61. Padre Eugenio Translate this page cuenta de que el Santo Padre, oído el informe favorable de que el ExcelentísimoSeñor José beltrami, Nuncio de Padre Capuchino Fray eugenio de Carcagente. http://es.geocities.com/padre_eugenio/

PAZ Y BIEN El Reverendísimo Padre EUGENIO DE CARCAIXENT (O.F.M.Cap.) (Juan Bautista Soler Rodríguez) Primer Prefecto Apostólico de San Andrés y Providencia (Colombia) Gracias por tu visita Hacer clic sobre cada vinculo para visualizar los diferentes temas Cronología La Orden Capuchina Bibliografía del Padre Eugenio Asociación y Calle Padre Eugenio ... Restos de Monseñor Eugenio de Carcagente e-mail: padre_eugenio@yahoo.es Apdo. Correos nº157 Carcaixent-Valencia-España Hacer clic sobre la imagen para ampliar-cargar en una ventana nueva (Trascripción de la P.N. Original) Hacer clic sobre la imagen para ampliar-cargar en una ventana nueva (Partida de Nacimiento Original) PARTIDA DE BAUTISMO DEL PADRE EUGENIO DE CARCAIXENT El infrafirmado Don VICENTE ANTONIO RICHART HOSTENCH, Cura Párroco de “La Asunción de Nuestra Señora”, de Carcaixent. CERTIFICO: Que en el libro de Bautismos, tomo 32, folio 12, núm. 32, de este Archivo Parroquial se encuentra una partida que dice así: “En la Parroquial Yglesia de la villa de Carcagente; á los veinte y cuatro de enero de mil ochocientos sesenta y cinco: Yo don Pedro Talens, coadjutor de la Parroquia de la Asunción

62. Opere Matematiche . Tomo Primo / Di Eugenio Beltrami Translate this page Opere matematiche . Tomo primo / di eugenio beltrami. INDICE DEL TOMOI.Prefazione alle Opere Roma. V. eugenio beltrami. - Estratto dalla http://gallica.bnf.fr/Fonds_Tables/009/M0099432.htm

Opere matematiche . Tomo primo / di Eugenio Beltrami INDICE DEL TOMOI. Prefazione alle Opere Matematiche di EUGENIO BELTRAMI; per Alberto Toneill, V EUGENIO BELTRAMI. - Estratto dalla Commemorazione letta da Luigi Cremona alla R. Accademia del Lincel, nell'adunanza solenne del 10 giugno 1900, onorata dalla presenza delle LL. MM. il Re e la Regina. IX I. Intorno ad alcuni sistemi di curve piane. Annali di Matematica pura ed applicata, serie I, tomo IV (1861), pp. 102-108. II. Sulla teoria delle sviluppoidi e delle sviluppanti. Annali di Matematica pura ed applicata, serie I, tomo IV (1861), pp. 257-283. III. Di alcune formole relative alla curvatura delle superficie (Lettera al professore B. TORTOLINI). Annali di Matematica pura ed applicata, serie I, tomo IV (1861), pp. 283-284. IV. Soluzione d'un problema relativo alle superficie di second'ordine. Giornale di Matematiche, vol. I (1863), pp. 68-73. V. Intorno alle coniche dei nove punti e ad alcune quistioni che ne dipendono. Memorie dell'Accademia delle Scienze dell'Istituto di Bologna, serie II, vol. II (1862), pp. 361-395. VI. Estensione allo spazio di tre dimensioni dei teoremi relativi alle coniche dei nove punti.

63. Verzeichnis | Mitglieder | Vorgängerakademien Translate this page BELOW, Georg Anton Hugo von, *19.01.1858, † 20.10.1927, beltrami, eugenio,*16.11.1835, † 18.02.1900, BELY (BEL), Matthias, *24.03.1684, † 29.08.1749, http://www.bbaw.de/archivbbaw/akademiemitglieder/vorgaengermitglieder_b.html

Archiv der Berlin- Brandenburgischen Akademie der Wissenschaften BBAW Akademie Archiv Leiter/Abteilungsleiter ... Abt. Sammlungen Mitgliederverzeichnisse Mitglieder der BBAW Homepage der BBAW Verzeichnis B Portraitansichten A B C D ... Z Name, Vorname Lebenszeit siehe: BAER, Karl Ernst von BAETHGEN, Friedrich BAEUMKER, Clemens ... BAIARDI, Octavio Antonio *um 1690 BAILY, Francis BAJEW, Alexander Alexandrowitsch BALBIS, Giovanni Battista BALEWSKI, Angel Toncev ... BEAUX *17. Jh. BEC(K)MANN, Johann Christoph BECKE, Friedrich BECKER, Heinz BECKER, Karl ... BEER (BEHR), Johann Heinrich gt. 31.05.1648 BEGER, Lorenz BEGUELIN, Nicolas de BEHRENS, Friedrich BEHRENS, Konrad Barthold ... BEKKER, Ernst Immanuel *um 1693 BELOW, Georg Anton Hugo von BELTRAMI, Eugenio BELY (BEL), Matthias BENECKE, Ernst Wilhelm ... BRANDES, Karl Philipp gt. 12.11.1720 BRANDI, Karl Maria Prosper Laurenz BRANDIS, Christian August BRANDL, Alois ... BUSSIUS, August Friedrich begr. 19.08.1727 BUTENANDT, Adolf Friedrich Johann BUTTMANN, Philipp Karl BUYS-BALLOT, Christoph Heinrich Dietrich BYWATER, Ingram

64. Matematica - Storia - Indice Translate this page Giusto BELLAVITIS. Antonio BELLINO ROSINA. Margherita BELOCH PIAZZOLLA. eugenio beltrami.Piero BENEDETTI. Rodolfo BENEVENTO sj. Vladimiro BERNSTEIN. eugenio BERTINI. http://matematica.uni-bocconi.it/storia/letterab/letterab.htm

Giuseppe BAGNERA Emilio BAIADA Mario BALDASSARRI Silvio BALLARIN Giuseppe BAGNERA Emilio BAIADA Mario BALDASSARRI Silvio BALLARIN ... Pietro BUZANO

65. Suche Nach Personen Translate this page 1929 Bell, Physik Ann Arbor 1922 Bell, Physiker Manchester 1933 Bellini, E.Bellini, Jacopo Giovanni (1430-1516) beltrami, eugenio (1835-1900) Bender, http://www.lrz-muenchen.de/~Sommerfeld/PersDat/B.html

Suche nach Personen A B C D ... Z B B., [Major] Ba Yin Baade, Walter (1893-1960) Babbage, Charles (1792-1871) ... Institutionen Ausgelesen am 29. Dezember 2002.

66. OPE-MAT - Historique Translate this page Anicus Briggs, Henry Bell, Eric Temple Bohl, Piers Brill, Alexander von Bellavitis,Giusto Bohr, Harald Brillouin, Marcel beltrami, eugenio Bohr, Niels Bring http://www.gci.ulaval.ca/PIIP/math-app/Historique/mat.htm

A Abel , Niels Akhiezer , Naum Anthemius of Tralles Abraham bar Hiyya al'Battani , Abu Allah Antiphon the Sophist Abraham, Max al'Biruni , Abu Arrayhan Apollonius of Perga Abu Kamil Shuja al'Haitam , Abu Ali Appell , Paul Abu'l-Wafa al'Buzjani al'Kashi , Ghiyath Arago , Francois Ackermann , Wilhelm al'Khwarizmi , Abu Arbogast , Louis Adams , John Couch Albert of Saxony Arbuthnot , John Adelard of Bath Albert , Abraham Archimedes of Syracuse Adler , August Alberti , Leone Battista Archytas of Tarentum Adrain , Robert Albertus Magnus, Saint Argand , Jean Aepinus , Franz Alcuin of York Aristaeus the Elder Agnesi , Maria Alekandrov , Pavel Aristarchus of Samos Ahmed ibn Yusuf Alexander , James Aristotle Ahmes Arnauld , Antoine Aida Yasuaki Amsler , Jacob Aronhold , Siegfried Aiken , Howard Anaxagoras of Clazomenae Artin , Emil Airy , George Anderson , Oskar Aryabhata the Elder Aitken , Alexander Angeli , Stefano degli Atwood , George Ajima , Chokuyen Anstice , Robert Richard Avicenna , Abu Ali B Babbage , Charles Betti , Enrico Bossut , Charles Bachet Beurling , Arne Bouguer , Pierre Bachmann , Paul Boulliau , Ismael Bacon , Roger Bhaskara Bouquet , Jean Backus , John Bianchi , Luigi Bour , Edmond Baer , Reinhold Bieberbach , Ludwig Bourgainville , Louis Baire Billy , Jacques de Boutroux , Pierre Baker , Henry Binet , Jacques Bowditch , Nathaniel Ball , W W Rouse Biot , Jean-Baptiste Bowen , Rufus Balmer , Johann Birkhoff , George Boyle , Robert Banach , Stefan Bjerknes, Carl

67. Antiquariat Renner - Searchengine / Suchmaschine Translate this page 12.- Wie neu. 100, Euro. beltrami, eugenio (35655), 2 offprints 1879-1904Un precursore italiane di Legendre e di Lobatschewsky. Saccheri. http://www.antiquar-renner.com/search.mv? showcat M2

68. The Science Bookstore - Chronology von Baeyer, Adolph Born 10/31/1835, 1835 AD, beltrami, eugenio Born 11/16/1835Died 2/18/1900, 1835 AD, Csoati, Felice Born 12/17/1835, 1835 AD, http://www.thesciencebookstore.com/chron.asp?pg=16

69. Mathematicians From DSB Translate this page Argand, Jean Robert, 1768-1822. Artin, Emil, 1898-1962. beltrami, eugenio, 1835-1899.Berkeley, George, 1685-1753. Bertrand, Joseph Louis François, 1822-1900. http://www.henrikkragh.dk/hom/dsb.htm

Last modification: document.write(document.lastModified) Webmaster Validate html Mathematicians from the Dictionary of Scientific Biography (DSB) Abel, Niels Henrik Argand, Jean Robert Artin, Emil Beltrami, Eugenio Berkeley, George Bertrand, Joseph Louis François Bianchi, Luigi Bolyai, János (Johann) Bolyai, Farkas (Wolfgang) Bolzano, Bernard Bombelli, Rafael Borel, Émile (Félix-Édouard-Justin) Bouquet, Jean-Claude Briot, Charles Auguste Cantor, Georg Carathéodory, Constantin Cardano, Girolamo Cauchy, Augustin-Louis Cayley, Arthur Chebyshev, Pafnuty Lvovich Clairaut, Alexis-Claude Clausen, Thomas Clebsch, Rudolf Friedrich Alfred Colden, Cadwallader Collinson, Peter Condorcet, Marie-Jean-Antoine-Nicolas Caritat, marquis de Cramer, Gabriel Crelle, August Leopold d'Alembert, Jean le Rond de Morgan, Augustus Dedekind, (Julius Wilhelm) Richard Delambre, Jean-Baptiste Joseph Descartes, René du Perron Dini, Ulisse Dirichlet, Gustav Peter Lejeune du Bois-Reymond, Paul David Gustav Duhamel, Jean Marie Constant Eisenstein, Ferdinand Gotthold Max Euclid

70. The Hyperbolic Geometry Exhibit eugenio beltrami. beltrami rescued hyperbolic geometry in 1868 by realizingit as a surface of constant negative curvature thereby http://www.math.ubc.ca/~robles/hyperbolic/eucl/prll/Beltrami-Klein-Poincare.html

Eugenio Beltrami Beltrami rescued hyperbolic geometry in 1868 by realizing it as a surface of constant negative curvature thereby showing hyperbolic geometry was part of classical differential geometry. Beltrami developed what has become known as the Klein-Beltrami disc model of hyperbolic geometry. The geodesics are chords in the disc and the isometries are projective isometries of the plane that map the unit disc to itself. As is so often the case in mathematics the nomenclature is somewhat misleading. This model would be more appropraitely labeled the Cayley-Beltrami model. Cayley contributed essential work on constant curvature metrics. Felix Klein Klein's speciality was projective geometry. He developed interpertations of hyperbolic geometry in projective geometry. Klein carried his development farther than Beltrami and among many results proved that spherical, euclidean and hyperbolic goemetery are all consistant if projective geometry is consistant. et hoc genus omne Riemann developed the line element for spaces of constant curvature) model and Liouville-Beltrami ( Liouville worked on the related constant curvature metric) model, respectively.

71. Liste Provisoire DicoMeca (A-E) Translate this page BELANGER, JB, PP, 38. BELIDOR (de), Bernard Forest, 1697 - 1761, PP,39. beltrami, eugenio, 1835 - 1900, PP, 40. BENARD, Henri, 1874 - 1939,PAB, 41. http://www.afm.asso.fr/aum/PROJETS/DicoMeca/ListDM_AE.html

(document de travail) Page 1 : A-E NOM Dates Responsable A b c d e ... n-z ACKERET Jakob [PAB] AGRICOLA [JF] AIRY George Bidell [JC] AL BIRUNI Abu Raihan [BE] AL-BAKRI A. A. [BE] AL-BATTANI (ALBATEGNUS) Mohammad Ibn Jabir ca. 868 - 929 [BE] AL-BETRUGI (ALPETRAGIUS) Nour Al-Dine - ca. 1100 [BE] AL-BUZJANI Abul Wafa Mohammad [BE] AL-FARABI (ABLUFARABIUS) Mohammed Abu Nasr (Avennasar) ca. 870 - 950 [BE] AL-FARGHANI (ALFRAGANUS) [BE] ALFVEN Hannes [BE] AL-KHAWARIZMI IBN MOUSA Mohammad ca. 800 - ca. 850 [BE] AL-KHAYYAM Omar ca. 1044 - 1123 [BE] AL-KHUJANDI Hamid Ibn Al-Khidr ca. 940 - 1000 [BE] ALMANSI Emilio [JC] AL-OURDI Mouayyed Al Dine [BE] AL-QUHI Abou Sahl Wayjan Ibn Rustom ca. 940 - ca. 1000 [BE] AL-SHIRAZI Qotb Al-Dine [BE] AL-TUSI Nasir Al-Dine [BE] AL-ZARQALI (ARZACHEL) Ibrahim Ibn Yahiya [BE] AMONTONS Guillaume [JF] APOLLONIOS de PERGA 200 AC - 100 AC [BE] APPELL Paul [JC] ARAGO [PO] ARCHARD John Frederic [JF] ARCHIMEDE ca. 287 AC - 212 AC [PAB] ARCHYTAS de TARENTE [BE] ARISTARQUE de SAMOS ca. 310 AC - ca. 230 AC [PAB] ARISTOTE 384 AC - 322 AC [PAB] ARYABHATA I [BE] ATWOOD George [PP] a B c d e f-m ... n-z BALIANI Giovan Battista [PAB] BARNARD Edward [BE] BARWELL [JF] BATCHELOR George Keith [AM] BAUSCHINGER [PP] BEECKMAN Isaac [PAB] BELANGER J.B.

72. Eugenio De Mello Translate this page eugenio De Mello nasce in Brasile dove danza con il Ballet de Camera coreografi qualiLouis Falco, Ranko Yokohama, Teri Weikel, Susanna beltrami, Robert Pomper http://cscanymore.it/eugenio.htm

Eugenio De Mello Coreografo fondatore della In Compagnia Coreografo residente e Direttore Artistico per il settore danza al Teatro Comuna Baires di Milano. Co-Direttore Artistico del Festival Danza Estate Bergamo-Europa. Direttore Artistico della Rassegna Uscite D'Emergenza. Eugenio De Mello nasce in Brasile dove danza con il Ballet de Camera della Città di San Paolo. In Italia nel 1982, interpreta ruoli solisti per vari coreografi quali: Louis Falco, Ranko Yokohama, Teri Weikel, Susanna Beltrami, Robert Pomper, Enzo Procopio, Martine Bucci, Luisa Casiraghi, Adailton Russo. Nel 1992, insieme ad altri coreografi di origine brasiliana, fonda la Compagnia Di Tre e nel 1995 In Compagnia. per la quale crea gli spettacoli "Il Mattino Sospeso" e "Sacri Segreti" presentati in diverse rassegne in Italia e all'estero Dal 1996 è il direttore artistico del settore danza presso il Teatro Comuna Baires di Milano, dove organizza la rassegna di danza contemporanea Uscite d'Emergenza, e co-direttore artistico del Festival Danzaestate - Bergamo-Europa. In Compagnia

73. People On Stage Bonnet, Ossian, 18191892, Ch.29. Riemann, Gorge Friedrich Bernhard, 1826-1866,Germany, Ch.a. beltrami, eugenio, 1835-1900, Italy, Ch.20. Weber, 1842-1913, Germany,Ch.26. http://www1.kcn.ne.jp/~iittoo/us_people.htm

Contents Ch. is the first chapter he appears. Zenon (of Elea) Greek Ch.15 Euclid Greek Ch.1 Mercator, Gerardus Holland Ch.2 Napier, John Scotland Ch.33 Euler, Leonhard Switzerland Ch.29 Lambert, Johann Heirich Switzerland Ch.9 Gauss, Carl Friedrich Germany Ch.7 Mobius, Augusttus Ferdinand Germany Ch.23 Lobachevsky, Nicolai Ivanovitch Russia Ch.5 Bolyai, Janos Hungary Ch.5 Bonnet, Ossian@ Ch.29 Riemann, Gorge Friedrich Bernhard Germany Ch.a Beltrami, Eugenio Italy Ch.20 Weber Germany Ch.26 Klein, Felix Germany Ch.3 Poincare, Henri France Ch.1 Hilbert, David Germany Ch.20 Minkowski, Hermann Russia Ch.20 Escher, Mauritz Cornels Holland Ch.10 Terasaka, Hidetaka Japan Ch.12 Kobayashi, Shoshichi Japan Ch.24 Ungar, Abraham A. USA Ch.28 Thurston, William P. USA Ch.30 Kojima, Sadayoshi Japan Ch.33 Oxaal, Ford USA Ch.1 Sakuma, Makoto Japan Ch.10 Weeks, Jeffrey R. USA Ch.29 Wada, Masaaki Japan Ch.2 Ahara, Kazushi Japan Ch.30 Kawazumi, Nariya Japan Ch.27 Ushijima, Akira Japan Ch.33 Rogmann, Sascha Germany Ch.26 Gunn, Charlie Ch.26 Hayakawa @ Japan Ch.33 Masuda @ Japan Ch.33 Nordstrand, Tore @ Norway Ch.20

74. Hyperbolic Geometry It was not until later that eugenio beltrami (1835 to 1900) in 1868 and FelixKlein (1849 to 1925) in 1871 showed that this geometry was as consistent as http://www.gap-system.org/~john/geometry/Lectures/L26.html

75. Liste Alphabétique Des Mathématiciens Translate this page Bayes (Thomas), Anglais (1702-1761). Bellavitis (Giusto), Italien (1803-1880).beltrami (eugenio), Italien (1835-1900). Bernays (Paul), Suisse (1888-1977). http://www.cegep-st-laurent.qc.ca/depar/maths/noms.htm

Abel (Niels Henrik) Agnesi (Maria Guetana) Italienne (1718-1799) Alembert (Jean Le Rond d') Alexander (James Waddell) Alexandroff (Pavel Sergeevich) Russe (1896-1982) Apian (Peter Benneuwitz, dit) Allemand (1495-1552) Apollonios de Perga Grec(v.~262-v.~180) Appel (Paul) Grec (~287-~212) Aristote Grec (~384-~322) Arzela (Cesare) Italien (1847-1912) Ascoli (Guilio) Italien (1843-1896) Babbage (Charles) Anglais (1792-1871) Banach (Stefan) Polonais (1892-1945) Argand (Jean Robert) Suisse (1768-1822) Barrow (Isaac) Anglais (1630-1677) Bayes (Thomas) Anglais (1702-1761) Bellavitis (Giusto) Italien (1803-1880) Beltrami (Eugenio) Italien (1835-1900) Bernays (Paul) Suisse (1888-1977) Bernoulli (Daniel) Suisse (1700-1782) Bernoulli (Jacques) Suisse (1654-1705) Bernoulli (Jean) Suisse (1667-1748) Allemand (1878-1956) Bernstein (Sergei Natanovich) Russe (1880-1968) Bertrand (Josepn) Bessel (Friedrich) Allemand (1784-1846) Birkoff (George David) Bliss (Gilbert Ames) Bochner (Salomon) Allemand (1899-1982) Bolyai (Janos) Hongrois (1802-1860) Bolzano (Bernhard) Bombelli (Raffaele) Italien (1522-1572) Bonnet (Ossian) Boole (George) Anglais (1815-1864) Bourbaki (Nicolas) Braikenridge (William) Anglais (v.1700-1762)

76. Le Romain Des Mots-croisés. **Mathématiciens Translate this page BELLAVITIS (COMTE GIUSTO) NÉ, A, BASSANO (1803-1880) beltrami (eugenio) NÉ,A, CREMONE(1835-1900) BOMBELLI (RAFFAELE) NÉ, A, BORGO PANIGALE (1526-1572 http://www.mots-croisiste.com/19.html

Index général aéroport affluents Centrale nucléaire et hydroélectriques Chefs-Lieux Collines de Rome Communes Compositeurs Constellations Cyclades Déesses Dieux Divinités Écrivains Fleuves Côtier FLeuves des enfers Fleuves Historiens Homme d'état Homme Politiques Lacs Massifs Mathématiciens Noms Peintres Poètes Ports et Ports Fluviaux Rivières Sculteurs Théologiens Torrents Villes MATHEMATICIENS MATHEMATICIENS, ALLEMANDS. ARTIN (EMIL) NÉ, A, VIENNE (1898-1962) CANTOR (GEORG) NÉ, A, ST-PETERSBOURG (1845-1918) DEDEKIND (RICHARD) NÉ, A, BRUNSWICK (1831-1916) DIRICHLET (GUSTAV LEJEUNE) NÉ, A, DUREN(1805-1859) FUCHS (LAZARUS) NÉ, A, MOSCHIN (1833-1902) GAUSS (CARL FRIEDRICH) NÉ, A, BRUNSWICK) (1777-1855) GRASSMANN (HERMANN) NÉ, A, STETTIN (1809-1877) HAUSDORFF(FELIX) NÉ, A, BRESLAU (1868-1942) HILBERT (DAVID) NÉ, A, KONIGSBERG (1862-1943) JACOBI (CARL) NÉ, A, , POTSDAM (1804-1851) KLEIN (FELIX) NÉ, A, DUSSELDORF (1849-1925) KRONECKER (LEOPOLD) NÉ, A, LIEGNITZ (1823-1891) KUMMER (ERNST EDUARD ) NÉ, A, SORAU (1810-1893) LEIBNIZ (GOTTFRIED WILHELM) NÉ, A, LEIPZIG (1646-1716) LINDEMANN (FERDINAND VON ) NÉ, A, HANOVRE (1852-1939)

77. Encyclopædia Britannica known for his works on history of mathematics. eugenio beltrami Universityof St. Andrews, Scotland Short biography of this Italian http://search.britannica.com/search?query=Eugenio Necochea

78. Encyclopædia Britannica beltrami, eugenio Italian mathematician known for his description of nonEuclideangeometry and for his theories of surfaces of constant curvature. http://search.britannica.com/search?query=magnetism&ct=eb&fuzzy=N&show=10&start=

79. Biography-center - Letter B gpe/drvbeljea.html; beltrami, eugenio www-history.mcs.st-and.ac.uk/~history/Mathematicians/beltrami.html;Bemis, Samuel www.getty http://www.biography-center.com/b.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish B 1122 biographies Baade, Walter www.treasure-troves.com/bios/Baade.html Baade, Wilhelm Heinrich Walter www.phys-astro.sonoma.edu/BruceMedalists/Baade/index.html Baastrup, Christian Ingerslev www.whonamedit.com/doctor.cfm/1242.html Babashoff, Shirley www.hickoksports.com/biograph/babashof.shtml Babbage, Charles www.norfacad.pvt.k12.va.us/project/babbage/babbage.htm Babbage, Charles www.ideafinder.com/history/inventors/babbage.htm Babbitt, Bruce www.doi.gov/bab_bio.html Babbitt, Platt D. www.getty.edu/art/collections/bio/a2841-1.html Babcock, George www.invent.org/hall_of_fame/6.html Babcock, Harold Delos www.phys-astro.sonoma.edu/BruceMedalists/BabcockHD/index.html Babcock, Horace Welcome www.phys-astro.sonoma.edu/BruceMedalists/BabcockHW/index.html Babcock, Stephen Moulton

80. Non-Euclidean Geometries, Models came in 1868 with the publication of Saggio di interpretazoine della geometrianon euclidea by the Italian mathematician eugenio beltrami (18351900). http://www.cut-the-knot.com/triangle/pythpar/Model.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Non-Euclidean Geometries As Good As Might Be In 1823, Janos Bolyai wrote to his father: "Out of nothing I have created a new universe." By which he meant that starting from the first 4 of Euclid's postulates and a modified fifth, he developed an expansive theory that, although quite unusual, did not seem to lead to any logical contradiction. Gauss expressed his conviction in consistency of the theory he had in mind in a letter in 1824. However, hesitant of the public reaction to the idea that, by the side of Euclidean, there is another geometry, he never published anything on the subject. From our perspective, the situation was exactly the same as with Euclidean geometry. Euclid built an axiomatic theory by deriving a lot of theorems from his five postulates. No one had ever proved that continuing in Euclid's footstep would not lead to a contradiction. However, a 2000 year history elevated Elements on a pedestal of infallibility. Kant even stipulated that the universe had been built according to Euclid. Lobachevsky was quite aware of the problem and in later publications tried without success to redefine the notions of line and plane. A breakthrough came in 1868 with the publication of Saggio di interpretazoine della geometria non euclidea by the Italian mathematician Eugenio Beltrami (1835-1900). Beltrami discovered that Lobachevsky's geometry admits an interpretation in terms of Euclidean geometry. From here it follows that if Lobachevsky's geometry leads to a contradiction, Euclidean geometry is as well contradictory. In other words, consistency of Euclidean geometry implies consistency of the geometry of Lobachevsky. The construction is now known as Beltrami-Klein model of Lobachevsky geometry. Sometimes it's called the

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