Arising of series: Sample of Archimedes and Madhava

In this thesis, the method of calculating the field of a parabola section of Archimedes and Madhava's series of studies on the series, especially the method of calculating the number with series is examined. However, examples of different civilizations' approaches to the series have been given. Series XIX. in the centuries until the cradle of different civilizations can be called as the application areas were found. For example, after examining the examples that relate to the series in Egypt and Mesopotamia, the area of the area was calculated by Eudoxos 'method of consumption, where Archimedes was also used as the starting point of the definite integral of Eudoxos' consumption method with the study of the Greeks