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This book reconstructs, from both historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried out in his final years. The work’s main purpose is to offer a better understanding of the philosophy of space and in general of the mature Leibnizean metaphysics. This is the first ever, comprehensive historical reconstruction of Leibniz’s geometry.
Silvestre François Lacroix was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral, which is an encyclopedic appraisal of 18th-century calculus that remained the standard reference on the subject through much of the 19th century. This book provides the first global and detailed study of Lacroix's Traité Traité du calcul.
The planet Venus is the closest neighbour to the Earth and in several respects similar to our globe. It revolves around the Sun at an average distance of 0. 72 astronomical units, in an elliptical orbit of eccentricity 0. 007. The corresponding 3 numbers for the Earth are 1 and 0. 017. The mean density of Venus is 5. 2 g/cm , 3 that of the Earth 5. 5 g/cm . Venus’ acceleration of gravity at its equator is 8. 9 2 2 m/s , compared with 9. 8 m/s at the Earth. The escape velocity is 10. 4 km/s, while the corresponding ?gure of the Earth is 11. 2 km/s. Although the mass of Venus is somewhat smaller than that of the Earth – the ratio is M /M =0. 815 V E – the diameters of the two planets are almost the same. In other words, Venus is indeed a sister planet of the Earth. In earlier times, when almost nothing was known about the physical con- tions of Venus, the similarity appeared even stronger than today. Not only was Venus’ period of rotation thought to be close to that of the Earth, it was also p- sible (and indeed common) to imagine intelligent life on Venus.
This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).

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