A Brief Historical Introduction

Abstract

The first problems belonging properly to mathematical analysis arose during fifth century bce, when Greek mathematicians became interested in the properties of various curved shapes and surfaces. The problem of squaring a circle (that is, constructing a square of the same area as a given circle with only a compass and straightedge) was well known by the second half of the century, and Hippias had already discovered a curve called the quadratix during an attempt at a solution. Hippocrates was also active during the second half of the fifth century bce, and he defined the areas of several regions bound by curves (“Hippocratic lunes”).