Gottfried Wilhelm von Gottfried Wilhelm von LeibnizLeibniz

Leibniz constructed the first Leibniz constructed the first mechanical calculatormechanical calculator, known as the , known as the Stepped ReckonerStepped Reckoner, capable of multiplication and division. He , capable of multiplication and division. He

also developed the modern form of the also developed the modern form of the binary numeral systembinary numeral system, , used in digital used in digital computercomputers. The Leibniz calculator incorporated a s. The Leibniz calculator incorporated a new mechanical feature, the stepped drum — a cylinder bearing new mechanical feature, the stepped drum — a cylinder bearing nine teeth of different lengths which increase in equal amounts nine teeth of different lengths which increase in equal amounts

around the drum. Although the Leibniz calculator was not around the drum. Although the Leibniz calculator was not developed for commercial production, the stepped drum developed for commercial production, the stepped drum

principle survived for 300 years and was used in many later principle survived for 300 years and was used in many later calculating systems.calculating systems.

Main contribution: CALCULUS!

Two other main ideas:

Universal language – a language which all knowledge could be formally expressed

Calculus of Reason – reduce all problems to numerical computation

Other things he contributed to:

•multiple indices to state the result of three linear equations

•study of differential equations •discovering the method of separation of variables •reduction of homogeneous equations to separable

ones•the procedure for solving first order linear

equations •laid the foundations of the theory of determinants•integrated rational fractions in trigonometric and

logarithmic functions•produced a theory of special curves

•one of the first to work out the properties of the binary number system