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The second and major section of the volume is devoted to what the editor describes as the autograph record of Newton's attempts, here published for the first time, to restore the methods of discovery of the ancient geometers. That the classical synthetic proofs were founded on a prior analysis seemed clear from the accounts given by Pappus of the works collectively described by him as 'The treasury of analysis'. Despite the attempt of Fermat, Euclid's Porisms, a key work of this collection (known only through the account of Pappus), remained essentially unexplained. Whiteside points to the conjecture, that the primary function of' The treasury of analysis' was to provide a collection of basic locus-constructions and curve properties of practical use to geometers in the solution of problems, as Newton's most significant achievement; the intersecting loci of the ancients were the equations of later mathematics. In his restoration of Euclid's Porisms, Newton employed the one-to-one correspondence defined by the general bilinear transformation--in effect, a theory of involution--and then, abandoning his role as classical interpreter, developed an innovatory treatise on curves, which includes, as its principal result, a projective classification of curves of the third degree. From David Gregory, who was allowed to read Newton's papers on the occasion of a visit in 1694, we learn that Newton intended to append his restoration of the geometry of the ancients and his method of quadratures to his projected new edition of the Principia. [ABSTRACT FROM AUTHOR]

From this brief survey of the manuscripts it will be evident that Leibniz's researches on the combinatorial art and its applications form an important if hitherto little known part of his work in mathematics, so that the publication of this source material represents a highly significant contribution to Leibnizian scholarship. The editor has carried through the difficult task of collation and transcription of the manuscripts with great skill and meticulous thoroughness. In particular, the arrangement of mathematical formulae and tables is always clear, while the volume concludes with an index of the manuscripts transcribed and an index of names cited in the manuscripts. Nevertheless, readers who are not specialists in the field may find the meaning of these notes, written by Leibniz without thought of publication and using unfamiliar notation and nomenclature, sometimes difficult to penetrate. Such readers will be further indebted to the editor for the invaluable assistance in the interpretation of Leibniz's ideas that he has provided in a commentary on the manuscripts, already published as a separate volume. [ABSTRACT FROM AUTHOR]

Reviews the book 'Ein Dialog zur Einführung in die Arithmetik und Algebra,' by G.W. Leibniz.

Reviews the book 'Blaise Pascal 1623–1662,' by Hans Loeffel.

The manuscripts are arranged systematically in relation to four themes: (1) systems of linear equations; (2) equations of higher degree with several variables; (3) elimination of a common variable from two equations of higher degree; and (4) algebraic division. In each case, Leibniz's text is presented very clearly and a date is assigned, using such evidence as watermarks and references to published works. Also the relation of the manuscript to others on the same theme is indicated, so that the reader can follow Leibniz's thought from his first attempts to his definitive solutions. There is an index of names and works cited in the manuscripts. Throughout, the author has displayed his usual sound scholarship and meticulous attention to detail. [ABSTRACT FROM AUTHOR]

Reviews the book 'Towards a Mechanistic Philosophy,' by David C. Goodman and John Hedley Brooke.

In Chapter 5 attention is directed to twentieth-century theories, particularly Special and General Relativity, and the author claims that these theories are less favourable to the relational concept of motion than are the classical theories. In the remaining chapters the relational view is considered further, in particular the difficulty it presents for the distribution, to which Kant to have been the first to draw on, between right-handedness and left-handedness Earman also argues that an absolute space is needed to support the existence of fields. Nevertheless, he concludes by claiming that a correct account of space and time can only found by going beyond the traditional absolute-relational controversy. [ABSTRACT FROM AUTHOR]

Reviews the book 'Sämtliche Schriften und Briefe,' by Gottfried Wilhelm Leibniz.

Reviews the book 'Leonhardi Euleri opera omnia, Series Secunds, Opera mechanica et astronomica,' edited by Charles Blanc and Pierre De Haller.

Reviews the book 'Theoria cum praxi. Zum Vernalthnis con Theorie und Praxis in 17.und 18. Jahrhundert,' edited by Albert Heinekamp and Ingeborg von Wilucki.

Reviews the book 'Theoria cum praxi. Zum Verhältnis von Theorie und Praxis im 17. und 18. Jahrhundert. Akten des III Internationalen Leibnizkongresses, Hannover, 12. bis 17. November 1977,' edited by Albert Heinekamp and Ingeborg von Wilucki.

An index to Gerhardt's edition of Leibniz's mathematical correspondence was prepared by Professor J. E. Hofmann for his own use. This publication of the index will be greeted by historians as an invaluable aid in the study of seventeenthcentury mathematics. Unfortunately Professor Hofmann only lived to see the beginning of the preparation for the press and the edition has been brought to completion by Professor Christoph J. Scriba with the help of colleagues in Hamburg, Hannover and Berlin. Although the edition is nominally a name index, it also serves as a bibliography, for it contains the complete titles of numerous books and articles for which the information given in Gerhardt is rather sketchy. In a modern edition of the correspondence, most of these details would appear as footnotes. [ABSTRACT FROM AUTHOR]

Reviews the book 'Der junge Leibniz II, Der Übergang vom Atomismus zu mechanistischen Aristotelismus. Der reviderte an Pierre Gassendi,' by Konrad Moll.