Euclid Vindicated From Every Blemish

Euclid Vindicated from Every Blemish

This first complete English language edition of Euclides vindicatus presents a corrected and revised edition of the classical English translation of Saccheri's text by G.B. Halsted. It is complemented with a historical introduction on the geometrical environment of the time and a detailed commentary that helps to understand the aims and subtleties of the work. Euclides vindicatus, written by the Jesuit mathematician Gerolamo Saccheri, was published in Milan in 1733. In it, Saccheri attempted to reform elementary geometry in two important directions: a demonstration of the famous Parallel Postulate and the theory of proportions. Both topics were of pivotal importance in the mathematics of the time. In particular, the Parallel Postulate had escaped demonstration since the first attempts at it in the Classical Age, and several books on the topic were published in the Early Modern Age. At the same time, the theory of proportion was the most important mathematical tool of the Galilean School in its pursuit of the mathematization of nature. Saccheri's attempt to prove the Parallel Postulate is today considered the most important breakthrough in geometry in the 18th century, as he was able to develop for hundreds of pages and dozens of theorems a system in geometry that denied the truth of the postulate (in the attempt to find a contradiction). This can be regarded as the first system of non-Euclidean geometry. Its later developments by Lambert, Bolyai, Lobachevsky and Gauss eventually opened the way to contemporary geometry. Occupying a unique position in the literature of mathematical history, Euclid Vindicated from Every Blemish will be of high interest to historians of mathematics as well as historians of philosophy interested in the development of non-Euclidean geometries.

Euclid Vindicated from Every Blemish

Diagrammatic Representation and Inference

This book constitutes the refereed proceedings of the 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020, held in Tallinn, Estonia, in August 2020.* The 20 full papers and 16 short papers presented together with 18 posters were carefully reviewed and selected from 82 submissions. The papers are organized in the following topical sections: diagrams in mathematics; diagram design, principles, and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; logic and diagrams; and posters. *The conference was held virtually due to the COVID-19 pandemic. The chapters ‘Modality and Uncertainty in Data Visualization: A Corpus Approach to the Use of Connecting Lines,’ ‘On Effects of Changing Multi-Attribute Table Design on Decision Making: An Eye Tracking Study,’ ‘Truth Graph: A Novel Method for Minimizing Boolean Algebra Expressions by Using Graphs,’ ‘The DNA Framework of Visualization’ and ‘Visualizing Curricula’ are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.