time and report the time using an arrow on a scale that signaled to the user the current time.

Ctesibius together with Philon Byzantius, and Hero were the three most famous engineers of Hellenistic Alexandria, whose studies mark a significant progress in hydraulics. This progress allowed installation of advanced water supply systems like that of the citadel at Pergamon, in which pressure pipes (probably made of metal) were implemented.
Ctesibius of Alexandria

Abū Bakr ibn Muḥammad ibn al Ḥusayn al-Karajī (980-1030)

Abū Bakr ibn Muḥammad ibn al Ḥusayn al-Karajī was a Persian mathematician and engineer. He made a great contribution to algebra by first treating numbers independently of geometry.

He held an official position in Baghdad during which time he wrote his three main works: Al-Badi' fi'l-hisab (Wonderful on calculation), Al-Fakhri fi'l-jabr wa'l-muqabala (Glorious on algebra), and Al-Kafi fi'l-hisab (Sufficient on calculation).

He was able to develop many of the basic algebraic properties of rational and irrational numbers, and therefore represents an important step in the evolution of algebraic calculus.

Al-Karaji is known as the first author of the algebra of polynomials. Al-Karaji work holds an especially important place in the history of mathematics. Woepcke (historian, Orientalist and mathematician) in 1853 remarked that “it offers the most complete or rather the only theory of algebraic calculus among the Arabs known to us to the present time”.

Al-Karaji employed an entirely new approach in the tradition of the Arab algebraist –al-Khwarizmi, Ibn al-Fath, Abu Kamil commencing with an exposition of the theory of algebraic calculus.
Abū Bakr ibn Muḥammad ibn al Ḥusayn al-Karajī (980-1030)