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Eugenio Beltrami

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Giovanni Saccheri and his Problems with Euclidian Geometry

Giovanni Saccheri and his Problems with Euclidian Geometry

Harald Sack
On September 5, 1667, Italian Jesuit priest, scholastic philosopher, and mathematician Giovanni Girolamo Saccheri was born. He is primarily known today for his last publication, Euclide Ab Omni Naevo Vindicatus (Euclid Freed of Every Flaw, 1733), now considered the second work in non-Euclidean geometry. First Contact with Euclid’s Elements Saccheri was born in Sanremo to his father Giovanni Felice Saccheri, a lawyer and notary.[6] As a child Saccheri ‘was notably precocious’.[1] He entered the…
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mathematics
Eugenio Beltrami and the Consistency of Non-Euclidian Geometry

Eugenio Beltrami and the Consistency of Non-Euclidian Geometry

Harald Sack
On November 16, 1835, Italian mathematician Eugenio Beltrami was born. He is most notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere. “Students should learn to study at an early stage the great works of the great masters instead of making their minds sterile through…
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