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

Lodovico Monza, Milan, 1678. 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

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Bookseller:
SOPHIA RARE BOOKS
[Koebenhavn V, Denmark]

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