De lineis rectis se invicem secantibus statica construction [Staticæ constructionis liber primus [-secundus]]

CEVA, Giovanni Benedetto

Edité par Lodovico Monza, Milan, 1678

A propos de cet article

CEVA'S THEOREM. First edition, rare, of Ceva's first and most important book. "Ceva's most important mathematical work is De lineis rectis (Milan, 1678), dedicated to Ferdinando Carlo. Chasles mentions it with praise in his Aperçu historique. In this work Ceva used the properties of the center of gravity of a system of points to obtain the relation of the segments which are produced by straight lines drawn through their intersections. He further utilized these properties in many theorems of the theory of transverse lines-for example, in placing at the points of intersection of the straight lines weights that are inversely proportional to the segments. From the relations of the weights, which are determined by the law of the lever, the relation of the segments is then derived. Ceva first applied his method, which is a combination of geometry and mechanics, to five basic figures, which he called 'elements.' He then used these in special problems, in which given relations are used to calculate others. The theorem of Menelaus concerning the segments produced by a transverse line of a triangle is proved, as is the transversal theorem concerning the concurrency of the transverse lines through the vertices of a triangle, which is named after Ceva. This theorem was established again by Johann I Bernoulli. Ceva worked with proportions and proved their expansion; he calculated many examples in detail and for all possible cases. (Occasionally he treated examples in a purely geometrical manner to demonstrate the advantage of his method.) In the second book of the De lineis, Ceva went on to more complex examples and applied his method to cylindrical sections, ellipses in the triangle, and conic sections and their tangents. In a geometrical supplement, not related to either of the first two books, Ceva dealt with classical geometrical theorems. He solved problems on plane figures bounded by arcs of circles and then calculated the volumes and centers of gravity of solid bodies, such as the paraboloid and the two hyperboloids of rotation. Cavalieri's indivisibles are used successfully in this case" (DSB). Only one other copy on ABPC/RBH since 1961. "Ceva's father, Carlo Francesco Ceva (1610-1690), was a man who undertook many different activities such as buying and selling houses and land. He also worked for the duke of Milan in an official capacity, collecting excise duty. This meant that he was a wealthy man, able to provide a high quality lifestyle for his family. He married Paola Columbo, the daughter of Cristoforo Columbo and Elisabetta Caballina, on 20 September 1639. They had several children [including] Giovanni Benedetto Ceva (born 1647) and Tommaso Ceva (born 1648, also a mathematician) . We know no details of Ceva's youth, but he does make an intriguing comment that his youth was saddened by 'many kinds of misfortune'. He also suggests that his family opposed his academic pursuits. "Giovanni Ceva was educated at the Collegio di Brera, a Jesuit college in Milan, where he showed a particular aptitude for science, particularly for mathematics. After leaving the College, he followed the same path as his father, engaging in business activities and in administrative political roles in Milan, Genoa and Mantua. But he was also interested in undertaking scientific activities and, in addition to the financial dealing he was doing, he studied geometry and hydraulics. He entered the university of Pisa in 1670 and there he studied under Donato Rossetti (1633-1686), the professor of logic, who was a strong supporter of atomic theories. He also studied under Alessandro Marchetti (1633-1714), who succeeded his teacher Giovanni Alfonso Borelli (1608-1679) as professor of mathematics at Pisa in 1679 . "While studying in Pisa, Ceva also met Michelangelo Ricci who, like Rossetti, was a member of the Mathematics-Physics Academy of Rome. It is highly likely, therefore, that Ceva spent some time at the Academy in Rome during his two years of residence in.

N° de réf. du vendeur 5193

Détails bibliographiques

• Titre: De lineis rectis se invicem secantibus statica construction [Staticæ constructionis liber primus [-secundus]]
• Éditeur: Lodovico Monza, Milan
• Date de parution: 1678
• Édition: First edition.
• Catalogues du vendeur:
  • Geometry, Number Theory
  • Mathematics, Analysis, Algebra