Prepared By- Abhinav Prepared By- Abhinav

In 18th century mathematics In 18th century mathematics was was already a modern science already a modern science

Mathematics begins to develop very Mathematics begins to develop very fast because of introducing it to fast because of introducing it to schoolsschools

Therefore everyone have a chance to Therefore everyone have a chance to learn the basic learnings of learn the basic learnings of mathematicsmathematics

LEONHARD EULERLEONHARD EULER

Leonhard Paul EulerLeonhard Paul Euler(1707-1783)(1707-1783)

He was a Swiss mathematicianHe was a Swiss mathematician Johann Bernoulli made the biggest Johann Bernoulli made the biggest

influence on influence on EulerEuler 1741 went in Berlin and worked in Berlin 1741 went in Berlin and worked in Berlin

Academy for 25 years and after that he Academy for 25 years and after that he returned in St Ptersburg where he spent returned in St Ptersburg where he spent the rest of his life.the rest of his life.

Euler worked in almost all areas of mathematics: Euler worked in almost all areas of mathematics: geometrygeometry, , calculuscalculus, , trigonometrytrigonometry, , algebraalgebra,,applied applied mathematics, graph theorymathematics, graph theory and and number theorynumber theory, , as well as , as well as , opticsoptics and other areas of phys and other areas of physicsics. .

He introduced several notational conventions in He introduced several notational conventions in mathematicsmathematics

He wrote 45 books an over 700 He wrote 45 books an over 700 theses.theses.

His main book is His main book is Introduction in Introduction in Analisyis of the Infinite.Analisyis of the Infinite.

AnalysisAnalysis

He defined the exponential function He defined the exponential function for complex numbers, and for complex numbers, and discovered its relation to the discovered its relation to the trigonometric functionstrigonometric functions

GeometryGeometry Euler (1765) showed that in any Euler (1765) showed that in any

triangle, the orthocenter, triangle, the orthocenter, circumcenter, centroid, and nine-circumcenter, centroid, and nine-point center are point center are collinear.collinear.

Because of that the line which Because of that the line which connects the points above is connects the points above is called called Euler line.Euler line.

Euclid of AlexandriaEuclid of Alexandria

He works on perspective, conic sections, He works on perspective, conic sections, spherical geometry, number theory spherical geometry, number theory

We just know that he went to Egypt where We just know that he went to Egypt where he taught mathematics in a maths school he taught mathematics in a maths school that he founded. During that time he also that he founded. During that time he also did many research one of his most did many research one of his most successful was « Elements ».successful was « Elements ».

AnalysisAnalysis He contributed greatly to the He contributed greatly to the

``geometrization'' of mathematics and set ``geometrization'' of mathematics and set the standard for rigor and logical the standard for rigor and logical structure for mathematical works.structure for mathematical works.