21 Facts About Bonaventura Cavalieri

Bonaventura Francesco Cavalieri was an Italian mathematician and a Jesuate.

Bonaventura Cavalieri is known for his work on the problems of optics and motion, work on indivisibles, the precursors of infinitesimal calculus, and the introduction of logarithms to Italy.

Bonaventura Cavalieri took his vows as a full member of the order in 1615, at the age of seventeen, and shortly after joined the Jesuat house in Pisa.

Bonaventura Cavalieri applied for the Chair of Mathematics at the University of Bologna but was turned down.

Bonaventura Cavalieri studied theology in the monastery of San Gerolamo in Milan, and was named prior of the monastery of St Peter in Lodi.

Bonaventura Cavalieri applied again to Bologna and then, in 1626, to Sapienza University, but was declined each time, despite taking six months' leave of absence to support his case to Sapienza in Rome.

Bonaventura Cavalieri was turned down from a position at the University of Parma, which he believed was due to his membership of the Jesuate order, as Parma was administered by the Jesuit order at the time.

Bonaventura Cavalieri published most of his work while at Bologna, though some of it had been written previously; his Geometria Indivisibilibus, where he outlined what would later become the method of indivisibles, was written in 1627 while in Parma and presented as part of his application to Bologna, but was not published until 1635.

Galileo exerted a strong influence on Cavalieri, and Cavalieri would write at least 112 letters to Galileo.

From 1632 to 1646, Bonaventura Cavalieri published eleven books dealing with problems in astronomy, optics, motion and geometry.

Bonaventura Cavalieri demonstrated that if, as was later shown, light has a finite and determinate speed, there is minimal interference in the image at the focus of a parabolic, hyperbolic or elliptic mirror, though this was theoretical since the mirrors required could not be constructed using contemporary technology.

Bonaventura Cavalieri then demonstrated similar results for hyperbolas and ellipses.

Bonaventura Cavalieri's work contained theoretical designs for a new type of telescope using mirrors, a reflecting telescope, initially developed to answer the question of Archimedes' Mirror and then applied on a much smaller scale as telescopes.

Bonaventura Cavalieri illustrated three different concepts for incorporating reflective mirrors within his telescope model.

Bonaventura Cavalieri used the method of indivisibles to calculate the result which is written, in the process of calculating the area enclosed in an Archimedean Spiral, which he later generalised to other figures, showing, for instance, that the volume of a cone is one-third of the volume of its circumscribed cylinder.

The method of indivisibles as set out by Bonaventura Cavalieri was powerful but was limited in its usefulness in two respects.

Andre Taquet and Paul Guldin both published responses to the Guldin's particularly in-depth critique suggested that Bonaventura Cavalieri's method was derived from the work of Johannes Kepler and Bartolomeo Sovero, attacked his method for a lack of rigorousness, and then argues that there can be no meaningful ratio between two infinities, and therefore it is meaningless to compare one to another.

Bonaventura Cavalieri argued, disingenuously, that his work regarded 'all the lines' as a separate entity from the area of a figure, and then argued that 'all the lines' and 'all the planes' dealt not with absolute but with relative infinity, and therefore could be compared.

Towards the end of his life, Bonaventura Cavalieri published two books on astronomy.

Bonaventura Cavalieri published tables of logarithms, emphasizing their practical use in the fields of astronomy and geography.

Bonaventura Cavalieri constructed a hydraulic pump for a monastery that he managed.