Geometry

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MENELAO di Alessandria MENELAUS ALEXANDRINUS - HALLEY, EdmondMareMagnum

Menelai Sphaericorum libri III. Quos olim, collatis mss. Hebraeis & Arabicis, typis exprimendos curavit vir Cl. Ed. Halleius ... Praefationem addidit G. Costard

1758In -8°, pp. (2), 112; mezza pergamena. Prima edizione in volume del trattato di Menelao Alessandrino (I sec. d.C.), considerato il primo trattato di trigonometria sferica che si conosca, e che contiene anche la dimostrazione del teorema ancor oggi noto come Teorema di Menelao. Una edizione precedente dei tre libri compare anche nell’insieme di testi curato da Francesco Maurolico, che tradusse Teodosio, Euclide, Autolico e appunto Menelao in un suo lavoro dedicato agli studi della sfera (Messina, 1558). Nel 1644 Mersenne ripubblica gli “Sphaericorum libri”, sempre in un volume che comprende altri scritti (“Universae geometriae...”, Parigi, Bertier: il volume è citato da Leopardi nella sua “Storia dell’astronomia”), e sulla base del volume precedentemente citato. La presente edizione era stata curata, su fonti non coincidenti con le edizioni rammentate, dal celebre astronomo Edmund Halley per la stampa universitaria oxfordiana, nel 1712. Ma l’edizione del ’12, stampata solo parzialmente, non fu completata se non nel ’58 come postuma, quando fu chiesto a George Costard e James Bradley, entrambi astronomi a Oxford di curare la pubblicazione del lavoro. Mancano, in questa copia, le otto pagine di prefazione di Costard, numerate a parte, mentre il trattato in sé è completo: la copia è perfettamente conforme a quella conservata nella biblioteca bodleiana di Oxford. Una copia, sempre conforme a questa, e qualificata come quella del 1713-14 è stata venduta nel 2005 da Sotheby’s, asta Macclesfield. First edition in a volume of the Menelaus Alexandrinus work, considered the first spheric trigonometry essay ever known, also containing the demonstration of the theorem still known after Menelaus name. An earlier edition of the three books was also published in a collection of texts edited by Francesco Maurolico, who translated Theodosius, Euclides, Autholicus and Menelaus in a work dedicated to sphere studies (Messina, 1558). In 1644 Mersenne republish the “Sphaericorum libri”, always in a volume including more works (“Universae geometriae…”, Paris, Bertier), based on the Maurolico’s work. The Oxford edition was edited, based on different sources than the Maurolico ones, by the famous astronomer Edmund Halley, in 1712. But that edition was never published, and it was only partially printed in 1713-14. Only in 1758 the book was completed by George Costard and James Bradley, both Oxford’s astronomers. In the present copy the eight introduction pages of Costard are missing, while the essay is complete: the copy is identical to the one kept by the Bodleian Library of Oxford. A copy, still similar to this one and qualified as the 1713-14’s one, was sold in 2005, at Sotheby’s, Macclesfield auction.

Libreria Antonio Pettini · Italy€1,800.00

L'HOSPITAL, (GUILLAUME FRANCOIS ANTOINE) MARQUIS DE - CARTESIAN GEOMETRY APPLIED TO THE CONIC SECTIONSBiblio.com

Traité Analytique des Sections Coniques et de leur Usage pour la Resolution des Equations dans les Problêmes tant déterminez qu'indéterminez. Ouvrage Posthume.

1707ref. 48217Paris Jean Boudot et Jean Boudet fils 1707. 4to. Contemporary full calf. A bit of cracking to front hinges so that cords are seen but cover not loosening. Spine with 6 raised bands richly gilt compartments. Wear to top of spine. Two small old paperlabels one to upper compartment one to frontcover. Covers slightly rubbed. 44595 pp. Large woodcut vignette on titlepage 2 other vignettes one engraved one in woodcut. 32 folded engraved plates and one smaller folded plate Fig. A. An old owners stamp on flyleaf. Internally clean and fine. A few tiny brownspots. Wide-margined and printed on good paper. Scarce first edition of l'Hôspital's second book - his second successfull textbook - the manuscript of which was left completed at his death in 1704. His first book "Analyse des infiniment petits pour l’intelligence des lignes courbes" 1696 was the first textbook of the differential calculus and his name lives on in the name of the rule for finding the limiting value of a fraction whose numerator and denominator tend to zero. His mathyematical teacher was Jean Bernoulli.The year in which Newton published the anti-Cartesian "Arithmeticus" there appeared in France a conspicuously successfull textbook on Cartesian geometry along the lines of that of Guisnée. This was the "Traité Analytique des Sections Coniques". a book which contains less original material than that of Guisnée but which is more extensive and closer to the modern manner of treatment. The work had been intended for publication at the time the authors famous calculus textbook appeared in 1696 but l'Hospital's illness apparently led to delay and it appeared posthumously in 1707. It is Cartesian in emphasis and although it consists of but one volume follows generally the tripartite plan of Lahire and Ozanam: first an algebraic quasi-analytic treatment of the Conic Sections along the lines of Apollonian theory; then an analytic study of the loci and finally a long section on the customary construction by conics of the roots of cubic and quartic polynominal equations. LHospital sometimes used two axes and seems to have recognized the interchangeability of these but he betrays some hesitation. In general L'Hospital like Descartes was more interested in analytic geometry as a measure of ecpressing loci algebraivcally than as a method of deriving the properties of a curve from its equation." Carl B. Boyer "History of Analytic geometry" pp. 150-154. hardcover

Herman H. J. Lynge & Søn A/S · DenmarkDKK 16,500.00≈ €2,207.42

RIEMANN, BERNHARD - FOUNDING A NEW GEOMETRYBiblio.com

On The Hypotheses which lie at the Bases of Geometry. Translated by W.K. Clifford. Ueber die Hypothesen welche der Geometrie zu Grunde liegen.

1873ref. 53254London and New York Macmillan and Co. 1873. 4to. Orig. full brown cloth gilt spine pictorial gilt frontcover. Near mint condition. Small embossed stamp at upper corner of title-page David Dunlop ObservatoRy Library. In: "Nature a weekly illustrated Journal of Science." Volume VIII May 1873 to October 1873. XII562 pp. Entire volume offered. Riemann's paper: pp. 14-17 a. 36-37. Internally clean and fine no traces of use. First English translation of this milestone work on the foundations of geometry. It "is one of the key work from which derives the modern study of differential geometry and especially the study of manifolds of dimension greater than two. It was to prove central to the overthrow of Euclidean geometry as the source of geometrical ideas and to Einstein's general theory of relativity after 1915." Grattan-Guiness "Landmark Writings in Western Mathematics 1640-1940.It is a translation of Riemann's famous Habilitationsvortrag held in 1854 in secondary literature it is often misidentified as his Habilitationsschift but that was concerned with Fourier series and was delivered the year before. Riemann begins his lecture with a remark about a certain darkness that lies at the foundation of geometry. This darkness obscures the relations between that which geometry assumes i.e. the notion of space and the first principles of constructions in space. In Riemann's oponion one must take another approach towards this problem than the usual axiomatic method used ever since Euclid. The approach taken by Riemann is to a large extent guided by Gauss's work on the intrinsic geometry of surfaces; 'Disquisitiones generales circa superficies curvas' 1828. In this work Gauss showed that the curvature of a surface can be determined without reference to the ambient Euclidean space in which it lies i.e. that the curvature is an intrinsic property of the surface. Based on this Gauss showed several fundamental theorems about figures on the surface by referring only to the surface itself i.e. indicating that the surface itself is a space with its own geometry independent of the geometry of the ambient Euclidean space. Riemann argues that the true objects and properties of geometry are those which can be studied within the space itself and he defines a general n-dimensional space in a similar manner to the parametric representation of a surface. Riemann believed that we know space only locally he therefore bases his study of the geometry of such a general space or manifold as they are known today on the infinitesimal methods of calculus. This choice is a crucial departure from the classical axiomatic methods used by Euclid Lobachevsky and Bolyai. The notion of distance or metric on a manifold is a generalization of the usual Euclidean distance formula in n-dimensions. Particular choices of space and metric reveal both the hyperbolic geometries of Lobachevsky and Bolyai and elliptic or Riemannian geometry. Riemann's approach to geometry is of paramount importance this work "did more to change our ideas about geometry and physical space than any work on the subject since Euclid's Elements." Landmark Writings in Western Mathematics p.507. "The importance of this treatise is not confined to pure mathematics. Without it Einstein would not have been able to develop his general theory of relativity." Printing and the Mind of Man p.177. hardcover

Herman H. J. Lynge & Søn A/S · DenmarkDKK 18,500.00≈ €2,474.99

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