Giovanni Ceva
Encyclopedia
Giovanni Ceva was an Italian
mathematician
widely known for proving Ceva's theorem
in elementary geometry
. His brother, Tommaso Ceva
was also a well known poet and mathematician.
Ceva received his education at a Jesuit college in Milan
. Later in his life, he studied at the University of Pisa
, where he subsequently became a professor. In 1686, however, he was designated as the Professor of Mathematics
at the University of Mantua and worked there for the rest of his life.
Ceva studied geometry
for most of his long life. In 1678, he published a now famous theorem on synthetic geometry
in a triangle called Ceva’s Theorem. The theorem 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 new theorem in De lineis rectis.
Ceva not only published his own theorem, but he also rediscovered and published Menelaus's theorem. He published Opuscula mathematica in 1682 and Geometria Motus in 1692, as well. In Geometria Motus, he anticipated the infinitesimal calculus
. Finally, Ceva wrote De Re Nummeraria in 1711, which was one of the first books in mathematical economics
.
Giovanni Ceva also studied applications of mechanics and statics
to geometric systems. At one point, however, he incorrectly resolved that the periods of oscillation
of two pendulums were in the same ratio as their lengths, but he later realized and corrected the error. Ceva also worked on hydraulics
. In 1728, he published Opus hydrostaticum which discusses his work in hydraulics
. In fact, he used his knowledge of hydraulics
to stop a project from diverting the river Reno into the river Po
.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
widely known for proving Ceva's theorem
Ceva's theorem
Ceva's theorem is a theorem about triangles in plane geometry. Given a triangle ABC, let the lines AO, BO and CO be drawn from the vertices to a common point O to meet opposite sides at D, E and F respectively...
in elementary geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
. His brother, Tommaso Ceva
Tommaso Ceva
Tommaso Ceva was an Italian Jesuit mathematician from Milan. He was the brother of Giovanni Ceva....
was also a well known poet and mathematician.
Ceva received his education at a Jesuit college in Milan
Milan
Milan is the second-largest city in Italy and the capital city of the region of Lombardy and of the province of Milan. The city proper has a population of about 1.3 million, while its urban area, roughly coinciding with its administrative province and the bordering Province of Monza and Brianza ,...
. Later in his life, he studied at the University of Pisa
University of Pisa
The University of Pisa , located in Pisa, Tuscany, is one of the oldest universities in Italy. It was formally founded on September 3, 1343 by an edict of Pope Clement VI, although there had been lectures on law in Pisa since the 11th century...
, where he subsequently became a professor. In 1686, however, he was designated as the Professor of Mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the University of Mantua and worked there for the rest of his life.
Ceva studied geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
for most of his long life. In 1678, he published a now famous theorem on synthetic geometry
Synthetic geometry
Synthetic or axiomatic geometry is the branch of geometry which makes use of axioms, theorems and logical arguments to draw conclusions, as opposed to analytic and algebraic geometries which use analysis and algebra to perform geometric computations and solve problems.-Logical synthesis:The process...
in a triangle called Ceva’s Theorem. The theorem 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 new theorem in De lineis rectis.
Ceva not only published his own theorem, but he also rediscovered and published Menelaus's theorem. He published Opuscula mathematica in 1682 and Geometria Motus in 1692, as well. In Geometria Motus, he anticipated the infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
. Finally, Ceva wrote De Re Nummeraria in 1711, which was one of the first books in mathematical economics
Mathematical economics
Mathematical economics is the application of mathematical methods to represent economic theories and analyze problems posed in economics. It allows formulation and derivation of key relationships in a theory with clarity, generality, rigor, and simplicity...
.
Giovanni Ceva also studied applications of mechanics and statics
Statics
Statics is the branch of mechanics concerned with the analysis of loads on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity...
to geometric systems. At one point, however, he incorrectly resolved that the periods of oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
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
Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control,...
. In 1728, he published Opus hydrostaticum which discusses his work in hydraulics
Hydraulics
Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control,...
. In fact, he used his knowledge of hydraulics
Hydraulics
Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control,...
to stop a project from diverting the river Reno into the river Po
Po River
The Po |Ligurian]]: Bodincus or Bodencus) is a river that flows either or – considering the length of the Maira, a right bank tributary – eastward across northern Italy, from a spring seeping from a stony hillside at Pian del Re, a flat place at the head of the Val Po under the northwest face...
.