This was one of the most complicated war machines of the antiquity, the main siege machine till the invention of the cannons. But despite its sophistication, the first catapult crafted by the Ancient Greeks did not employ complicated math formulas. Archimedes' theories improved the weapon.

"The first catapult in Europe flung into action around the fourth century B.C., prior to the invention of mathematical models that revolutionized ancient technologies," said lead author Mark Schiefsky, a Harvard University classics professor.

"It seems that the early stages of catapult development did not involve any mathematical theory at all. We are talking about so-called torsion artillery, basically an extension of the simple bow by means of animal sinews into something like the crossbow." said Schiefsky.

Later the Greek engineers employed the principles of Archimedes during the third century B.C., making the weapon more accurate, powerful and with a crucial impact in the ancient warfare, permitting the attack of previously impenetrable cities.

"These machines changed the course of history. Before the mathematical models were figured out by Archimedes and his contemporaries, it was assumed that craftsmen didn't have enough theoretical knowledge to construct contraptions such as the catapult and scale balance," said Schiefsky.

Schiefsky together with a team from the Max Planck Institute for the History of Science, in Berlin, investigated technical books and instruction manuals back to the 5th century BC, finding that the ancient Greeks were already building catapults.

"They didn't all go to Plato's Academy to learn geometry, and yet they were able to construct precisely calibrated devices. Craftsmen combined some improvisational trial and error with years of practice to make their machines functional," said Schiefsky.

"The steelyard, which used unequal arms and weights to weigh items, was one device in use well before the advent of the math that explained it. It was a simple case of necessity being the mother of invention, with things like meat needing to be weighed and some method required to do so," said Schiefsky.

Athenians constructed the compound pulley well before Archimedes, enabling them to dominate sea battles, as the machine enabled them to hoist and topple enemy ships during naval battles.

"When the mathematical theories were developed, construction became much more systematic," said Schiefsky.

The ancient texts revealed how the new mathematical advances were incorporated in developing better catapults.

"At some point in the third century B.C., as a result of a process of intensive testing and experimentation fostered by the Alexandrian kings, a standard method for constructing these devices was developed," Schiefsky told LiveScience.

"This method involved a fairly complex mathematical procedure (the extraction of a cube root) and seems to reflect the effort to apply geometry to an important engineering problem," he said.

# First Catapults and Advanced Mathematics

Catapults appeared much before Archimedes