Da Vinci's first record of laws of friction discovered

Scientists have identified a page of scribbles in a tiny notebook dating back to 1493 as the place where Italian polymath Leonardo da Vinci first recorded the laws of friction.

The detailed study of notes and sketches by da Vinci also shows that he went on to apply this knowledge repeatedly to mechanical problems for more than 20 years.

The research by Ian Hutchings, professor at University of Cambridge in the UK, is the first detailed chronological study of da Vinci's work on friction, and has also shown how he continued to apply his knowledge of the subject to wider work on machines over the next two decades.

It is widely known that da Vinci conducted the first systematic study of friction, which underpins the modern science of "tribology", but exactly when and how he developed these ideas has been uncertain until now.

Hutchings has discovered that da Vinci's first statement of the laws of friction is in a tiny notebook measuring just 92mm x 63mm.

The book, which dates from 1493 and is now held in the Victoria and Albert Museum in the UK, contains a statement scribbled quickly in da Vinci's characteristic "mirror writing" from right to left.

The page had already attracted interest because it also carries a sketch of an old woman in black pencil with a line below reading "mortal beauty passes and does not last".

Amid  debate surrounding the significance of the quote and speculation that the sketch could represent an aged Helen of Troy, the Director of the Victoria and Albert Museum in the 1920s referred to the jottings below as "irrelevant notes and diagrams in red chalk".

The study, however, showed that the script and diagrams in red are of great interest to the history of tribology, marking a pivotal moment in da Vinci's work on the subject.

The rough geometrical figures underneath the red notes show rows of blocks being pulled by a weight hanging over a pulley - in exactly the same kind of experiment students might do today to demonstrate the laws of friction.

"The sketches and text show Leonardo understood the fundamentals of friction in 1493," said Hutchings.

"He knew that the force of friction acting between two sliding surfaces is proportional to the load pressing the surfaces together and that friction is independent of the apparent area of contact between the two surfaces," he said.

"These are the 'laws of friction' that we nowadays usually credit to a French scientist, Guillaume Amontons, working two hundred years later," he added.

The research traces a clear path of development in da Vinci's studies of friction and shows that he realised that friction, while sometimes useful and even essential, also played a key role in limiting the efficiency of machines.