Vitale Giordano
Encyclopedia
Giordano Vitale or Vitale Giordano (October 15, 1633 – November 3, 1711) was an Italian
mathematician. He is best known for his theorem on Saccheri quadrilaterals
. He is also referred to as Vitale Giordani, Vitale Giordano da Bitonto, and simply Giordano.
, in southeastern Italy
, 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
. 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
and Michelangelo Ricci, who became his friends. He was employed for a year as a mathematician by ex-Queen Christina of Sweden
during her final stay in Rome. In 1667, a year after its foundation by Louis XIV, he became a lecturer in mathematics at the French Academy in Rome
, and in 1685 he gained the chair of mathematics at the prestigious Sapienza University of Rome. Friend of Vincenzo Viviani
, Giordano met Leibniz 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
basilica church in Rome.
Giordano is most noted nowadays for a theorem on Saccheri quadrilaterals
that he proved in his 1668 book Euclide restituo (named after Borelli's Euclides Restitutus of 1658).
In examining Borelli's proof of the parallel postulate
, 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, 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:
The interesting bit is the second part (the first part had already been proved by Omar Khayyám
in the 11th century), which can be restated as:
Which is the first real advance in understanding the parallel postulate
in 600 years.
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. He is best known for his theorem on Saccheri quadrilaterals
Saccheri quadrilateral
A 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 Euclid vindicatus , an attempt to prove the parallel postulate using the method Reductio ad absurdum...
. He is also referred to as Vitale Giordani, Vitale Giordano da Bitonto, and simply Giordano.
Life
Giordano was born in BitontoBitonto
Bitonto is a city and comune in the province of Bari , Italy. It is nicknamed the "City of Olives" due to the numerous olive groves surrounding the city.-Geography:...
, in southeastern Italy
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...
, 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
Christopher Clavius was a German Jesuit mathematician and astronomer who was the main architect of the modern Gregorian calendar...
. At twenty-eight, living in Rome, he decided to devote himself to mathematics. The most important book he studied was Euclid's Elements
Euclid's Elements
Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...
in the Italian translation by Commandino
Federico Commandino
Federico Commandino was an Italian humanist and mathematician.Born in Urbino, he studied at Padua and at Ferrara, where he received his doctorate in medicine. He translated the works of ancient mathematicians and was responsible for the publication of the works of Archimedes...
.
In Rome he made acquaintance with the renowned mathematicians Giovanni Borelli
Giovanni Alfonso Borelli
Giovanni Alfonso Borelli was a Renaissance Italian physiologist, physicist, and mathematician. He contributed to the modern principle of scientific investigation by continuing Galileo's custom of testing hypotheses against observation...
and Michelangelo Ricci, who became his friends. He was employed for a year as a mathematician by ex-Queen Christina of Sweden
Christina of Sweden
Christina , later adopted the name Christina Alexandra, was Queen regnant of Swedes, Goths and Vandals, Grand Princess of Finland, and Duchess of Ingria, Estonia, Livonia and Karelia, from 1633 to 1654. She was the only surviving legitimate child of King Gustav II Adolph and his wife Maria Eleonora...
during her final stay in Rome. In 1667, a year after its foundation by Louis XIV, he became a lecturer in mathematics at the French Academy in Rome
French Academy in Rome
The French Academy in Rome is an Academy located in the Villa Medici, within the Villa Borghese, on the Pincio in Rome, Italy.-History:...
, and in 1685 he gained the chair of mathematics at the prestigious Sapienza University of Rome. Friend of Vincenzo Viviani
Vincenzo Viviani
Vincenzo Viviani was an Italian mathematician and scientist. He was a pupil of Torricelli and a disciple of Galileo.-Biography:...
, Giordano met Leibniz 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
San Lorenzo in Damaso
San Lorenzo in Damaso is a basilica church in Rome, Italy, one of several dedicated to the Roman deacon and martyr Saint Lawrence...
basilica church in Rome.
Work
Saccheri quadrilateral
A 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 Euclid vindicatus , an attempt to prove the parallel postulate using the method Reductio ad absurdum...
that he proved in his 1668 book Euclide restituo (named after Borelli's Euclides Restitutus of 1658).
In examining Borelli's proof of the parallel postulate
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...
, 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, 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
Omar Khayyám
Omar Khayyám was aPersian polymath: philosopher, mathematician, astronomer and poet. He also wrote treatises on mechanics, geography, mineralogy, music, climatology and theology....
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
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...
in 600 years.
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)
External links
- Roberto Bonola (1912) Non-Euclidean Geometry, Open Court, Chicago. English translation by H. S. Carslaw.