Giovanni Ceva (September 1, 1647 – May 13, 1734) was an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

widely known for proving

Ceva's theorem In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle , let the lines be drawn from the vertices to a common point (not on one of the sides of ), to meet opposite sides at respectively. (The segments are kn ...

in elementary

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

. His brother,

Tommaso Ceva Tommaso Ceva (December 20, 1648 – February 3, 1737) was an Italian Jesuit mathematician from Milan. He was the brother of Giovanni Ceva. Biography From a wealthy Milanese family, Ceva entered the Society of Jesus in 1663. He taught math ...

was also a well-known poet and mathematician.

Life

Ceva received his education at a

Jesuit , image = Ihs-logo.svg , image_size = 175px , caption = ChristogramOfficial seal of the Jesuits , abbreviation = SJ , nickname = Jesuits , formation = , founders ...

college in

Milan Milan ( , , Lombard: ; it, Milano ) is a city in northern Italy, capital of Lombardy, and the second-most populous city proper in Italy after Rome. The city proper has a population of about 1.4 million, while its metropolitan city h ...

. Later in his life, he studied at the

University of Pisa The University of Pisa ( it, Università di Pisa, UniPi), officially founded in 1343, is one of the oldest universities in Europe. History The Origins The University of Pisa was officially founded in 1343, although various scholars place ...

, where he subsequently became a professor. In 1686, however, he was designated as the Professor of

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

at the University of Mantua and worked there for the rest of his life.

Work

Ceva studied

for most of his long life. In 1678, he published a now famous theorem on

synthetic geometry Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates or formulae. It relies on the axiomatic method and the tools directly related to them, that is, compa ...

in a triangle called Ceva's Theorem. The theorem, already known to Yusuf Al-Mu'taman ibn Hűd in 11th century, states that if three line segments are drawn from the vertices of a triangle to the opposite sides, then the three line segments are concurrent if, and only if, the product of the ratios of the newly created line segments on each side of the triangle is equal to one. He published this theorem in ''De lineis rectis''. Ceva also rediscovered and published

Menelaus's theorem Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ''ABC'', and a transversal line that crosses ''BC'', ''AC'', and ''AB'' at points ''D'', ''E'', and ''F'' respe ...

. He published ''Opuscula mathematica'' in 1682 and ''Geometria Motus'' in 1692, as well. In ''Geometria Motus'', he anticipated the

infinitesimal calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

. Finally, Ceva wrote ''De Re Nummeraria'' in 1711, which was one of the first books in

mathematical economics Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference an ...

. Giovanni Ceva also studied applications of mechanics and

statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with ...

to geometric systems. At one point, however, he incorrectly resolved that the periods of

oscillation Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

of two pendulums were in the same ratio as their lengths, but he later realized and corrected the error. Ceva also worked on

hydraulics Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...

. In 1728, he published ''Opus hydrostaticum'' which discusses his work in

. In fact, he used his knowledge of

to stop a project from diverting the river Reno into the river Po.

List of works

* * * ''Geometria Motus'', 1692 * * * * Giovanni Benedetto Ceva – Ragioni del signor Giovanni Ceva commissario dell', 1716 - BEIC 2053918.tif, ''Ragioni ..contra l'introduzione del Reno nel Pò'', 1716 Giovanni Benedetto Ceva – Replica di Giovanni Ceva, commissario dell'arciduc, 1717 - BEIC 13326368.tif, ''Replica ..in difesa delle sue dimostrazioni, e ragioni per la quali non debbasi introdurre Reno in Po'', 1717

References

* "Ceva, Giovanni." MacTutor History of Mathematics archive. 2006. O'Connor, John J., and Edmund F. Robertson. http://www-history.mcs.st-andrews.ac.uk/Biographies/Ceva_Giovanni.html * "Ceva, Giovanni." Encyclopædia Britannica. 2005. Encyclopædia Britannica Online. https://www.britannica.com/biography/Giovanni-Ceva. {{DEFAULTSORT:Ceva, Giovanni 1647 births 1734 deaths Scientists from Milan 17th-century Italian mathematicians 18th-century Italian mathematicians

Life

Work

List of works

See also

References