Giambattista Benedetti

Giovanni Battista Benedetti ( born August 14, 1530 in Venice, † January 20, 1590 in Turin) was a mathematician, physicist, astronomer, architect and philosopher. He is known as a precursor of Galileo Galilei in the theory of free fall and in the critique of mechanics of Aristotle.

Life

Was taught Benedetti, who came from better Venetian circles, from his father, who was himself very interested in philosophy and the natural sciences and of Spanish origin. Nicolo Tartaglia taught him from 1546 to 1548 in the first four books of Euclid's Elements. Everything he had studied other with their own effort and work, because for the inquisitive nothing is difficult ( Moritz Cantor. Preferences on the History of Mathematics, Vol 2 Chap 67 p 566. ). He did not go to university.

1558 was Benedetti Court scholar and mathematician of Ottavio Farnese, Duke of Parma. During this time he oversaw public works, led by astronomical observations and astrological works and calculated, among other sundials (3). During this time, he was paid only sporadically, but could the bridge because he was wealthy by default. 1559/60 he held in Rome lectures on Aristotle.

In 1567 he accepted an invitation from the Duke of Savoy, Emanuele Filiberto to Turin where he lived until his death. His reputation as a mathematician was now strengthened by his writings. In Turin he also lectured at the University and was a good teacher in mathematics ( he never referred to himself as a professor, including actually a university degree was required). The Duke was very interested in the advancement of science and the development of infrastructure. Benedetti was his adviser and employed as engineer.

He was married - a daughter was born in 1554.

Services

Benedetti's first publication ( 1) of the 1553 treated elementary geometric constructions under the constraint of a fixed circular opening ( practically a rusted compass ). Although this was a popular topic at that time under Italian mathematicians (Ferrari, Cardano, Tartaglia ) and had already been solved before him to Benedetti's work is characterized by more elegance and intelligibility. In two letters Benedetti brought for the first time, the consonance and dissonance of two tones with the frequency of vibrations of the air in conjunction. He constructed wells, focusing on a calendar reform ( 4), took care of fortifications and showed in his views ( 2) the rate of fall of different body as a precursor of Galileo.

Benedetti had his thoughts on free fall, published in the form of a letter to the Spanish Dominicans Gabriel de Guzman ( Abbot of Pontelungo ), with whom he had discussed in Venice in its resolutions of 1553 to preempt priority claims. Detailed he put Represent in his demonstrations of 1554

Benedetti here refuted the false hypothesis of Aristotle, according to which a body falling more quickly must the heavier it is, with a simple thought experiment: If two falling balls connected to a ( massless ) rod, nothing changes on the rate of fall, although the mass of the total body increases.

The thought experiment of Benedetti to the free fall is also published in the Discorsi (published in 1638) of Galileo and was often attributed to this. Galileo mentioned Benedetti not in his work, but knew Benedetti's work almost certainly about the philosopher Jacopo Mazzoni, with whom he discussed in 1590 in Pisa on mechanics and demonstrably treated in his writings Benedetti. Influential Benedetti was stressed for Galileo did not last as a vehement critic of the mechanics of Aristotle, such as Alexandre Koyré. The other hand, Galileo's early work De motu by Stillman Drake no special influence Benedetti, who could not be attributed to other sources, such as the medieval impetus theory (Jean Buridan ).

Benedetti also looked at already friction effects in free fall, which lead to the same case, different speeds heavy body can only be achieved in a vacuum. He already took to correct that the friction depended on the surface area.

In 1585 he published an anthology of various works, among other things, perspective and music and geometry ( such as isoperimetric figures, spherical triangles, regular polyhedra, a commentary on the fifth book of Euclid ). For example, it showed that the construction of the Pentagon with ruler and compass fixed orifice by Albrecht Dürer is not exact. There is also a further critique of the mechanics of Aristotle and that of Tartaglia. Benedetti wrote here as one of the first explicitly that a body moves tangentially to the circle in circular motion after the abolition of coercive forces on a straight line. He also reiterated his arguments to the free fall was correct that this acts a constant acceleration. But unlike Galileo, he was no mathematical formulation of the acceleration. Benedetti also dealt with the hydraulics and said correctly predicted that winds due to different air densities, generated by differential heating by the sun arise, and found a qualitatively correct explanation for clouds.

Also reflections on music can be found in his book of 1585, but which he has a letter against the choirmaster in Parma Cipriano da Rore 1561/62 made ​​. He led the consonance and dissonance of tones to the superposition of air waves that produce the musical instruments back. He had influence on later discussions with Isaac Beeckman and Marin Mersenne.

Another section of the work was a representation of the perspective ( De rationibus operationum perspectivae ), where he used three-dimensional structures and resorted to Euclid 's Optics. He also corrects errors of Dürer.

He said in his last book, also his death in 1592 from astrological calculations beforehand what he corrected on his deathbed in 1590 and attributed to an error in the output data.

Works

• ( 1) De resolutione omnium Euclidis problematum aliorumque una tantummodo Circuli data apertura, Venice 1553
• ( 2) demonstrations proportionum motuum localium, Venice 1554
• ( 3) De gnomonum umbrarumque solarium usu liber, 1573 ( on sundials )
• ( 4) De temporum emendatione opinio, Augustae Taurinorum, 1578 (Calendar)
• Consideratione d' intorno al discorso della della terra grandezza e dell ' acqua di Berga, Turin 1579 (his contribution to a contemporary controversy about the relative volumes of water and earth; Antonio Berga was a professor of philosophy from 1569 in Turin)
• Diversarum speculationum mathematical corum et physicarum liber, Turin 1585 (see here)

A collection of letters and manuscripts by Benedetti in the National Library in Turin ( and the only known portrait ) were destroyed in 1904 by fire.