The ancient Babylonians used a complex form of geometry to compute the movements of Jupiter about 1400 years earlier than the invention of the same technique in medieval Europe – a technique that became the basis of modern-day graphs, a study has found.

An historian of science has discovered evidence that Babylonian priests living between 350BC and 50BC invented and used an abstract form of geometry that until now was thought to have been invented in the 14th Century, eventually evolving into calculus, the mathematical study of how something changes over time.

One of the clay tablets containing the cuneiform text

Although algebra and geometry were both well known in ancient Babylonia – a culture extending back to 1800BC – as well as in the later period of ancient Greece, this is the first time that anyone has found evidence to show that Babylonian scholars knew how to use geometry to plot the irregular movements of a planet, said Mathieu Ossendrijer, professor of the history of ancient science at Humboldt University in Berlin.

“What is new is that the Babylonians also used geometry in their astronomy. We have evidence that they used geometrical figures to gauge the motion of planets but the really exciting thing is that the kind of geometry they used is very special,” Professor Ossendrijver said.

“What we have found essentially is almost like a modern-day graph – a geometrical figure that represents an abstract mathematical space. That’s really new and exciting as it was thought to have been first invented much later, around 1350,” he said.

Babylonian cuneiform text etched onto clay tablets held in the British Museum in London has revealed that the priests were calculating the movements of Jupiter during the first 60 days it appeared above the horizon by plotting the planet’s irregular motion away from the regular path of the Sun.

Babylonian ruler King Marduk-Nadin-Akke pictured on a boundary stone (Getty)

Jupiter’s movement across the sky appears to slow, although it is in fact due to the relative movements of its orbit with respect to the Earth’s. A graph of Jupiter’s apparent velocity against time would therefore slope down so that the area under the curve forms a trapezoid – a four-sided shape with a sloping top.

It is clear from the clay tablets that the Babylonians were able to plot Jupiter’s movements as a line on a graph of movement against time, and then calculating the distance moved by measuring the area formed by the four-sided trapezoid shape of the graph – a shape the Babylonian priests called the “oxen head”.

It was this ability to compute the movements of an object moving with a changing velocity using geometric principles that was unheard of before the 14th Century AD, Professor Ossendriver said.

Science news in pictures Show all 20 1 /20 Science news in pictures Science news in pictures Pluto has 'beating heart' of frozen nitrogen Pluto has a 'beating heart' of frozen nitrogen that is doing strange things to its surface, Nasa has found. The mysterious core seems to be the cause of features on its surface that have fascinated scientists since they were spotted by Nasa's New Horizons mission. "Before New Horizons, everyone thought Pluto was going to be a netball - completely flat, almost no diversity," said Tanguy Bertrand, an astrophysicist and planetary scientist at NASA's Ames Research Center and the lead author on the new study. "But it's completely different. It has a lot of different landscapes and we are trying to understand what's going on there." Getty Science news in pictures Over 400 species discovered this year by Natural History Museum The ancient invertabrate worm-like species rhenopyrgus viviani (pictured) is one of over 400 species previously unknown to science that were discovered by experts at the Natural History Museum this year PA Science news in pictures Jackdaws can identify 'dangerous' humans Jackdaws can identify “dangerous” humans from listening to each other’s warning calls, scientists say. The highly social birds will also remember that person if they come near their nests again, according to researchers from the University of Exeter. In the study, a person unknown to the wild jackdaws approached their nest. At the same time scientists played a recording of a warning call (threatening) or “contact calls” (non-threatening). The next time jackdaws saw this same person, the birds that had previously heard the warning call were defensive and returned to their nests more than twice as quickly on average. Getty Science news in pictures Turtle embryos influence sex by shaking The sex of the turtle is determined by the temperatures at which they are incubated. Warm temperatures favour females. But by wiggling around the egg, embryos can find the “Goldilocks Zone” which means they are able to shield themselves against extreme thermal conditions and produce a balanced sex ratio, according to the new study published in Current Biology journal Ye et al/Current Biology Science news in pictures Elephant poaching rates drop in Africa African elephant poaching rates have dropped by 60 per cent in six years, an international study has found. It is thought the decline could be associated with the ivory trade ban introduced in China in 2017. Reuters Science news in pictures Ancient four-legged whale discovered in Peru Scientists have identified a four-legged creature with webbed feet to be an ancestor of the whale. Fossils unearthed in Peru have led scientists to conclude that the enormous creatures that traverse the planet’s oceans today are descended from small hoofed ancestors that lived in south Asia 50 million years ago A. Gennari Science news in pictures Animal with transient anus discovered A scientist has stumbled upon a creature with a “transient anus” that appears only when it is needed, before vanishing completely. Dr Sidney Tamm of the Marine Biological Laboratory could not initially find any trace of an anus on the species. However, as the animal gets full, a pore opens up to dispose of waste Steven G Johnson Science news in pictures Giant bee spotted Feared extinct, the Wallace's Giant bee has been spotted for the first time in nearly 40 years. An international team of conservationists spotted the bee, that is four times the size of a typical honeybee, on an expedition to a group of Indonesian Islands Clay Bolt Science news in pictures New mammal species found inside crocodile Fossilised bones digested by crocodiles have revealed the existence of three new mammal species that roamed the Cayman Islands 300 years ago. The bones belonged to two large rodent species and a small shrew-like animal New Mexico Museum of Natural History Science news in pictures Fabric that changes according to temperature created Scientists at the University of Maryland have created a fabric that adapts to heat, expanding to allow more heat to escape the body when warm and compacting to retain more heat when cold Faye Levine, University of Maryland Science news in pictures Baby mice tears could be used in pest control A study from the University of Tokyo has found that the tears of baby mice cause female mice to be less interested in the sexual advances of males Getty Science news in pictures Final warning to limit "climate catastrophe" The Intergovernmental Panel on Climate Change has issued a report which projects the impact of a rise in global temperatures of 1.5 degrees Celsius and warns against a higher increase Getty Science news in pictures Nobel prize for evolution chemists The nobel prize for chemistry has been awarded to three chemists working with evolution. Frances Smith is being awarded the prize for her work on directing the evolution of enzymes, while Gregory Winter and George Smith take the prize for their work on phage display of peptides and antibodies Getty/AFP Science news in pictures Nobel prize for laser physicists The nobel prize for physics has been awarded to three physicists working with lasers. Arthur Ashkin (L) was awarded for his "optical tweezers" which use lasers to grab particles, atoms, viruses and other living cells. Donna Strickland and Gérard Mourou were jointly awarded the prize for developing chirped-pulse amplification of lasers Reuters/AP Science news in pictures Discovery of a new species of dinosaur The Ledumahadi Mafube roamed around 200 million years ago in what is now South Africa. Recently discovered by a team of international scientists, it was the largest land animal of its time, weighing 12 tons and standing at 13 feet. In Sesotho, the South African language of the region in which the dinosaur was discovered, its name means "a giant thunderclap at dawn" Viktor Radermacher / SWNS Science news in pictures Birth of a planet Scientists have witnessed the birth of a planet for the first time ever. This spectacular image from the SPHERE instrument on ESO's Very Large Telescope is the first clear image of a planet caught in the very act of formation around the dwarf star PDS 70. The planet stands clearly out, visible as a bright point to the right of the center of the image, which is blacked out by the coronagraph mask used to block the blinding light of the central star. ESO/A. Müller et al Science news in pictures New human organ discovered that was previously missed by scientists Layers long thought to be dense, connective tissue are actually a series of fluid-filled compartments researchers have termed the “interstitium”. These compartments are found beneath the skin, as well as lining the gut, lungs, blood vessels and muscles, and join together to form a network supported by a mesh of strong, flexible proteins Getty Science news in pictures Previously unknown society lived in Amazon rainforest before Europeans arrived, say archaeologists Working in the Brazilian state of Mato Grosso, a team led by archaeologists at the University of Exeter unearthed hundreds of villages hidden in the depths of the rainforest. These excavations included evidence of fortifications and mysterious earthworks called geoglyphs José Iriarte Science news in pictures One in 10 people have traces of cocaine or heroin on fingerprints, study finds More than one in 10 people were found to have traces of class A drugs on their fingers by scientists developing a new fingerprint-based drug test. Using sensitive analysis of the chemical composition of sweat, researchers were able to tell the difference between those who had been directly exposed to heroin and cocaine, and those who had encountered it indirectly. Getty Science news in pictures Nasa releases stunning images of Jupiter's great red spot The storm bigger than the Earth, has been swhirling for 350 years. The image's colours have been enhanced after it was sent back to Earth. Pictures by: Tom Momary

“It’s like a precursor if you like of what we know today as integral calculus, which allows us to calculate the movements of decelerating or accelerating objects. It’s a concept that was invented twice; once in ancient Babylonia and then re-invented around 1350 in medieval Europe. The ancient Greeks never did this,” he said.

There are no geometrical shapes or graphs depicted on the clay tablets, and all the descriptions are in cuneiform script. However, it is clear from the well-documented terminology used by the priests that they were referring to this form of abstract geometrical calculation, Professor Ossendrijver said.

“The tablets were written by priests in the temple. They computed the position of all five planets that they knew about, but Jupiter had the largest number of texts devoted to it. This was probably because Jupiter was associated with the supreme god of Babylon, Marduk,” Professor Ossendrijver said.