 While Galileo 's application of mathematics to experimental physics was innovative , his mathematical methods were the standard ones of the day , including dozens of examples of an inverse proportion square root method passed down from Fibonacci and Archimedes . The analysis and proofs relied heavily on the Eudoxian theory of proportion , as set forth in the fifth book of Euclid 's Elements . This theory had become available only a century before , thanks to accurate translations by Tartaglia and others ; but by the end of Galileo 's life , it was being superseded by the algebraic methods of Descartes . 
