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Euclid and his twentieth century rivals. Diagrams in the logic of Euclidean geometry. (English) Zbl 1129.01001

Studies in the Theory and Applications of Diagrams. Chicago, IL: University of Chicago Press (ISBN 978-1-57586-507-2/hbk; 978-1-57586-508-9/pbk). 140 p. (2007).
The author invites his readers to a fascinating survey in the history of diagrams, starting from Euclid’s Geometry.
A first important book here mentioned is Euclid and his Modern Rivals, written by Ch. Dodgson, the mathematician, who is the same with Lewis Carroll, the famous author of Alice…
In an imagined dialogue, all modern rivals of Euclid are considered, the conclusion reached in each case being that no one surpassed him – a quite unique attitude in a period in which, along with rapid changes in both logic and geometry, Euclid’s indisputable position seemed somehow attacked.
Quite soon, the axiomatization of Hilbert came to replace the theoretical basis for geometry provided by Euclid in his Elements, the way being thus opened for most rigorous demonstrations and formalism. Ample space is devoted in the volume to the explanation of the notions of FG (formal geometry) and CDFG (computerized diagrammatic formal geometry), starting from Hilbert’s Foundations of Geometry.
Euclid and Hilbert remain unaffected by one another, their contributions enriching in a most personal manner the science of humanity.

MSC:

01-02 Research exposition (monographs, survey articles) pertaining to history and biography
51-03 History of geometry
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