Giambattista Benedetti

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Giambattista Benedetti
BornAugust 14, 1530
DiedJanuary 20, 1590 (59 years)
Nationality Italian
Scientific career
Fields Mathematician

Giambattista (Gianbattista) Benedetti (August 14, 1530 in Venice January 20, 1590 in Turin) was an Italian mathematician from Venice who was also interested in physics, mechanics, the construction of sundials, and the science of music. [1]

Venice Comune in Veneto, Italy

Venice is a city in northeastern Italy and the capital of the Veneto region. It is situated on a group of 118 small islands that are separated by canals and linked by over 400 bridges. The islands are located in the shallow Venetian Lagoon, an enclosed bay that lies between the mouths of the Po and the Piave rivers. In 2018, 260,897 people resided in the Comune di Venezia, of whom around 55,000 live in the historical city of Venice. Together with Padua and Treviso, the city is included in the Padua-Treviso-Venice Metropolitan Area (PATREVE), which is considered a statistical metropolitan area, with a total population of 2.6 million.

Turin Comune in Piedmont, Italy

Turin is a city and an important business and cultural centre in northern Italy. It is the capital city of the Metropolitan City of Turin and of the Piedmont region, and was the first capital city of Italy from 1861 to 1865. The city is located mainly on the western bank of the Po River, in front of Susa Valley, and is surrounded by the western Alpine arch and Superga Hill. The population of the city proper is 878,074 while the population of the urban area is estimated by Eurostat to be 1.7 million inhabitants. The Turin metropolitan area is estimated by the OECD to have a population of 2.2 million.

Italy republic in Southern Europe

Italy, officially the Italian Republic, is a country in Southern Europe. Located in the middle of the Mediterranean Sea, Italy shares open land borders with France, Switzerland, Austria, Slovenia and the enclaved microstates San Marino and Vatican City. Italy covers an area of 301,340 km2 (116,350 sq mi) and has a largely temperate seasonal and Mediterranean climate. With around 61 million inhabitants, it is the fourth-most populous EU member state and the most populous country in Southern Europe.


Resolutio omnium Euclidis problematum, 1553 Benedetti - Resolutio omnium Euclidis problematum, 1553 - 11183.jpg
Resolutio omnium Euclidis problematum, 1553

Science of motion

In his works Resolutio omnium Euclidis problematum (1553) and Demonstratio proportionum motuum localium (1554), Benedetti proposed a new doctrine of the speed of bodies in free fall. The accepted Aristotelian doctrine at that time was that the speed of a freely falling body is directly proportional to the total weight of the body and inversely proportional to the density of the medium. Benedetti's view was that the speed depends on just the difference between the specific gravity of the body and that of the medium. As opposed to the Aristotelian theory, his theory predicts that two objects of the same material but of different weights would fall at the same speed, and also that objects of different materials in a vacuum would fall at different though finite speeds. [1] [2]

Aristotelian physics is a form of natural science described in the works of the Greek philosopher Aristotle (384–322 BCE). In his work Physics, Aristotle intended to establish general principles of change that govern all natural bodies, both living and inanimate, celestial and terrestrial – including all motion, quantitative change, qualitative change, and substantial change.

Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water. The term "relative density" is often preferred in scientific usage. It is defined as a ratio of density of particular substance with that of water.

In a second edition of the Demonstratio (also 1554), he extended this theory to include the effect of the resistance of the medium, which he said was proportional to the cross section or the surface area of the body. Thus two objects of the same material but of different surface areas would only fall at equal speeds in a vacuum. He repeated this version of his theory in his later Diversarum speculationum mathematicarum et physicarum liber (1585). In this work he explains his theory in terms of the then current theory of impetus. [1] [2]

Theory of impetus

The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics, put forth initially to explain projectile motion against gravity. It was introduced by John Philoponus in the 6th century and elaborated by Nur ad-Din al-Bitruji at the end of the 12th century, but was only established in western scientific thought by Jean Buridan in the 14th century. It is the intellectual precursor to the concepts of inertia, momentum and acceleration in classical mechanics.

It is thought that Galileo derived his initial theory of the speed of a freely falling body from his reading of Benedetti's works. Thus the account found in Galileo's De motu, his early work on the science of motion, follows Benedetti's initial theory as described above. It omits the later development which included the resistance of the medium and not just its density. In this early work, Galileo also subscribes to the theory of impetus. [3]

In 1572, the Jesuit Jean Taisner published from the press of Johann Birkmann of Cologne a work entitled Opusculum perpetua memoria dignissimum, de natura magnetis et ejus effectibus, Item de motu continuo. This is considered a piece of plagiarism, as Taisnier presents, as though his own, the Epistola de magnete of Peter of Maricourt and the second edition of Benedetti's Demonstratio. [4]

Cologne Place in North Rhine-Westphalia, Germany

Cologne is the largest city of Germany's most populous federal state of North Rhine-Westphalia, and its 1 million+ (2016) inhabitants make it the fourth most populous city in Germany after Berlin, Hamburg, and Munich. The largest city on the Rhine, it is also the most populous city both of the Rhine-Ruhr Metropolitan Region, which is Germany's largest and one of Europe's major metropolitan areas, and of the Rhineland. Centred on the left bank of the Rhine, Cologne is about 45 kilometres (28 mi) southeast of North Rhine-Westphalia's capital of Düsseldorf and 25 kilometres (16 mi) northwest of Bonn. It is the largest city in the Central Franconian and Ripuarian dialect areas.

Plagiarism using another authors work as if it was ones own original work

Plagiarism is the "wrongful appropriation" and "stealing and publication" of another author's "language, thoughts, ideas, or expressions" and the representation of them as one's own original work.


In a letter to Cipriano de Rore dated from around 1563, Benedetti proposed a new theory of the cause of consonance, arguing that since sound consists of air waves or vibrations, in the more consonant intervals the shorter, more frequent waves concurred with the longer, more frequent waves at regular intervals. Isaac Beeckman and Marin Mersenne both adopted this theory in the next century. In the same letter, he proposed a measure of consonance by taking the product of the numerator and the denominator of a rational interval in lowest terms. James Tenney also used this method to develop his measure of "harmonic distance" (log(ab) is the harmonic distance for the ratio b/a measured from an arbitrary tonal center 1/1). When they sought Descartes' opinion on Benedetti's theory, Descartes declined to judge the goodness of consonances by such a rational method. Descartes argued that the ear prefers one or another according to the musical context rather than because of any concordance of vibrations. [5]

Cipriano de Rore Italian composer

Cyprien «Cipriano» de Rore was a Franco-Flemish composer of the Renaissance, active in Italy. Not only was he a central representative of the generation of Franco-Flemish composers after Josquin des Prez who went to live and work in Italy, but he was one of the most prominent composers of madrigals in the middle of the 16th century. His experimental, chromatic, and highly expressive style had a decisive influence on the subsequent development of that secular music form.

Consonance and dissonance categorizations of simultaneous or successive sounds

In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Consonance is associated with sweetness, pleasantness, and acceptability; dissonance is associated with harshness, unpleasantness, or unacceptability.

Sound mechanical wave that is an oscillation of pressure transmitted through a solid, liquid, or gas, composed of frequencies within the range of hearing; pressure wave, generated by vibrating structure

In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.

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Inertia is the resistance, of any physical object, to any change in its velocity. This includes changes to the object's speed, or direction of motion.

Light electromagnetic radiation in or near visible spectrum

Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, which is the visible spectrum that is visible to the human eye and is responsible for the sense of sight. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), or 4.00 × 10−7 to 7.00 × 10−7 m, between the infrared and the ultraviolet. This wavelength means a frequency range of roughly 430–750 terahertz (THz).

Mass Quantity of matter

Mass is both a property of a physical body and a measure of its resistance to acceleration when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies.

Mechanics is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece with the writings of Aristotle and Archimedes. During the early modern period, scientists such as Galileo, Kepler, and Newton laid the foundation for what is now known as classical mechanics. It is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as a branch of science which deals with the motion of and forces on objects. The field is yet less widely understood in terms of quantum theory.

Timeline of classical mechanics:

Marin Mersenne French theologian, philosopher, mathematician and music theorist, often referred to as the "father of acoustics"

Marin Mersenne, Marin Mersennus or le PèreMersenne was a French polymath, whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for Mersenne prime numbers, those which can be written in the form Mn = 2n − 1 for some integer n. He also developed Mersenne's laws, which describe the harmonics of a vibrating string, and his seminal work on music theory, Harmonie universelle, for which he is referred to as the "father of acoustics". Mersenne, an ordained priest, had many contacts in the scientific world and has been called "the center of the world of science and mathematics during the first half of the 1600s" and, because of his ability to make connections between people and ideas, "the post-box of Europe". He was also a member of the Minim religious order and wrote and lectured on theology and philosophy.

Jean Buridan medieval philosopher

Jean Buridan was an influential 14th century French philosopher.

<i>Two New Sciences</i> book by Galileo

The Discourses and Mathematical Demonstrations Relating to Two New Sciences, published in 1638 was Galileo's final book and a scientific testament covering much of his work in physics over the preceding thirty years.

Nicole Oresme French philosopher

Nicole Oresme, also known as Nicolas Oresme, Nicholas Oresme, or Nicolas d'Oresme, was a significant philosopher of the later Middle Ages. He wrote influential works on economics, mathematics, physics, astrology and astronomy, philosophy, and theology; was Bishop of Lisieux, a translator, a counselor of King Charles V of France, and probably one of the most original thinkers of 14th-century Europe.

John Philoponus, also known as John the Grammarian or John of Alexandria, was a Byzantine Alexandrian philologist, Aristotelian commentator and Christian theologian, author of a considerable number of philosophical treatises and theological works. A rigorous, sometimes polemical writer and an original thinker who was controversial in his own time, John Philoponus broke from the Aristotelian–Neoplatonic tradition, questioning methodology and eventually leading to empiricism in the natural sciences. He was one of the first to propose a "theory of impetus" similar to the modern concept of inertia over Aristotelian dynamics.

This article deals with the history of classical mechanics.

Jean Taisner was a musician, astrologer, and self-styled mathematician who published a number of works.

Galileos Leaning Tower of Pisa experiment celebrated demonstration of gravity

Between 1589–92, the Italian scientist Galileo Galilei is said to have dropped two spheres of different masses from the Leaning Tower of Pisa to demonstrate that their time of descent was independent of their mass, according to a biography by Galileo's pupil Vincenzo Viviani, composed in 1654 and published in 1717.

Mechanical explanations of gravitation are attempts to explain the action of gravity by aid of basic mechanical processes, such as pressure forces caused by pushes, without the use of any action at a distance. These theories were developed from the 16th until the 19th century in connection with the aether. However, such models are no longer regarded as viable theories within the mainstream scientific community and general relativity is now the standard model to describe gravitation without the use of actions at a distance. Modern "quantum gravity" hypotheses also attempt to describe gravity by more fundamental processes such as particle fields, but they are not based on classical mechanics.

Quaestiones quaedam philosophicae is the name given to a set of notes that Isaac Newton kept for himself during his earlier years in Cambridge. They concern questions in the natural philosophy of the day that interested him. Apart from the light it throws on the formation of his own agenda for research, the major interest in these notes is the documentation of the unaided development of the scientific method in the mind of Newton, whereby every question is put to experimental test.

The year 1554 CE in science and technology included a number of events, some of which are listed here.

De Motu Antiquiora, or simply De Motu, is Galileo Galilei's early written work on motion. It was written largely between 1589 and 1592, but was not published until 1687, after his death. It was never published during his lifetime due to a few uncertainties in his mathematics and certain parts of his understanding. Because it was never published during his life, he never composed a final draft. In the last parts of his work, the writing style changes from an essay to a dialogue between two people who strongly uphold his views.

Jacques Alexandre Le Tenneur French mathematician

Jacques-Alexandre Le Tenneur was a French mathematician who defended Galileo Galilei’s ideas. He corresponded with fellow mathematicians such as Pierre Gassendi, Pierre Hérigone and Marin Mersenne. It is unclear when or where he died but he probably lived from 1610 to 1660.


  1. 1 2 3 "Benedetti, Giovanni Battista". The Archimedes Project. Retrieved 2010-03-11.
  2. 1 2 Drabkin, I. E. (1963). "Two Versions of G. B. Benedetti's Demonstratio Proportionum Motuum Localium". Isis. 54 (2): 259–262. doi:10.1086/349706. ISSN   0021-1753. JSTOR   228543.
  3. Wallace, William A. (1998). "Galileo's Pisan studies in science and philosophy". In Peter K. Machamer (ed.). The Cambridge Companion to Galileo. Cambridge University Press. pp. 27–52. ISBN   978-0-521-58841-6.
  4. Duhem, Pierre (1911). "Pierre de Maricourt". The Catholic Encyclopedia. 12. New York: Robert Appleton Company.
  5. Palisca, Claude V. (1973). "Music and Science". In Philip Paul Wiener (ed.). Dictionary of the History of Ideas: Studies of Selected Pivotal Ideas. 3. New York: Charles Scribner's Sons. ISBN   978-0-684-16424-3.