Giusto Bellavitis (22 November 1803 – 6 November 1880) 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 ...

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, and

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. Charles Laisant (1880) "Giusto Bellavitis. Nécrologie", ''Bulletin des sciences mathématiques et astronomiques'', 2nd série, 4(1): 343–8 According to Charles Laisant, :His principle achievement, which marks his place, in the future and the present, among the names of geometers that will endure, is the invention of the method of equipollences, a new method of

analytic geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineerin ...

that is both philosophical and fruitful. Born in

Bassano del Grappa Bassano del Grappa ( vec, Basan or ''Bassan'', ) is a city and ''comune'', in the Vicenza province, in the region of Veneto, in northern Italy. It bounds the communes of Cassola, Marostica, Solagna, Pove del Grappa, Romano d'Ezzelino, Campolongo ...

in 1803 to Ernesto Bellavitis and Giovanna Navarini, Giusto studied largely alone. In 1840 he entered Institut Venitian and in 1842 began instructing at Lycee de Vicence. In 1845 he became professor of descriptive geometry at

University of Padua The University of Padua ( it, Università degli Studi di Padova, UNIPD) is an Italian university located in the city of Padua, region of Veneto, northern Italy. The University of Padua was founded in 1222 by a group of students and teachers from B ...

. With the

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he took the opportunity to revise the curriculum to include complementary algebra and analytic geometry. Bellavitis married in 1842 and had one son who also taught geometry at the University of Padua. Bellavitis anticipated the idea of a

Euclidean vector In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors ac ...

with his notion of equipollence. Two line segments ''AB'' and ''CD'' are equipollent if they are

parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster of ...

and have the same length and direction. The relation is denoted

AB \bumpeq CD .

In modern terminology, this relation between line segments is an example of an

equivalence relation In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. Each equivalence relation ...

. The concept of

vector addition In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors ac ...

was written by Bellavitis as :

AB + BC \bumpeq AC .

According to Laissant, Bellavitis published works in "arithmetic, algebra, geometry, infinitesimal calculus, probability, mechanics, physics, astronomy, chemistry, mineralogy, geodesy, geography, telegraphy, social science, philosophy, and literature."

Works

* 1847: via

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* 1852
Saggio sull'algebra degli immaginari
link from

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* 1854
Sposizione del Metodo della Equipollenze
link from

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. * 1858
Calcolo dei Quaternioni di W.R. Hamilton e sua Relazione col Metodo delle Equipollenze
link from HathiTrust. * 1868
Lezioni di Geometria Descrittiva, 2nd edition
link from HathiTrust *

Awards

* Fellow of the Istituto Veneto in 1840 * Fellow of the Società Italiana dei Quaranta in 1850 * Member of the

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in 1879

References

* Michael J. Crowe (1967)

A History of Vector Analysis ''A History of Vector Analysis'' (1967) is a book on the history of vector analysis by Michael J. Crowe, originally published by the University of Notre Dame Press. As a scholarly treatment of a reformation in technical communication, the text i ...

, "Giusto Bellavitis and His Calculus of Equipollences", pp 52–4,

University of Notre Dame Press The University of Notre Dame Press is a university press that is part of the University of Notre Dame in Notre Dame, Indiana, United States. The press was founded in 1949, and is the largest Catholic university Catholic higher education i ...

. *

Charles-Ange Laisant Charles-Ange Laisant (1 November 1841 – 5 May 1920), French politician and mathematician, was born at Indre, near Nantes on 1 November 1841, and was educated at the École Polytechnique as a military engineer. He was a Freemason and a liberta ...

(1887
Theorie et Applications des Equipollence
Gauthier-Villars, link from

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

Historical Math Collection. * Lena L. Severance (1930
The Theory of Equipollences; Method of Analytical Geometry of Sig. Bellavitis
link from HathiTrust. * {{DEFAULTSORT:Bellavitis, Giusto 1803 births 1880 deaths 19th-century Italian mathematicians Algebraic geometers People from Bassano del Grappa