Introduction

Abacuses with a “quinary” numeral system, were in use since the 6th century B.C., in order to rapidly calculate complex mathematic operations, based on the acrophonic (“Attic”) numeral system, according to each category (one, five, ten, etc) indicate by the first letters of them. Apollonius of Perga, in his lost “Okytokion” treatise, described a quick way to calculate multiplications, divisions, etc., which can be considered as a precursor to modern calculators. Kinematic computing devices such as Eratosthenes’s “mesolabe”, Plato’s cubist, Nicomedes’ conchoid and algorithms, such as the sieve of Eratosthenes, were used to solve complex equations and calculate complex numbers. To calculate calendars and periodic astronomical phenomena, ingenious and complex computational mechanisms were invented, such as the planetaria and celestial globes of Archimedes and Posidonius (3rd century B.C.) that used interlocking toothed gearwork to simulate the orbits and eclipses of the sun, the moon and the five known planets with exquisite accuracy (according to Cicero). It is extremely important that a similar mechanism built in the 2nd century B.C. survived (from the Antikythera shipwreck) and its fragments are on display at the National Archaeological Museum in Athens.