Algebra and geometry in Pietro Mengoli (1625–1686)

AbstractAn important step in 17th-century research on quadratures involved the use of algebraic procedures. Pietro Mengoli (1625–1686), probably the most original student of Bonaventura Cavalieri (1598–1647), was one of several scholars who developed such procedures. Algebra and geometry are closely related in his works, particularly in Geometriae Speciosae Elementa [Bologna, 1659]. Mengoli considered curves determined by equations that are now represented by y=K⋅xm⋅(t−x)n. This paper analyzes the interrelation between algebra and geometry in this work, showing the complementary nature of the two disciplines and how their combination allowed Mengoli to calculate quadratures in a new way