An online geodesic bibliography

Here is a list of the older mathematical treatments of the geodesic problem for an ellipsoid, together with links to online copies. This includes also some more recent works which are available online (chiefly works funded by the US Government). Unfortunately, the fold-out pages of figures in some books are usually not scanned properly by Google; in some cases I have been able to scan the missing pages, see geodesic-papers. Please let me, Charles Karney <charles@karney.com>, know of errors, omissions, etc.

This bibliography was started on 2009-06-06 (at http://trac.osgeo.org/proj/wiki/GeodesicCalculations). The last update was on 2012-04-09.

• I. Newton,
  Philosophiae Naturalis Principia Mathematica (3rd edition, Roy. Soc., 1726), Book 3, Prop. 19, Prob. 3, pp. 412–416.
  http://books.google.com/books?id=0xYOAAAAQAAJ&pg=PA412
  English translation: Newton's Principia: The Mathematical Principles of Natural Philosophy, by A. Motte (Adee, New York, 1848), pp. 405–409.
  http://books.google.com/books?id=KaAIAAAAIAAJ&pg=PA405
• Jac. Bernoulli,
  Solutio sex problematum fraternorum [Solution of six problems posed by my brother], Acta Erud. 226–232 (1698), in Jacobi Bernoulli, Basileensis, Opera, Vol. 2 (Cramer, Geneva, 1744), pp 796–806 + figures.
  http://books.google.com/books?id=TvJaAAAAQAAJ&pg=RA1-PA226
  http://books.google.com/books?id=CPEuAAAAIAAJ&pg=PA794
• Jean Bernoulli,
  In superficie quacunque curva ducere lineam inter duo puncta brevissimam [Drawing the shortest line between two points on a curved surface], letter to S. Klingenstierna (1728), in Johannis Bernoulli, Opera Omnia, Vol. 4 (Bousquet, Geneva, 1742), 108–128.
  http://books.google.com/books?id=Yw1bAAAAQAAJ&pg=PA108 (figures missing)
• A. C. Clairaut,
  Détermination géometrique de la perpendiculaire à la méridienne tracée par M. Cassini [Geometrical determination of the perpendicular to the meridian drawn by Jacques Cassini], Mém. de l'Acad. Roy. des Sciences de Paris, 406–416 (1733, publ. 1735).
  http://books.google.com/books?id=GOAEAAAAQAAJ&pg=PA406
  alt: http://gallica.bnf.fr/ark:/12148/bpt6k3530m.image.f566
• A. C. Clairaut,
  Suite d'un Mémoire donné en 1733, qui a pour titre: Détermination géometrique de la perpendiculaire à la méridienne tracée, &c [Continuation of a paper presented in 1733 entitled: Geometrical determination of the perpendicular to the meridian, etc.], Mém. de l'Acad. Roy. des Sciences de Paris, 83–96 (1739, publ. 1741).
  http://books.google.com/books?id=5OAEAAAAQAAJ&pg=RA1-PA83
  alt: http://gallica.bnf.fr/ark:/12148/bpt6k3536g
• A. C. Clairaut,
  Théorie de la Figure de la Terre Tirée des Principes de l'Hydrostatique [The Theory of Figure of the Earth Drawn from Hydrostatic Principles] (Durand, Paris, 1743).
  http://books.google.com/books?id=X6wWAAAAQAAJ
• L. Euler,
  Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes [A method for finding curved lines enjoying properties of maximum or minimum] (Bousquet, Lausanne, 1744).
  http://books.google.com/books?id=dA1bAAAAQAAJ
  alt: http://math.dartmouth.edu/~euler/pages/E065.html
  figures: http://math.dartmouth.edu/~euler/docs/originals/E065h pp. 15, 17, 19, 21, 23.
• L. Euler,
  Principes de la trigonométrie sphérique tirés de la méthode des plus grands et plus petits [Principles of spherical trigonometry taken from the method of maxima and minima], Mém. de l'Acad. Roy. des Sciences de Berlin 9, 223–257 (1753, publ. 1755).
  http://books.google.com/books?id=QIIfAAAAYAAJ&pg=PA223
  figures: http://books.google.com/books?id=QIIfAAAAYAAJ&pg=PA361
  alt: http://math.dartmouth.edu/~euler/pages/E214.html
  German translation: Grundzüge der sphärischen Trigonometrie in Zwei Abhandlungen über sphärische Trigonometrie by E. Hammer, Ostwald's Klass. ex. Wiss., No. 73 (Engelmann, Leipzig 1896), pp. 3–39.
  http://books.google.com/books?id=dPbhs0MSJOgC&pg=PA3
• L. Euler,
  Élémens de la trigonométrie sphéroïdique tirés de la méthode des plus grands et plus petits [Elements of spheroidal trigonometry taken from the method of maxima and minima], Mém. de l'Acad. Roy. des Sciences de Berlin 9, 258–293 (1753, publ. 1755).
  http://books.google.com/books?id=QIIfAAAAYAAJ&pg=PA258
  figures: http://books.google.com/books?id=QIIfAAAAYAAJ&pg=PA363
  alt: http://math.dartmouth.edu/~euler/pages/E215.html
• J. L. Lagrange,
  Nouvelle méthode pour résoudre les équations littérales par le moyen des séries [New method for solving explicit equations by means of a series], Mém. de l'Acad. Roy. des Sciences de Berlin 24, 251–326 (1768, publ. 1770), in Oeuvres de Lagrange, Vol. 3 (Gauthier-Villars, Paris, 1869), pp. 5–73.
  http://books.google.com/books?id=YywPAAAAIAAJ&pg=PA5
• A. P. Dionis du Séjour,
  Nouvelles méthodes analytiques pour résoudre différentes questions astronomiques; treizième mémoire [New analytical methods for solving various astronomical questions, part 13], Mém. de l'Acad. Roy. des Sciences de Paris, 73–192 + 3 plates (1778, publ. 1781).
  http://books.google.com/books?id=8uEEAAAAQAAJ&pg=RA1-PA73 (pp. 112–113 missing)
• A. P. Dionis du Séjour,
  Traité Analytique des Mouvemens apparens des Corps Célestes [Analytical Treatise on the Apparent Movement of Heavenly Bodies], Vol. 2 (Valade, Paris, 1789), Book 1, Chaps. 1–3.
  http://books.google.com/books?id=tnHOAAAAMAAJ&pg=PA3
  figures: http://geographiclib.sf.net/geodesic-papers/dusejour89-fig.pdf
• T. Valperga di Caluso,
  De la navigation sur le spheroïde elliptique, ses loxodromies et son plus court chemin [Navigation on the ellipsoid, its loxodromes, and the shortest path], Mém. l'Acad. Roy. des Sciences de Turin 4, 325–368 + figures (1788–89, publ. 1790).
  http://books.google.com/books?id=ZO-DiSOtC0kC&pg=RA1-PA313-IA4 (figures missing)
• T. Valperga di Caluso,
  Applications des formules du plus court chemin sur le spheroïde elliptique [Application of the formulas for the shortest path on an ellipsoid], Mém. l'Acad. Roy. des Sciences de Turin 5, 100–121 (1790–91, publ. 1793).
  http://books.google.com/books?id=yZH2VQBt4CkC&pg=PA100
• P. S. Laplace,
  Traité de Mécanique Céleste, Vol. 2 (Duprat, Paris, 1798/1799), Book 3, Chap. 5; reprinted in Oeuvres complètes de Laplace, Vol. 2 (Imprim. Royale, 1843), pp. 127–180 (early use of geodesic line in French).
  http://books.google.com/books?id=qZQAAAAAMAAJ&pg=RA1-PA127
  

  Nous désignerons cette ligne sous le nom ligne géodésique [We call this line the geodesic line].

  Translation with commentary: Celestial Mechanics by N. Bowditch, Vol. 2 (Boston, 1832), pp. 358–491.
  http://geographiclib.sf.net/geodesic-papers/laplace99a.pdf
• J. B. J. Delambre and A. M. Legendre,
  Méthodes analytiques pour la Détermination d'un arc du Méridien [Analytical methods for determination an arc of the meridian] (Crapelet, Paris, 1799).
  http://books.google.com/books?id=DBAOAAAAQAAJ
• A. M. Legendre,
  Mémoire sur les opérations trigonométriques, dont les résultats dépendent de la figure de la terre [Trigonometric operations which depend on the shape of the earth], Mém. de l'Acad. Roy. des Sciences de Paris, 352–383 (1787, publ. 1789).
  http://books.google.com/books?id=0uIEAAAAQAAJ&pg=PA352 (figures missing)
• A. M. Legendre,
  Analyse des triangles tracés sur la surface d'un sphéroïde [Analysis of spheroidal triangles], Mém. de l'Inst. Nat. de France, 130–161 (1st semester, 1806).
  http://books.google.com/books?id=-d0EAAAAQAAJ&pg=PA130-IA4
  missing pages: http://geographiclib.sf.net/geodesic-papers/legendre06-add.pdf
  Review: http://books.google.com/books?id=DYoCAAAAYAAJ&pg=PA504
• A. M. Legendre,
  Exercices de Calcul Intégral sur Divers Ordres de Transcendantes et sur les Quadratures [Exercises in Integral Calculus], Vol. 1 (Courcier, Paris, 1811), pp. 178–182.
  http://books.google.com/books?id=riIOAAAAQAAJ&pg=PA178
  figures: http://www.archive.org/stream/exercicescalculi01legerich#page/389
• A. M. Legendre,
  Traité des Fonctions Elliptiques et des Intégrales Eulériennes [Treatise on Elliptic Functions and Eulerian Integrals], Vol. 1 (Huzard-Courcier, Paris, 1825), pp. 360–364.
  http://books.google.com/books?id=vaAKAAAAYAAJ&pg=PA360
  figures: http://geographiclib.sf.net/geodesic-papers/legendre25-fig.pdf
• J. G. Soldner,
  Über die kürzeste Linie auf dem Sphäroide [The shortest line on the spheroid], Monat. Corr. Zach 11, 7–23 (Gotha, 1805).
  http://books.google.com/books?id=454AAAAAMAAJ&pg=PA5
• J. G. Soldner,
  Theorie der Landesvermessung (1810) [Theory of Surveying], edited by J. Frischauf, Ostwald's Klass. ex. Wiss., No. 184 (Engelmann, Leipzig, 1911), Part 1.
  http://geographiclib.sf.net/geodesic-papers/soldner10.pdf
• B. Oriani,
  Auszug aus einem Schreiben des Astronomen Oriani [Excerpt from a paper by Oriani], Monat. Corr. Zach 10, 244–251 (Gotha, 1804).
  http://books.google.com/books?id=d54AAAAAMAAJ&pg=PA244
• B. Oriani,
  Auszug aus einem Briefen von Oriani [Excerpt from a letter from Oriani], Monat. Corr. Zach 11, 551–560 (Gotha, 1805).
  http://books.google.com/books?id=454AAAAAMAAJ&pg=PA553
• B. Oriani,
  Elementi di trigonometria sferoidica [Elements of spheroidal trigonometry], Part 1: Mem. dell'Ist. Naz. Ital. 1(1), 118–198 (Bologna, 1806); Part 2: 2(1), 1–58 (Bologna, 1808); Part 3: 2(2), 1–58 (Bologna, 1810); Addendum: Mem. dell'Imp. Reg. Ist. del Regno Lombardo-Veneto 4, 325–331 (Milan, 1833).
  http://books.google.com/books?id=SydFAAAAcAAJ&pg=PA118
  http://www.archive.org/stream/memoriedellistit21isti#page/1
  http://www.archive.org/stream/memoriedellistit22isti#page/1
  http://books.google.com/books?id=6bsAAAAAYAAJ&pg=PA325
  Errata: http://books.google.com/books?id=6bsAAAAAYAAJ&pg=RA1-PA333
  Review: http://books.google.com/books?id=PzICAAAAYAAJ&pg=RA1-PA494
• B. Oriani,
  Auszug aus einem Briefe des Herrn Oriani an den Herausgeber [Excerpt from a letter to the editor], Astron. Nachr. 4(94), 461–466 (1826).
  http://adsabs.harvard.edu/full/1826AN......4..461O
• B. Oriani,
  Essempi di calcolo nella soluzione di alcuni problemi di trigonometria sferoidica [Examples of solving some problems in spheroidal trigonometry], Effemeridi astronomiche di Milano 1827, 3–24 (1826); 1828, 3–32 (1827); 1829, 3–24 (Milan 1828).
  http://books.google.com/books?id=02QEAAAAYAAJ&pg=RA1-PA3
  http://books.google.com/books?id=9GQEAAAAYAAJ&pg=RA1-PA3
  http://books.google.com/books?id=D2UEAAAAYAAJ&pg=RA1-PA3
• C. Hutton,
  A Course of Mathematics in Three Volumes Composed for the Use of the Royal Military Academy, Vol. 3 (London, 1811), p 115 (early use of geodesic line in English).
  http://books.google.com/books?id=BtM2AAAAMAAJ&pg=PA115
  

  A line traced in the manner we have now been describing, or deduced from trigonometrical measures, by the means we have indicated, is called a geodetic or geodesic line: it has the property of being the shortest which can be drawn between its two extremities on the surface of the earth; and it is therefore the proper itinerary measure of the distance between those two points.

• E. G. F. Thune,
  Tentamen circa trigonometriam sphaeroidicam [Essay on spheroidal trigonometry] (Schultz, Copenhagen, 1815)
  http://geographiclib.sf.net/geodesic-papers/thune15.pdf
  http://books.google.com/books?id=AoU_AAAAcAAJ
• L. Puissant,
  Traité de Géodésie ou Exposition des Méthodes Trigonométriques et Astronomiques [Treatise on Geodesy], Vol. 2 (2nd edition, Courcier, Paris, 1819), Book 6, Chap. 1.
  http://books.google.com/books?id=PZEAAAAAMAAJ&pg=PA212
  unreadable pages: http://geographiclib.sf.net/geodesic-papers/puissant19b-add.pdf
  figures: http://geographiclib.sf.net/geodesic-papers/puissant19b-fig.pdf
• L. Puissant,
  Note sur la trigonométrie sphéroïde, dans laquelle on détermine généralement la plus courte distance de deux point donnés sur la terre par leur latitude et leur longitude [Note on spheroidal trigonometry and the determination of the shortest path between two points on the earth], Conn. des Tems 1832, 34–48 (Bachelier, Paris, 1829).
  http://books.google.com/books?id=Eoo3AAAAMAAJ&pg=RA1-PA34
• L. Puissant,
  Suite de la note sur la trigonométrie sphéroïde, insérée dans la Connaissance des tems pour 1832 [Addendum to a note on spheroidal trigonometry in Conn. des. Tems 1832], Conn. des Tems 1833, 77–85 (Bachelier, Paris, 1830).
  http://books.google.com/books?id=h4o3AAAAMAAJ&pg=RA1-PA77
• L. Puissant,
  Nouvel essai de trigonométrie sphéroïdique [New essay on spheroidal trigonometry], Mém. l'Acad. Roy. des Sciences de l'Inst. de France 10, 457–529 (1831).
  http://books.google.com/books?id=KcjOAAAAMAAJ&pg=RA2-PA457
  errata: http://books.google.com/books?id=KcjOAAAAMAAJ&pg=PR7
• J. J. Littrow,
  Theoretische und practishe Astronomie [Theoretical and Practical Astronomy], Vol. 1 (Vienna, 1821), Chap. 10.
  http://books.google.com/books?id=3fk4AAAAMAAJ&pg=RA1-PA270 (figures missing)
• J. P. W. Stein,
  Geographische Trigonometrie oder die Auflösung der geradlinigen, sphärischen und sphäroidischen Dreiecke [Geographic trigonometry or the solution of plane, spherical, and spheroidal triangles] (Mainz, 1825), Part 2, Chap 2.
  http://books.google.com/books?id=2S9NAAAAMAAJ&pg=PA80 (figures missing)
• F. W. Bessel,
  Ueber Berechnung geodätischer Vermessungen [Calculating geodesic surveys], Astron. Nachr. 1(3), 33–36 (1823).
  http://books.google.com/books?id=D58RAAAAYAAJ&pg=PA37
• F. W. Bessel,
  Berechnung eines Dreiecks, dessen Seiten geodätischer Linien sind [Calculations of a geodesic triangle], Astron. Nachr. 1(6), 85–90 (1823).
  http://books.google.com/books?id=D58RAAAAYAAJ&pg=PA64
• F. W. Bessel,
  Ueber die Berechnung der geographischen Längen und Breiten aus geodätischen Vermessungen [The calculation of longitude and latitude from geodesic measurements], Astron. Nachr. 4(86), 241–254 + tables (1825).
  http://adsabs.harvard.edu/full/1825AN......4..241B
  With corrections: http://arxiv.org/abs/0908.1823
  Partial English translation: Calculation of longitudes and latitudes on a spheroid, Quart. Jour. Roy. Inst. 21(41), 138–152 (1826).
  http://geographiclib.sf.net/geodesic-papers/quartjour26-extracts.pdf
  Modern English translation: by C. F. F. Karney and D. E. Deakin, Astron. Nachr. 331(8), 852–861 (2010).
  http://dx.doi.org/10.1002/asna.201011352
  preprint: http://arxiv.org/abs/0908.1824
• F. W. Bessel,
  Ueber den Einfluss der Unregelmässigkeiten der Figur der Erde auf geodätische Arbeiten und ihre Vergleichung mit den astronomischen Bestimmungen [The effect of irregularities in the shape of the earth on geodetic work and their comparison with the astronomical measurements], Astron. Nachr. 14(329), 269–312 (1837).
  http://articles.adsabs.harvard.edu/full/1837AN.....14..269B
  
• F. W. Bessel,
  Abhandlungen von Friedrich Wilhelm Bessel [The Works of Bessel], Vol. 3 (W. Engelmann, Leipzig, 1876), Part 6 contains the previous 4 papers.
  http://books.google.com/books?id=vX4EAAAAYAAJ&pg=PR6
• J. Ivory,
  Solution of a geodetical problem, Phil. Mag. 64(315), 35–39 (1824).
  http://books.google.com/books?id=xk0wAAAAIAAJ&pg=PA35
  Errata: Phil. Mag. 65(324), 249–250 (1825).
  http://books.google.com/books?id=_UwwAAAAIAAJ&pg=PA249
• J. Ivory,
  On the properties of a line of shortest distance traced on the surface of an oblate spheroid, Phil. Mag. 67(336), 241–249 and 67(337), 340–352 (1826).
  http://books.google.com/books?id=PkwwAAAAIAAJ&pg=PA241
  http://books.google.com/books?id=PkwwAAAAIAAJ&pg=PA340
  Mr. Ivory's mode of finding the length of the geodetic curve, Quart. Jour. Roy. Inst. 21(42), 361–363 (1826).
  http://geographiclib.sf.net/geodesic-papers/quartjour26-extracts.pdf
  F. W. Bessel, Ueber einen Aufsatz von Ivory im Philosophical Magazine [Comments on a paper by Ivory in the Philosophical Magazine], Astron. Nachr. 5(108), 177–180 (1927).
  http://adsabs.harvard.edu/full/1826AN......5..177B
• J. Ivory,
  A direct method of finding the shortest distance between two points on the Earth's surface when their geographical position is given, Phil. Mag. 8, 30–34 and 114–117 (misprinted as 134–137) (1830).
  http://books.google.com/books?id=j4EqAAAAYAAJ&pg=PA30
  http://books.google.com/books?id=j4EqAAAAYAAJ&pg=PA134
• F. T. Poselger,
  Anleitung zu Rechnungen der Geodäsie [Guide to the Calculations of Geodesy] (Dümmler, Berlin, 1831), Chap. 4.
  http://books.google.com/books?id=OVkOAAAAYAAJ&pg=PA39
• C. F. Gauss,
  Disquisitiones generales circa superficies curvas (Dieterich, Göttingen, 1828).
  http://books.google.com/books?id=bX0AAAAAMAAJ&pg=PA3
  alt: http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN236005081
  French translation: Recherches générales sur les surfaces courbes, by E. Roger (Grenoble, 1855).
  http://books.google.com/books?id=PxcOAAAAQAAJ
  German translation: Allgemeine Flächentheorie, by A. Wangerin, Ostwald's Klass. ex. Wiss., No. 5 (Engelmann, Leipzig, 1889).
  http://books.google.com/books?id=W2UEAAAAYAAJ
  English translation: General Investigations of Curved Surfaces of 1827 and 1825, by J. C. Morehead and A. M. Hiltebeitel (Princeton Univ. Lib., 1902).
  http://books.google.com/books?id=a1wTJR3kHwUC
• C. F. Gauss,
  Untersuchungen über Gegenstände der höheren Geodäsie, [Investigations on Higher Geodesy, Parts 1 & 2], Abhandl. Math. Cl. Kön. Ges. Wiss. zu Göttingen 2, 3–45 (1843); 3, 3–43 (1846).
  Reprint: edited by J. Frischauf, Ostwald's Klass. ex. Wiss., No. 177 (Engelmann, Leipzig, 1910).
  http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=39018
  http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=39036
  http://geographiclib.sf.net/geodesic-papers/gauss43.pdf
• C. F. Gauss,
  Erdellipsoid und geodätischen linie [Geodesic lines on an ellipsoidal earth], in Carl Friedrich Gauss Werke, Vol. 9 (Ges. Wiss., Göttingen, 1903), pp. 65–104.
  http://books.google.com/books?id=ICwPAAAAIAAJ&pg=PA65
  alt: http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN23601515X
• A. Galle,
  Über die geodätischen Arbeiten von Gauss [The Geodetic Works of Gauss], in Carl Friedrich Gauss Werke, Vol. 11 (Ges. Wiss., Göttingen, 1863), Part 2, 1–161.
  http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=139786
• C. G. J. Jacobi,
  Fundamenta nova theoriae functionum ellipticarum [A Fundamental New Theory of Elliptic Functions] (Borntraeger, Könisberg, 1829).
  http://books.google.com/books?id=_CAOAAAAQAAJ&pg=PR1
• C. G. J. Jacobi,
  Demonstratio et amplificatio nova theorematis Gaussiani de quadratura integra trianguli in data superficie e lineis brevissimis formati [Demonstration and extension of a new theorem by Gauss on the integral over triangles formed by geodesics on a given surface], Jour. Crelle 16, 344–350 (1837).
  http://books.google.com/books?id=2qrxAAAAMAAJ&pg=PA344
• C. G. J. Jacobi,
  Note von der geodätischen Linie auf einem Ellipsoid und den verschiedenen Anwendungen einer merkwürdigen analytischen Substitution [The geodesic on an ellipsoid and various applications of a remarkable analytical substitution], Jour. Crelle 19, 309–313 (1839).
  http://books.google.com/books?id=RbwGAAAAYAAJ&pg=PA309
  French translation: Jour. Liouville 6, 267–272 (1841).
  http://books.google.com/books?id=Rh8GAAAAYAAJ&pg=RA1-PA267
• C. G. J. Jacobi and E. Luther,
  Solution nouvelle d'un problème fondamental de géodésie [A new solution to a fundamental problem of geodesy], Astron. Nachr. 41(974), 209–216 (1855); 42(1006), 337–358 (1856).
  http://adsabs.harvard.edu/full/1855AN.....41..209J
  http://adsabs.harvard.edu/full/1856AN.....42..337J
  also in Jour. Crelle 53, 335–365 (1857).
  http://books.google.com/books?id=vc0GAAAAYAAJ&pg=PA335
• C. G. J. Jacobi,
  Vorlesungen über Dynamik [Lessons on Dynamics], edited by A. Clebsch (Berlin, 1866), Secs. 6 & 28.
  http://books.google.com/books?id=ryEOAAAAQAAJ&pg=PA43
  http://books.google.com/books?id=ryEOAAAAQAAJ&pg=PA212
• C. G. J. Jacobi,
  Über die Curve, welche alle von einem Punkte ausgehenden geodätischen Linien eines Rotationsellipsoides berührt [The envelope of geodesic lines emanating from a single point on an ellipsoid], Op. Post., completed by A. Wangerin, in C. G. J. Jacobi's Gesammelte Werke, Vol. 7 (Reimer, Berlin, 1891), pp. 72–87.
  http://books.google.com/books?id=_09tAAAAMAAJ&pg=PA72
• F. Minding,
  Über die Curven des kürzesten Perimeters auf krummen Flächen [Curves of minimum perimeter on curved surfaces], Jour. Crelle 5, 297–304 (1830).
  http://books.google.com/books?id=Y6wGAAAAYAAJ&pg=PA297
• F. Minding, Beiträge zur Theorie der kürzesten Linien auf krummen Flächen [Contributions to the theory of shortest lines on curved suraces], Jour. Crelle 20, 323–327 (1840).
  http://books.google.com/books?id=bLwGAAAAYAAJ&pg=PA323
• F. Minding,
  Zur Theorie der Curven kürzesten Umrings, bei gegebenem Flächeninhalt auf krummen Flächen [The shortest curves encirling a given area on a curved surface], Jour. Crelle 86, 279–289 (1879).
  http://books.google.com/books?id=85HxAAAAMAAJ&pg=PA279
• J. Liouville,
  De la ligne géodésique sur un ellipsoïde quelconque [The geodesic on an arbitrary ellipsoid], Jour. Liouville 9, 401–408 (1844).
  http://books.google.com/books?id=7oYGAAAAYAAJ&pg=PA401
• J. Liouville,
  Sur la théorie générale des surfaces [On the general theory of surfaces], Jour. Liouville 16, 130–132 (1851).
  http://books.google.com/books?id=TFdOAAAAMAAJ&pg=PA130
• M. Roberts,
  Sur quelques propriétés des lignes géodésiques et des lignes de courbure de l'ellipsoïde [Properties of geodesics and lines of curvature on an allispoid], Jour. Liouville 11, 1–4 (1846).
  http://books.google.com/books?id=qTUGAAAAYAAJ&pg=PA1
• P. O. Bonnet,
  Mémoire sur la théorie générale des surfaces [On the general theory of surfaces], Jour. l'École Polytechnique 19(32), 1–146 (1848).
  http://books.google.com/books?id=VGo_AAAAcAAJ&pg=PA1
• G. Monge and J. Liouville,
  Application de l'Analyse à la Géometrie [Application of analysis to geometry] (5th edition, Bachelier, Paris, 1850), pp. 547–600.
  http://books.google.com/books?id=Nf5zhlffjd0C&pg=PA547
• K. T. W. Weierstrass,
  Über die geodätischen Linien auf dem dreiaxigen Ellipsoid [Geodesic lines on a triaxial ellipsoid], Monat. König. Akad. Wiss. 988–997 (Berlin, 1861), in Mathematische Werke, Vol. 1 (Berlin, 1894), pp. 257–266.
  http://books.google.com/books?id=9O4GAAAAYAAJ&pg=PA257
• P. A. Gordan,
  De linea geodetica [On geodesic lines] (Berolini, 1862).
  http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN270894012
• J. J. Baeyer,
  Das Messen auf der sphäroidischen Erdoberfläche als Erläuterung meines Entwurfes zu einer mitteleuropäischen Gradmessung [The measurement of the spheroidal Earth as an illustration of my specification for a Central European Survey] (Reimer, Berlin, 1862), Sec. 2.
  http://books.google.com/books?id=1loOAAAAYAAJ&pg=PA27
• J. J. Baeyer,
  Über die Auflösung grosser sphäroidischer Dreiecke [Solving large spheroidal triangles], Astron. Nachr. 61(1455) 225–240 (1864).
  http://adsabs.harvard.edu/full/1864AN.....61..225V
• J. J. Baeyer,
  Über die Berechnung sphäroidischer Dreiecke und den Lauf der geodätischen Linie [Geodesic triangles and the course of the geodesic], Astron. Nachr. 71(1699–1700), 289–314 (1868).
  http://adsabs.harvard.edu/full/1868AN.....71..289V
• J. Weingarten,
  Über die Oberflächen für welche einer der beiden Hauptkrümmungshalbmesser eine Function des anderen ist [Surfaces for which one of the two principal radii of curvature is a function of the other], Jour. Crelle 62, 160–173 (1863).
  http://books.google.com/books?id=ggRCAAAAcAAJ&pg=PA160
• J. Weingarten,
  Ueber die Reduction der Winkel eines sphäroidischen Dreiecks auf die eines ebenen oder sphärischen [Reducing the angles of a spheroidal triangle to those of a plane or spherical triangle], Astron. Nachr. 75(1782) 91–96 (1869).
  http://adsabs.harvard.edu/full/1869AN.....75...91W
• P. A. Hansen,
  Geodätische Untersuchungen [Geodetic investigations] (Hirzel, Leipzig, 1865), Sec. 1.
  http://books.google.com/books?id=WlsOAAAAYAAJ&pg=PA1
• E. B. Christoffel,
  Allgemeine Theorie der geodätischen Dreiecke [General theory of geodesic triangles], Math. Abhand. König. Akad. der Wiss. zu Berlin 8, 119–176 (1868).
  http://books.google.com/books?id=EEtFAAAAcAAJ&pg=PA119
• E. Beltrami,
  Risoluzione del Problema: Riportare i punti di una superficie sopra un piano in modo che le linee geodetiche vengano rappresentate da linee rette [Mapping a surface to a plane so that geodesics are represented by straight lines], Ann. Mat. Pura App. 7, 185–204 (1865).
  http://books.google.com/books?id=dfgEAAAAYAAJ&pg=PA185
• E. Beltrami,
  Sulla teoria delle linee geodetiche [On the theory of geodesic lines], Rendiconti del Reale Istituto Lombardo Ser. 2, 1, 708–718 (1868), in Opere matematiche di Eugenio Beltrami (Vol. 1, Hoepli, Milan, 1902), pp. 366–373.
  http://books.google.com/books?id=c48vHvLN--kC&pg=PA366
• A. Cayley,
  On the geodesic lines on an oblate spheroid, Phil. Mag. 40 (4th ser.), 329–340 (1870), in The Collected Mathematical Papers of Arthur Cayley, Vol. 7 (Cambridge Univ. Press, 1894), paper 422, pp. 15–25.
  http://books.google.com/books?id=Zk0wAAAAIAAJ&pg=PA329
  http://books.google.com/books?id=4XGIOoCMYYAC&pg=PA15
• A. R. Clarke,
  On the course of geodetic lines on the earth's surface, Phil. Mag. 39 (4th ser.), 352–363 (1870).
  http://books.google.com/books?id=i2swAAAAIAAJ&pg=PA352
• A. R. Clarke,
  Geodesy (Clarendon Press, Oxford, 1880), Chap. 6.
  http://books.google.com/books?id=lfIoAAAAYAAJ&pg=PA124
• F. Joachimsthal,
  Anwendung der Differential- und Integralrechnung auf die allgemeine Theorie der Flächen und der Linien doppelter Krümmung [Application of differential and integral calculus to the general theory of surfaces and lines of double curvature] (Teubner, Leipzig, 1872), Chap. 9, pp. 131–157.
  http://books.google.com/books?id=BvQoAAAAYAAJ&pg=PA131
• I. Todhunter,
  A history of the mathematical theories of attraction and the figure of the earth from the time of Newton to that of Laplace, 2 Vols. (Macmillan, 1873).
  http://books.google.com/books?id=6GMSAAAAIAAJ&pg=PR3
  http://books.google.com/books?id=xmMSAAAAIAAJ&pg=PP7
• F. J. van den Berg,
  Sur les écarts de la ligne géodésique et des sections planes normales entre deux points rapprochés d'une surface courbe [On the difference between geodesic lines and normal sections], Archives néerlandaises des sciences exactes et naturelles 12, 353–398 (1877).
  http://books.google.com/books?id=CycYAAAAYAAJ&pg=PA353
• C. Winterberg,
  Über die geodätische Linie: Bestimmung von Azimuth, Breite und Länge einer geodätische Linie auf dem Erdsphäroid als Function der Bogenlänge, wenn Breite und Azimuth des Anfangspunks gegeben sind [The direct geodesic problem], Astron. Nachr. 89(2119), 103–110; 89(2120), 113–128 (1877).
  http://adsabs.harvard.edu/full/1877AN.....89..103W
  http://adsabs.harvard.edu/full/1877AN.....89..113W
• C. Winterberg,
  Über die geodätische Linie: Bestimmung der Bogenlänge und der Azimuthe beider Endpuncte einer geodätische Linie in Function der Breiten und der Längendifferenz dieser Puncte [The inverse geodesic problem], Astron. Nachr. 91(2168), 113–120 (1878).
  http://adsabs.harvard.edu/full/1877AN.....91..113W
• C. Winterberg,
  Über die geodätische Linie: Dritte allgemeine Aufgabe. Auflösung der sphäroidischen Dreicke [Solution of geodesic triangles], Astron. Nachr. 95(2271), 223–228; 95(2272) 239–250; 95(2274) 271–280 (1879).
  http://adsabs.harvard.edu/full/1879AN.....95..223W
  http://adsabs.harvard.edu/full/1879AN.....95..239W
  http://adsabs.harvard.edu/full/1879AN.....95..271W
• A. v. Braunmühl,
  Ueber Enveloppen geodätischer Linien [The envelopes of geodesic lines], Math. Ann. 14, 557–566 (1879).
  http://books.google.com/books?id=CwgPAAAAIAAJ&pg=PA557
• A. v. Braunmühl,
  Geodätische Linien und ihre Enveloppen auf dreiaxigen Flächen zweiten Grades [Geodesic lines and their envelopes on three-dimensional surfaces of second order], Math. Ann. 20, 557–586 (1882).
  http://books.google.com/books?id=YQkPAAAAIAAJ&pg=PA557
• F. R. Helmert,
  Die geodätische Uebertragung geographischer Coordinaten [The geodesic applied to geographic coordinates], Astron. Nachr. 94(2252), 313–320 (1879).
  http://adsabs.harvard.edu/full/1879AN.....94..313H
• F. R. Helmert,
  Die Mathematischen und Physikalischen Theorieen der Höheren Geodäsie [Mathematical and Physical Theories of Higher Geodesy], Vol. 1 (Teubner, Leipzig, 1880), Chaps. 5–7.
  http://books.google.com/books?id=qt2CAAAAIAAJ&pg=PA212
  English translation: by Aeronautical Chart and Information Center (St. Louis, 1964).
  http://geographiclib.sf.net/geodesic-papers/helmert80-en.html
• M. Sadebeck,
  Hilfstafel für die Differenz zwischen dem sphäroidischen und dem sphärischen Längenunterschiede zweier Punkte auf der Erdoberfläche [Table of differences between the spheroidal and spherical longitude differences of two points on the Earth], Astron. Nachr. 95(2270), 209–220 (1879).
  http://adsabs.harvard.edu/full/1879AN.....95..207S
• C. T. Albrecht,
  Über die Umkehrung der Bessel'schen Methode der sphäroidischen Übertragung [Inverting Bessel's method for the spheroidal problem], Astron. Nachr. 96(2294), 209–218 (1880).
  http://adsabs.harvard.edu/full/1880AN.....96..209A
• C. T. Albrecht,
  Formeln und Hülfstafeln für geographische Ortsbestimmungen [Formulas and tables for geographic calculations] (3rd edition, Engelmann, Leipzig, 1894).
  http://books.google.com/books?id=muYRAAAAYAAJ
• J. H. L. Krüger,
  Die geodätische Linie des Sphäroids und Untersuchung darüber, wann dieselbe aufhört, kürzeste Linie zu sein [The geodesic line on a spheroid and an investigation on the properties when it ceases being the shortest path], Inaugural-Dissertation, Univ. Tübingen (Schade, Berlin, 1883).
  http://geographiclib.sf.net/geodesic-papers/krueger83.pdf
• J. H. L. Krüger,
  Konforme Abbildung des Erdellipsoids in der Ebene [Conformal mapping of the ellipsoidal earth to the plane], Royal Prussian Geodetic Institute, New Series 52, 172 pp. (1912), Secs. 24–40.
  http://dx.doi.org/10.2312/GFZ.b103-krueger28
• W. Jordan,
  Neue Auflösung der geodätischen Hauptaufgabe und ihrer Umkehrung [A new solution of the geodesic problem and its inverse], Z. f. Vermessungswesen 12(3), 65–82 (1883).
  http://books.google.com/books?id=QrBIAAAAMAAJ&pg=PA65
• W. Jordan,
  Handbuch der Vermessungskunde [Handbook of Surveying], Vol. 3 (4th edition, Metzler, Stuggart, 1896), Chaps. 6 & 9.
  http://books.google.com/books?id=4KgRAAAAYAAJ&pg=PA361
  http://books.google.com/books?id=4KgRAAAAYAAJ&pg=PA518
• C. H. Kummell,
  On the determination of the shortest distance between two points on a spheroid, Astron. Nachr. 112(2671), 97–108 (1885).
  http://books.google.com/books?id=kN4zAQAAIAAJ&pg=PA206
• J. Knoblauch,
  Einleitung in die allgemeine Theorie der krummen Flächen [Introduction to the general theory of curved surfaces] (Teubner, Leipzig, 1888), Secs. 53–59, pp. 137–159.
  http://books.google.com/books?id=zPdMAAAAMAAJ&pg=PA137
• O. Börsch,
  Geodätische Literatur [Geodetic Bibliography] (Internationale Erdmessung, 1889).
  http://books.google.com/books?id=AZUZAAAAMAAJ
• J. H. Gore,
  A bibliography of geodesy (US Coast and Geodetic Survey, 1889).
  http://books.google.com/books?id=K38hAAAAMAAJ
  1903 edition: http://www.archive.org/stream/bibliographyofge00gorerich#page/431
• J. H. Gore,
  Elements of geodesy (3rd edition, Wiley, 1893), Chap. 1.
  http://books.google.com/books?id=h-8ZAAAAYAAJ&pg=PA1
• J. G. Darboux,
  Leçons sur la théorie générale des surfaces [Lessons on the general theory of surfaces], Vol. 3 (Gauthier-Villars, 1894), Book 6.
  http://books.google.com/books?id=hGMSAAAAIAAJ&pg=PA1
• A. R. Forsyth,
  Geodesics on an oblate spheroid, Mess. Math. 25, 81–124 (1896); Conjugate points of geodesics on an oblate spheroid, Mess. Math. 25, 161–169 (1896).
  http://books.google.com/books?id=YsAKAAAAIAAJ&pg=PA81
  http://books.google.com/books?id=YsAKAAAAIAAJ&pg=PA161
  unreadable page: http://geographiclib.sf.net/geodesic-papers/forsyth96b-add.pdf
• R. Fricke,
  Kurzgefasste Vorlesungen über verschiedene Gebiete der höheren Mathematik mit Berücksichtigung der Anwendungen [Concise lectures on various areas of higher mathematics, with applications] (Teubner, Leipzig 1900), Chap. 5, Sec. 3, pp. 293–305.
  http://books.google.com/books?id=bSsLAAAAYAAJ&pg=PA293
• L. P. Eisenhart,
  A Treatise on the Differential Geometry of Curves and Surfaces (Ginn & Co., Boston, 1909).
  http://books.google.com/books?id=hkENAAAAYAAJ
• P. D. Thomas,
  Conformal Projections in Geodesy and Cartography, Spec. Pub. 251 (US Coast and Geodetic Survey, 1952), pp. 63–66.
  http://docs.lib.noaa.gov/rescue/cgs_specpubs/QB275U35no2511952.pdf
• P. D. Thomas,
  Mathematical Models for Navigation Systems, TR-182 (U.S. Naval Oceanographic Office, 1965).
  http://handle.dtic.mil/100.2/AD0627893
• P. D. Thomas,
  Spheroidal Geodesics, Reference Systems, and Local Geometry, SP-138 (U.S. Naval Oceanographic Office, 1970).
  http://handle.dtic.mil/100.2/AD703541
• G. V. Bagratuni,
  Kurs Sferoidicheskoi Geodezii (Moscow, 1962).
  English translation: Course in Spheroidal Geodesy, FTD-MT-64-390 (US Air Force, Feb. 1967).
  http://handle.dtic.mil/100.2/AD650520
  clean copy: http://geographiclib.sf.net/geodesic-papers/bagratuni67.pdf
• E. M. Sodano and T. A. Robinson,
  Direct and Inverse Solutions of Geodesics, Tech. Rep. 7 Rev. (Army Map Service, 1963).
  http://handle.dtic.mil/100.2/AD657591
  
• E. A. Lewis,
  Parametric Formulas for Geodesic Curves and Distances on a Slightly Oblate Earth, AFCRL-63-485 (US Air Force, Apr. 1963).
  http://handle.dtic.mil/100.2/AD0412501
  
• W. Köhnlein,
  Geodesics on an Equipotential Surface of Revolution, Special Report 144, Smithsonian Astrophysical Observatory (1964).
  http://adsabs.harvard.edu/full/1964SAOSR.144.....K
• T. Vincenty,
  Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations, Survey Review 23 (misprinted as 22) (176), 88–93 (1975); Addendum: Survey Review 23(180), 294 (1976).
  http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
• T. Vincenty,
  Geodetic inverse solution between antipodal points, unpublished report dated Aug. 28, 1975.
  http://geographiclib.sf.net/geodesic-papers/vincenty75b.pdf
• R. H. Rapp,
  Geometric geodesy, Part I, Ohio State Univ. (1991), Chap. 4.
  http://hdl.handle.net/1811/24333
• R. H. Rapp,
  Geometric geodesy, Part II, Ohio State Univ. (1993), Chap. 1.
  http://hdl.handle.net/1811/24409
• C. F. F. Karney,
  Geodesics on an ellipsoid of revolution (Feb. 2011).
  http://arxiv.org/abs/1102.1215
• C. F. F. Karney,
  Algorithms for geodesics (Sept. 2011).
  http://arxiv.org/abs/1109.4448