the Quadrature of Parabola

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Quadrature of the Parabola is a treatise on geometry, written by Archimedes in the 3rd century B.C. Written as a letter to his friend Dositheus, the work presents 24 propositions regarding parabolas, culminating in a proof that the area of a parabolic segment (the region enclosed by a parabola and a line) is 4/3 that of a certain inscribed triangle. The proof uses the method of exhaustion. Archimedes dissects the area into infinitely many triangles whose areas form a geometric progression. He computes the sum of the resulting geometric series, and proves that this is the area of the parabolic segment. This represents the most sophisticated use of the method of exhaustion in ancient mathematics, and remained unsurpassed until the development of integral calculus in the 17th century.