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Achillini, Alessandro

Agricola, Georgius

Alberti, Leone Battista



Babington, John

Baif, Lazare de

Baldi, Bernardino

Baliani, Giovanni Battista

Barocius, Franciscus

Benedetti, Giovanni Battista

Berga, Antonio

Biancani, Giuseppe

Borelli, Giovanni Alfonso

Borro, Girolamo

Boyle, Robert

Branca, Giovanni

Buonamici, Francesco

Buteo, Johannes

Cardano, Girolamo

Casati, Paolo

Castelli, Benedetto

Cataneo, Girolamo

Ceredi, Giuseppe

Ceva, Giovanni

Cicero, M. Tullius

Commandino, Federico

Delfino, Federico

Descartes, Rene



Fabri, Honore

Foscarini, Paolo Antonio

Galilei, Galileo

Gassendi, Pierre

Ghetaldi, Marino

Giphanius, Hubert

Guevara, Giovanni di

Heron Alexandrinus

Heytesbury, William

Hutton, Charles

Jordanus de Nemore

Landi, Bassiano

Lorini, Buonaiuto


Manuzio, Paolo

Marci of Kronland, Johannes Marcus

Mellini, Domenico

Mersenne, Marin

Monantheuil, Henri de

Monte, Guidobaldo del

Morelli, Gregorio

Newton, Isaac

Pacioli, Luca

Pappus Alexandrinus

Salusbury, Thomas

Santbech, Daniel

Schott, Gaspar

Schreck, Johann Terrenz

Stelliola, Niccolò Antonio

Stevin, Simon

Tartaglia, Niccolò

Thomaz, Alvaro


Torricelli, Evangelista

Valerio, Luca

Varro, Michel

Vitruvius Pollio

Wolff, Christian von

Benedetti, Giovanni Battista
born on 14.8.1530 in Venice, died on 20.1.1590 in Turin, Italian mathematician and physicist

Benedetti hailed from a rich patrician family in Venice, but apparently was not related to the other established Venetian patrician families of the same name. Through his ancestry and his wealth, Benedetti was economically independent his entire life. He received his first and only systematic education in philosophy, music and mathematics from his father, who was Spanish and himself very interested in philosophy and the natural sciences. Because Benedetti never attended a university and accordingly had no academic certification, he was never able to teach at a university. In the years 1546 – 1548 Benedetti studied the first four books of Euclid’s Elements under the guidance of Niccolò Tartaglia, but there appears to have been no closer relationship between Benedetti and Tartaglia, as Tartaglia never mentions Benedetti as his pupil.
In 1558 Benedetti became court mathematician for Duke Ottavio Farnese in Parma. In winter 1559/60 he held lectures in Rome on Aristotle’s natural science and impressed his listeners with his acumen, intellectual independence and eloquence. At court in Parma Benedetti gave lessons, served as astrologist and was an adviser in the execution of public construction. Here he also made astronomical observations and built sundials, whose construction he later described in his own book. In 1567 he was invited by the Duke of Savoy, Emanule Filiberto, to the court in Turin, where until his death he remained an important adviser to Emanuele Filiberto, who made great efforts to renew and support the sciences in his country.
Benedetti supplied the first evidence of his great mathematical talent with his work “Resolutio omnium Euclidis problematum,” published in Venice in 1553, in which he deals with the general solution of all problems in Euclid’s Elements utilizing a compass with fixed radius. Benedetti’s solution is more comprehensive and elegant than those given by Tartaglia and Ludovico Ferrara; it is also more systematic than the solution Tartaglia offers in his final work, “Trattato generale di numeri e misure” from 1560, in which Tartaglia makes no mention of his former pupil Benedetti. The dedication to the Spanish Dominican monk Gabriel de Guzman that opens the “Resolutio” includes the first proof by Benedetti demonstrating that bodies with the same specific weight fall through a medium with the same velocity, and not, as Aristotle claimed, with a velocity proportional to the entire weight of the body. For his proof Benedetti used the Archimedean principle.
Although Benedetti’s views about free fall in media were never discussed directly in works printed during the period, they do indeed appear to have provoked far-reaching discussions among his contemporaries, for in 1554 he published in Venice his “Demonstratio proportionum motuum localium,” in which he discusses Aristotle’s views at length and responds to his critics. In the second edition of his “Demonstratio,” also published in Venice in 1554, Benedetti shows that the resistance that a falling body incurs in a medium depends not on its volume, but on its surface area. The consequence of this is that the absolute equality of the velocity of falling bodies of the same specific weight, but different total weights, can be determined only in a vacuum. Benedetti repeats this correction to his law of fall in his “Diversarum speculationum mathematicarum et physicarum liber,” published in Turin in 1585, whereby here he explains further the increase in the acceleration of the falling bodies, fully in the spirit of the theories of impetus predominant at the time, that the impetus of the falling body increases constantly as it falls.
In two letters of the year 1563 to Cipriano da Rore, choirmaster at the Parma court, Benedetti attributes for the first time the musical consonance and dissonance of two tones to the ratio of the frequency of oscillations of the airwaves generated by the resounding strings or instruments. By claiming and presuming that the frequency of two strings of equal tension must have an inverse ratio to the lengths of the strings, he was able to describe mathematically the degree of consonance or dissonance of two tones. These letters so important for the science of acoustics and musical theory were not published until 1585.
In his book “De gnomon umbrarumque solium usu liber” of 1573 he deals at length with the construction of sundials with faces of varying inclinations. The subject of his tract “De temporum emendatione opinion” of 1578 is the correction and reform of the calendar. In 1578, the Duke of Savoy, Emanuele Filiberto, initiated a public disputation at the University of Turin, at which Benedetti argued with Antonio Berga about whether there was more water or more land on the earth. The views which Benedetti brought forth against Berga in this debate were published in Turin in 1579 under the title “Consideratione .... d’intorno al discorso della grandezza terra, et dell’acqua.”
His final work, “Diversarum speculationum mathematicorum et physicarum liber” (Turin 1585) is considered his magnum opus and was probably the most important contribution to physics in Italy until Galileo. The mathematical section concerns arithmetical principles, but proves them geometrically; further it includes a discussion of perspective and a commentary on the fifth book of Euclid’s Elements. The mechanical section is a fundamental critique of a number of sections of the Pseudo-Aristotelian tract on mechanics and also investigates issues of hydrostatics.
Benedetti constructed a variety of fountains and also executed other public tasks: in Turin he supervised and also improved military fortifications and was held in high esteem at court. With his scientific writings Benedetti contributed much to surmounting Aristotelian physics as taught and imparted by academia and paved the way for the later development of physics.

Digital facsimiles (1 texts)



Consideratione d'intorno al discorso della grandezza della terra e dell' acqua di Berga