First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

The aggregate EIRP of an N-element antenna array is proportional to N 2. This observation illustrates an effective approach for providing deep space networks with very powerful uplinks. The increased aggregate EIRP can be employed in a number of ways, including improved emergency communications, reaching farther into deep space, increased uplink data rates, and the flexibility of simultaneously providing more than one uplink beam with the array. Furthermore, potential for cost savings also exists since the array can be formed using (...) small apertures. (shrink)

I trace the development of arguments for the consistency of non-Euclidean geometries and for the independence of the parallel postulate, showing how the arguments become more rigorous as a formal conception of geometry is introduced. I analyze the kinds of arguments offered by Jules Hoüel in 1860-1870 for the unprovability of the parallel postulate and for the existence of non-Euclidean geometries, especially his reaction to the publication of Beltrami’s seminal papers, showing that Beltrami was much more concerned with the existence (...) of non-Euclidean objects than he was with the formal consistency of non-Euclidean geometries. The final step towards rigorous consistency proofs is taken in the 1880s by Henri Poincaré. It is the formal conception of geometry, stripping the geometric primitive terms of their usual meanings, that allows the introduction of a modern fully rigorous consistency proof. (shrink)

A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions — rather than strictly historical and mathematical issues — and features several helpful appendixes.

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

Beltrami's first allegedly true interpretation of lobachevsky's geometry can be conceived as (i) pursuing a kantian program insofar as it shows that all the geometrical lobachevskian concepts are constructible in the euclidean space of our human representation, And (ii) proving, Even to kant, That a non-Euclidean geometry is not only logically possible (something that kant never denied) but also mathematically acceptable from a kantian point of view (something that kant would have accepted only after beltrami's interpretation).

One of Hume's most well-known works and a masterpiece of philosophy, A Treatise of Human Nature is indubitably worth taking the time to read.

The material contained in the following translation was given in substance by Professor Hilbertas a course of lectures on euclidean geometry at the University of G]ottingen during the wintersemester of 1898-1899. The results of his investigation were re-arranged and put into the formin which they appear here as a memorial address published in connection with the celebration atthe unveiling of the Gauss-Weber monument at G]ottingen, in June, 1899. In the French edition, which appeared soon after, Professor Hilbert made some additions, (...) particularly in the concludingremarks, where he gave an account of the results of a recent investigation made by Dr. Dehn.These additions have been incorporated in the following translation.Geometry, like arithmetic, requires for its logical development only a small number ofsimple, fundamental principles. These fundamental principles are called the axioms ofgeometry. The choice of the axioms and the investigation of their relations to one anotheris a problem which, since the time of Euclid, has been discussed in numerous excellentmemoirs to be found in the mathematical literature.1 This problem is tantamount to thelogical analysis of our intuition of space. (shrink)

In this new book, Michael Friedman argues that Kant's continuing efforts to find a metaphysics that could provide a foundation for the sciences is of the utmost ...

This book provides a reading of Kant's theory of the construction of mathematical concepts through a fully contextualised analysis. In this work the author argues that it is only through an understanding of the relevant eighteenth century mathematics textbooks, and the related mathematical practice, that the material and context necessary for a successful interpretation of Kant's philosophy can be provided.