Giulio Carlo de' Toschi di Fagnano
Encyclopedia
Giulio Carlo, Count Fagnano, and Marquis de Toschi (December 6, 1682 – September 26, 1766) was an Italian
mathematician
. He was probably the first to direct attention to the theory of elliptic integral
s. Fagnano was born in Senigallia
.
; this seems also to have been in his own estimation his most important work, since he had the figure of the lemniscate with the inscription: "Multifariam divisa atque dimensa Deo veritatis gloria", engraved on the title-page of his Produzioni Matematiche, which he published in two volumes (Pesaro, 1750), and dedicated to Pope Benedict XIV
. The same figure and words "Deo veritatis gloria" also appear on his tomb.
Failing to rectify
the ellipse
or hyperbola
, Fagnano attempted to determine arc
s whose difference should be rectifiable. He also pointed out the remarkable analogy existing between the integral
s which represent the arc of a circle
and the arc of a lemniscate
. Finally he proved the formula
where i stands for
.
His works were collected and published in two volumes at Pesaro
in 1750.
Some mathematicians objected to his methods of analysis founded on the infinitesimal calculus
. The most prominent of these were Viviani
, De la Hire
and Rolle
.
in Rome
and there won great distinction, except with mathematics, to which his adversion was extreme. Only after his college course that he took up its study. Later, without the help of any teacher, he mastered it from its foundations. Most of his important researches were published on the Giornale de' Letterati d'Italia.
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....
. He was probably the first to direct attention to the theory of elliptic integral
Elliptic integral
In integral calculus, elliptic integrals originally arose in connection with the problem of giving the arc length of an ellipse. They were first studied by Giulio Fagnano and Leonhard Euler...
s. Fagnano was born in Senigallia
Senigallia
Senigallia is a comune and port town on Italy's Adriatic coast, 25 km by rail north of Ancona, in the Marche region, province of Ancona....
.
Work
Fagnano is best known for investigations on the length and division of arcs of certain curves, especially the lemniscateLemniscate
In algebraic geometry, a lemniscate refers to any of several figure-eight or ∞ shaped curves. It may refer to:*The lemniscate of Bernoulli, often simply called the lemniscate, the locus of points whose product of distances from two foci equals the square of half the interfocal distance*The...
; this seems also to have been in his own estimation his most important work, since he had the figure of the lemniscate with the inscription: "Multifariam divisa atque dimensa Deo veritatis gloria", engraved on the title-page of his Produzioni Matematiche, which he published in two volumes (Pesaro, 1750), and dedicated to Pope Benedict XIV
Pope Benedict XIV
Pope Benedict XIV , born Prospero Lorenzo Lambertini, was Pope from 17 August 1740 to 3 May 1758.-Life:...
. The same figure and words "Deo veritatis gloria" also appear on his tomb.
Failing to rectify
Arc length
Determining the length of an irregular arc segment is also called rectification of a curve. Historically, many methods were used for specific curves...
the ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
or hyperbola
Hyperbola
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...
, Fagnano attempted to determine arc
Arc (geometry)
In geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle...
s whose difference should be rectifiable. He also pointed out the remarkable analogy existing between the integral
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
s which represent the arc of a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
and the arc of a lemniscate
Lemniscate
In algebraic geometry, a lemniscate refers to any of several figure-eight or ∞ shaped curves. It may refer to:*The lemniscate of Bernoulli, often simply called the lemniscate, the locus of points whose product of distances from two foci equals the square of half the interfocal distance*The...
. Finally he proved the formula
where i stands for
.His works were collected and published in two volumes at Pesaro
Pesaro
Pesaro is a town and comune in the Italian region of the Marche, capital of the Pesaro e Urbino province, on the Adriatic. According to the 2007 census, its population was 92,206....
in 1750.
Some mathematicians objected to his methods of analysis founded on 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...
. The most prominent of these were Viviani
Vincenzo Viviani
Vincenzo Viviani was an Italian mathematician and scientist. He was a pupil of Torricelli and a disciple of Galileo.-Biography:...
, De la Hire
Philippe de La Hire
Philippe de La Hire was a French mathematician and astronomer. According to Bernard le Bovier de Fontenelle he was an "academy unto himself"....
and Rolle
Michel Rolle
Michel Rolle was a French mathematician. He is best known for Rolle's theorem , and he deserves to be known as the co-inventor in Europe of Gaussian elimination .-Life:...
.
Life
He made his higher studies at the Collegio ClementinoCollegio Clementino
The Collegio Clementino is a palace in Rome, central Italy, sited between the Strada del'Orso and the banks of the Tiber. It was founded by Pope Clement VIII in 1595, to host Slavonian refugees. Giacomo della Porta was commissioned to erect a suitable building to house them, which would be one of...
in Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
and there won great distinction, except with mathematics, to which his adversion was extreme. Only after his college course that he took up its study. Later, without the help of any teacher, he mastered it from its foundations. Most of his important researches were published on the Giornale de' Letterati d'Italia.