Giordano Vitale or Vitale Giordano (October 15, 1633 – November 3, 1711) was an
Italian mathematician
A list of notable mathematicians from Italy by century:
12th–15th centuries
12th century
*Plato Tiburtinus
13th century
*Guido Bonatti
* Campano da Novara
*Leonardo Fibonacci
14th century
*Paolo dell'Abbaco
* Giovanni di Gherardo da Prato
...
. He is best known for his theorem on
Saccheri quadrilateral
A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base. It is named after Giovanni Gerolamo Saccheri, who used it extensively in his book ''Euclides ab omni na ...
s. He may also be referred to as Vitale Giordani, Vitale Giordano da Bitonto, and simply Giordano.
Life
Giordano was born in
Bitonto
Bitonto (; nap, label= Bitontino, Vetònde) is a city and ''comune'' in the Metropolitan City of Bari (Apulia region), Italy. It lies to the west of Bari. It is nicknamed the "City of Olives", due to the numerous olive groves surrounding the cit ...
, in southeastern
Italy
Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...
, probably on October 15, 1633. As an adolescent he left (or was forced to leave) his city and, after an adventurous youth (that included killing his brother-in-law for calling him lazy) he became a soldier in the Pontifical army. During these adventures he read his first book of mathematics, the ''Aritmetica prattica'' by
Clavius
Christopher Clavius, SJ (25 March 1538 – 6 February 1612) was a Jesuit German mathematician, head of mathematicians at the Collegio Romano, and astronomer who was a member of the Vatican commission that accepted the proposed calendar inve ...
. At twenty-eight, living in Rome, he decided to devote himself to mathematics. The most important book he studied was
Euclid's ''Elements'' in the Italian translation by
Commandino.
In Rome he made acquaintance with the renowned mathematicians
Giovanni Borelli
Giovanni Alfonso Borelli (; 28 January 1608 – 31 December 1679) was a Renaissance Italian physiologist, physicist, and mathematician. He contributed to the modern principle of scientific investigation by continuing Galileo's practice of testi ...
and
Michelangelo Ricci
Michelangelo Ricci (1619–1682) was an Italian mathematician and a Cardinal of the Roman Catholic Church.
Biography
Michelangelo Ricci was born on 30 January 1619 in Rome, then capital of the Papal States, to a family of low social standing t ...
, who became his friends. He was employed for a year as a mathematician by ex-Queen
Christina of Sweden
Christina ( sv, Kristina, 18 December ( New Style) 1626 – 19 April 1689), a member of the House of Vasa, was Queen of Sweden in her own right from 1632 until her abdication in 1654. She succeeded her father Gustavus Adolphus upon his death ...
during her final stay in Rome. In 1667, a year after its foundation by
Louis XIV
, house = Bourbon
, father = Louis XIII
, mother = Anne of Austria
, birth_date =
, birth_place = Château de Saint-Germain-en-Laye, Saint-Germain-en-Laye, France
, death_date =
, death_place = Palace of Vers ...
, he became a lecturer in mathematics at the
French Academy in Rome
The French Academy in Rome (french: Académie de France à Rome) is an Academy located in the Villa Medici, within the Villa Borghese, on the Pincio (Pincian Hill) in Rome, Italy.
History
The Academy was founded at the Palazzo Capranica in 1 ...
, and in 1685 he gained the chair of mathematics at the prestigious
Sapienza University of Rome
The Sapienza University of Rome ( it, Sapienza – Università di Roma), also called simply Sapienza or the University of Rome, and formally the Università degli Studi di Roma "La Sapienza", is a Public university, public research university l ...
. Friend of
Vincenzo Viviani
Vincenzo Viviani (April 5, 1622 – September 22, 1703) was an Italian mathematician and scientist. He was a pupil of Torricelli and a disciple of Galileo. , Giordano met
Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...
in Rome when Leibniz stayed there during his journey through Italy in the years 1689–90. He gave Leibniz a copy of the second edition of his book ''Euclide restituto''. Giordano died on November 3, 1711, and was buried in the
San Lorenzo in Damaso
The Minor Basilica of St. Lawrence in Damaso (Basilica Minore di San Lorenzo in Damaso) or simply San Lorenzo in Damaso is a parish and titular church in central Rome, Italy that is dedicated to St. Lawrence, deacon and martyr. It is incorporated ...
basilica church in Rome.
Work
Giordano is most noted nowadays for a theorem on
Saccheri quadrilateral
A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base. It is named after Giovanni Gerolamo Saccheri, who used it extensively in his book ''Euclides ab omni na ...
s that he proved in his 1668 book ''Euclide restituto'' (named after
Borelli's ''Euclides Restitutus'' of 1658).
In examining Borelli's proof of the
parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
''If a line segment ...
, Giordano noted that it depended upon the assumption that a line everywhere equidistant from a straight line is itself straight. This in turn is due to
Clavius
Christopher Clavius, SJ (25 March 1538 – 6 February 1612) was a Jesuit German mathematician, head of mathematicians at the Collegio Romano, and astronomer who was a member of the Vatican commission that accepted the proposed calendar inve ...
, whose proof of the assumption in his 1574 ''Commentary on Euclid'' is faulty. So using a figure he found in Clavius, now called a Saccheri quadrilateral, Giordano tried to come up with his own proof of the assumption, in the course of which he proved:
:If ABCD is a Saccheri quadrilateral (angles A and B right angles, sides AD and BC equal) and HK is any perpendicular from DC to AB, then
:*(i) the angles at C and D are equal, and
:*(ii) if in addition HK is equal to AD, then angles C and D are right angles, and DC is equidistant from AB.
The interesting bit is the second part (the first part had already been proved by
Omar Khayyám
Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīsābūrī (18 May 1048 – 4 December 1131), commonly known as Omar Khayyam ( fa, عمر خیّام), was a polymath, known for his contributions to mathematics, astronomy, philosophy, an ...
in the 11th century), which can be restated as:
:If 3 points of a line CD are equidistant from a line AB then all points are equidistant.
Which is the first real advance in understanding the
parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
''If a line segment ...
in 600 years.
[ eorge Edward Martin (1998), "The Foundations of Geometry and the Non-Euclidean Plane", p.272, Springer/ref>
]
Publications
Giordano's published work includes:
*''Lexicon mathematicum astronomicum geometricum'' (1st edition 1668, Paris. 2nd edition with additions 1690, Rome)
*''Euclide restituto, ovvero gli antichi elementi geometrici ristaurati e facilitati da Vitale Giordano da Bitonto. Libri XV.'' ("Euclid Restored, or the ancient geometric elements rebuilt and facilitated by Giordano Vitale, 15 Books"), (1st edition 1680, Rome. 2nd edition with additions 1686, Rome)
*''Fundamentum doctrinae motus grauium et comparatio momentorum grauis in planis seiunctis ad grauitationes'' (1689, Rome)
Notes
References
*M. Teresa Borgato, manoscritti non pubblicati di Vitale Giordano, corrispondente di Leibniz.
*Leibniz Tradition und Aktualitat V. Internationaler Leibniz-Kongress, unter der Schirmherrschaft des Niedersachsischen Ministerprasidenten Dr. Ernst Albrecht, Vortrage Hannover 14–19 November 1988.
*Francisco Tampoia, Vitale Giordano, Un matematico bitontino nella Roma barocca, Arming Publisher Rome 2005.
External links
*
*Roberto Bonola (1912
Non-Euclidean Geometry
Open Court, Chicago. English translation by H. S. Carslaw.
{{DEFAULTSORT:Vitale, Giordano
1633 births
1711 deaths
17th-century Italian mathematicians
18th-century Italian mathematicians
People from Bitonto