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Giordano Vitale or Vitale Giordano (born Bitonto, October 15, 1633 – November 3, 1711) was an Italian mathematician. He is best known for his theorem on Saccheri quadrilaterals. He may also be referred to as Vitale Giordani, Vitale Giordano da Bitonto, and simply Giordano.
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.
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.T.George 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 part is the second part (the first part had already been proved by Omar Khayyám in the 11th century), which can be restated as:
This is the first real advance in understanding the parallel postulate in 600 years.RobertoGeorge
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