Giusto Bellavitis (22 November 1803 – 6 November 1880) was an Italian

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, and municipal councilor. 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 that is both philosophical and fruitful. Born in

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

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. He became professor of descriptive geometry at University of Padua in 1845. 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

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with his notion of '' equipollence''. Two line segments ''AB'' and ''CD'' are equipollent if they are parallel 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. The concept of vector addition 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 Biblioteca europea di informazione e cultura * 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 Accademia dei Lincei in 1879

References

* Michael J. Crowe (1967) A History of Vector Analysis, "Giusto Bellavitis and His Calculus of Equipollences", pp 52–4,

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. * Charles-Ange Laisant (1887
Theorie et Applications des Equipollence
Gauthier-Villars, link from

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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 Mathematicians from the Austrian Empire 19th-century Italian mathematicians Algebraic geometers People from Bassano del Grappa