GeezerVison

A 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 some more recent works which are available online (chiefly works funded by the US Government). Where available, links to translations, especially into English, have been added. 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. In addition, readers may not have access to the full text of some Google Books; in those cases, I have provided a "pdf" link. See the files in geodesic-papers. Please let me, Charles Karney <[email protected]>, know of errors, omissions, etc. In particular, I'm interested to learn of any cases where I have mis-translated the title of a paper. In addition, the links to Google Books occasionally get out of date; let me know if this happens.

This bibliography was started on 2009-06-06 (at http://trac.osgeo.org/proj/wiki/GeodesicCalculations, now defunct) and moved to this site on 2011-02-01. The last update was on 2026-02-19.

• I. Newton,
  Philosophiae Naturalis Principia Mathematica (3rd edition, Roy. Soc., 1726), Book 3, Prop. 19, Prob. 3, pp. 412–416.
  https://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.
  https://books.google.com/books?id=KaAIAAAAIAAJ&pg=PA405
• J. Picard,
  Mesure de la Terre [Measuring the Earth] (1650).
  https://books.google.com/books?id=1COZ-ZexeWYC
• 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.
  https://books.google.com/books?id=TvJaAAAAQAAJ&pg=RA1-PA226
  https://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.
  https://books.google.com/books?id=Yw1bAAAAQAAJ&pg=PA108
  figures: https://geographiclib.sourceforge.io/geodesic-papers/bernoulli28-fig.pdf
• L. Godin,
  Méthode pratique de tracer sur terre un parallele par un degré de latitude donné [A practical method of drawing a given circle of latitude], Mém. de l'Acad. Roy. des Sciences de Paris, 223–232 (1733, publ. 1735).
  https://books.google.com/books?id=GOAEAAAAQAAJ&pg=PA223
• J. Cassini,
  De la carte de la France et de la perpendiculaire a la méridienne de Paris [The map of France and the perpendicular to the meridian of Paris], Mém. de l'Acad. Roy. des Sciences de Paris, 389–405 (1733, publ. 1735).
  https://books.google.com/books?id=GOAEAAAAQAAJ&pg=PA389
• A. C. Clairaut,
  Détermination géométrique 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).
  https://books.google.com/books?id=GOAEAAAAQAAJ&pg=PA406
  alt: https://gallica.bnf.fr/ark:/12148/bpt6k3530m/f566
• A. C. Clairaut,
  Suite d'un Mémoire donné en 1733, qui a pour titre: Détermination géométrique 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).
  https://books.google.com/books?id=5OAEAAAAQAAJ&pg=RA1-PA83
  alt: https://gallica.bnf.fr/ark:/12148/bpt6k3536g/f183
• A. C. Clairaut,
  Théorie de la Figure de la Terre Tirée des Principes de l'Hydrostatique [The Theory of the Figure of the Earth Drawn from Hydrostatic Principles] (Durand, Paris, 1743).
  https://books.google.com/books?id=X6wWAAAAQAAJ
• P. L. Maupertuis,
  La Figure de la Terre déterminée par les Observations de MM. de Maupertius, Calariaut, Camus, le Monnier, Outhier, et Celsius [The Figure of the Earth determined by the Observations of ...], (Paris, 1738).
  https://books.google.com/books?id=caCpNBzVBSYC
• P. L. Maupertuis, A. C. Clairaut, C. É. L. Camus, and P. C. le Monnier,
  Dégré du Méridien entre Paris et Amiens par la Mesure de M. Picard [The meridian degree between Paris and Amiens according to the method of J. Picard], (Paris, 1740).
  https://books.google.com/books?id=xCLrDACWLNEC
• 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).
  https://books.google.com/books?id=dA1bAAAAQAAJ
  alt: http://eulerarchive.maa.org/pages/E065.html
  figures: http://eulerarchive.maa.org/docs/originals/E065h pp. 15, 17, 19, 21, 23.
  German translation: by A. Aycock and A. Diener.
  http://eulerarchive.maa.org/docs/translations/E065de.pdf
• 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).
  https://books.google.com/books?id=QIIfAAAAYAAJ&pg=PA223
  figures: https://books.google.com/books?id=QIIfAAAAYAAJ&pg=PA361
  alt: http://eulerarchive.maa.org/pages/E214.html
  English translation: by G. W. Heine.
  http://eulerarchive.maa.org/docs/translations/E214en.pdf
  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.
  https://books.google.com/books?id=dPbhs0MSJOgC&pg=PA3 (pdf)
• 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).
  https://books.google.com/books?id=QIIfAAAAYAAJ&pg=PA258
  figures: https://books.google.com/books?id=QIIfAAAAYAAJ&pg=PA362-IA1
  alt: http://eulerarchive.maa.org/pages/E215.html
  Draft English translation: by G. Heine.
  http://eulerarchive.maa.org/docs/translations/E215en.pdf
• L. Euler,
  Recherches sur la courbure des surfaces [The curvature of surfaces], Mém. de l'Acad. Roy. des Sciences de Berlin 16, 119–143 (1760, publ. 1767).
  https://books.google.com/books?id=IanNh6WO1-AC&pg=PA119
  figures: http://eulerarchive.maa.org/pages/E333.html
  Partial English translation: by J. Lodder.
  http://eulerarchive.maa.org/docs/translations/E333.pdf
• 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.
  https://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).
  https://books.google.com/books?id=8uEEAAAAQAAJ&pg=RA1-PA75 (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.
  https://books.google.com/books?id=tnHOAAAAMAAJ&pg=PA3
  figures: https://geographiclib.sourceforge.io/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).
  https://books.google.com/books?id=ZO-DiSOtC0kC&pg=PA321 (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).
  https://books.google.com/books?id=yZH2VQBt4CkC&pg=PA100
• G. Monge,
  Des lignes de courbure de la surface de l'ellipsoïde [On the lines of curvature on the surface of the ellipsoid] (1796), in Application de l'Analyse à la Géometrie (5th edition, Bachelier, Paris, 1850), pp. 139–160.
  https://doi.org/10.3931/e-rara-57893
• 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.
  https://books.google.com/books?id=qZQAAAAAMAAJ&pg=RA1-PA127
  Early use of geodesic line in French:

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

  Translation with commentary: Celestial Mechanics by N. Bowditch, Vol. 2 (Boston, 1832), pp. 358–491.
  https://archive.org/details/mcaniquecles02laplrich
• 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).
  https://gallica.bnf.fr/ark:/12148/btv1b73003724
• J. B. J. Delambre and P. Méchain,
  Base du système métrique décimal, ou Mesure de l'arc du méridien compris entre les parralèles de Dunkerque et Barcelone [Basis of the metric system, or the measurement of the meridian arc between the parallels of Dunkirk and Barcelona] (Baudouin, Paris), Vol. 1 (1806), Vol. 2 (1807), Vol. 3 (1810).
  https://books.google.com/books?id=6DEVAAAAQAAJ
  https://books.google.com/books?id=4HVFAAAAcAAJ
  https://books.google.com/books?id=ZFpDAAAAcAAJ
• 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).
  https://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).
  https://books.google.com/books?id=EnVFAAAAcAAJ&pg=PA130
  Review: https://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.
  https://lillonum.univ-lille.fr/s/lillonum/ark:/72505/bjZbcq
• 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.
  https://gallica.bnf.fr/ark:/12148/bpt6k110147r
• N. Bowditch,
  The New American Practical Navigator (Newburyport, Mass., 1802).
  1802 edition: https://archive.org/details/newamericanpract00bowd
  1888 edition: https://archive.org/stream/practica00bowdamericanrich
  NGA editions: https://msi.nga.mil/Publications/APN
• J. G. Soldner,
  Über die kürzeste Linie auf dem Sphäroide [The shortest line on the spheroid], Monat. Corr. Zach 11, 7–23 (Gotha, 1805).
  https://books.google.com/books?id=454AAAAAMAAJ&pg=PA5
  Early use of geodesic line in German (noted by Jordan, Vol. 3, Chap. 6, Sec. 68, p. 374):

  Man weiss, dass die geodätisch gerade Linie LM die Eigenschaft hat, dass sie die kürzeste ist, die man zwischen den zwey Puncten L und M ziehen kann [We know that the geodesic straight line LM has the property that it is the shortest that can be drawn between the two points L and M].

• 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.
  https://geographiclib.sourceforge.io/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).
  https://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).
  https://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).
  https://books.google.com/books?id=SydFAAAAcAAJ&pg=PA118
  https://books.google.com/books?id=XSdFAAAAcAAJ&pg=PA1
  https://books.google.com/books?id=qaosAQAAMAAJ&pg=PA1
  https://books.google.com/books?id=6bsAAAAAYAAJ&pg=PA325
  Errata: https://books.google.com/books?id=6bsAAAAAYAAJ&pg=PA333
  Review: https://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).
  https://ui.adsabs.harvard.edu/abs/1826AN......4..461O
  https://doi.org/10.1002/asna.18260043201
• 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).
  https://books.google.com/books?id=02QEAAAAYAAJ&pg=RA1-PA3
  https://books.google.com/books?id=9GQEAAAAYAAJ&pg=RA1-PA3
  https://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.
  https://books.google.com/books?id=BtM2AAAAMAAJ&pg=PA115
  Early use of geodesic line in English:

  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.

• P. C. F. Dupin,
  Développements de géométrie [Developments in geometry] (Courcier, Paris, 1813), Part 5.
  https://gallica.bnf.fr/ark:/12148/bpt6k9734773w/f327
• E. G. F. Thune,
  Tentamen circa trigonometriam sphaeroidicam [Essay on spheroidal trigonometry] (Schultz, Copenhagen, 1815)
  https://geographiclib.sourceforge.io/geodesic-papers/thune15.pdf
  https://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.
  https://books.google.com/books?id=PZEAAAAAMAAJ&pg=PA212
  unreadable pages: https://geographiclib.sourceforge.io/geodesic-papers/puissant19b-add.pdf
  figures: https://geographiclib.sourceforge.io/geodesic-papers/puissant19b-fig.pdf
• L. Puissant,
  Moyen d'évaluer rigoureusement la longueur d'une ligne géodésique [The rigorous calculation of the length of a geodesic], Bull. Sci. Math. 2, 275–279 (1824).
  https://books.google.com/books?id=h5JfAAAAcAAJ&pg=PA275
• 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).
  https://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).
  https://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).
  https://books.google.com/books?id=KcjOAAAAMAAJ&pg=RA2-PA457
  errata: https://books.google.com/books?id=KcjOAAAAMAAJ&pg=PP11
• L. Puissant,
  Note sur un nouveau moyen d'abréger considérablement les calculs rélatifs à la rectification d'un arc de méridien [A new way to shorten the rectification of a meridian arc], Comptes Rendus 13, 53–55 (1841).
  https://gallica.bnf.fr/ark:/12148/bpt6k29723/f55
• J. J. Littrow,
  Theoretische und practishe Astronomie [Theoretical and Practical Astronomy], Vol. 1 (Vienna, 1821), Chap. 10.
  https://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.
  https://books.google.com/books?id=2S9NAAAAMAAJ&pg=PA80 (figures missing)
• F. W. Bessel,
  Über Berechnung geodätischer Vermessungen [Calculating geodesic surveys], Astron. Nachr. 1(3), 33–36 (1823).
  https://books.google.com/books?id=D58RAAAAYAAJ&pg=PA37
  https://doi.org/10.1002/asna.18230010302
• F. W. Bessel,
  Berechnung eines Dreiecks, dessen Seiten geodätischer Linien sind [Calculations of a geodesic triangle], Astron. Nachr. 1(6), 85–90 (1823).
  https://books.google.com/books?id=D58RAAAAYAAJ&pg=PA64
  https://doi.org/10.1002/asna.18230010603
• F. W. Bessel,
  Über 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).
  https://ui.adsabs.harvard.edu/abs/1825AN......4..241B
  https://doi.org/10.1002/asna.18260041601
  With corrections: https://arxiv.org/abs/0908.1823
  Partial English translation: Calculation of geographical longitudes and latitudes on a spheroid, Quart. Jour. Roy. Inst. 21(41), 138–152 (1826).
  https://books.google.com/books?id=ei1GAAAAcAAJ&pg=PA138
  Modern English translation: by C. F. F. Karney and R. E. Deakin, Astron. Nachr. 331(8), 852–861 (2010).
  https://doi.org/10.1002/asna.201011352
  preprint: https://arxiv.org/abs/0908.1824
• F. W. Bessel,
  Über 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).
  https://ui.adsabs.harvard.edu/abs/1837AN.....14..269B
  https://doi.org/10.1002/asna.18370141901
• F. W. Bessel,
  Bestimmung der Axen des elliptischen Rotationssphäroids, welches den vorhandenen Messungen von Meridianbögen der Erde am meisten entspricht [Estimation of the axes of the ellipsoid through measurements of the meridian arc], Astron. Nachr. 14(333), 333–346 (1837).
  https://ui.adsabs.harvard.edu/abs/1837AN.....14..333B
  https://doi.org/10.1002/asna.18370142301
• F. W. Bessel,
  Über einen Fehler in der Berechnung der französischen Gradmessung und seinen Einfluß auf die Bestimmung der Figur der Erde [Concerning an error in the calculation of the French survey and its influence on the determination of the figure of the Earth], Astron. Nachr. 19(438), 97–116 (1841).
  https://ui.adsabs.harvard.edu/abs/1841AN.....19...97B
  https://doi.org/10.1002/asna.18420190702
• F. W. Bessel and J. J. Baeyer,
  Gradmessung in Ostpreussen und ihre Verbindung mit Preussischen und Russischen Dreiecksketten [The East Prussian Survey and its connection with the Prussian and Russian networks], (Dümmler, Berlin, 1838).
  https://books.google.com/books?id=3wg_AAAAcAAJ
• F. W. Bessel,
  Abhandlungen von Friedrich Wilhelm Bessel [The Works of Bessel], Vol. 3 (W. Engelmann, Leipzig, 1876), Part 6 contains the previous 6 papers.
  https://books.google.com/books?id=vX4EAAAAYAAJ&pg=RA1-PR6 (pdf)
• J. Ivory,
  A new series for the rectification of the ellipsis, Trans. Roy. Soc. Edinburgh 4(2), 177–190 (1798).
  https://books.google.com/books?id=FaUaqZZYYPAC&pg=PA177
  https://doi.org/10.1017/S0080456800030817
• J. Ivory,
  Solution of a geodetical problem, Phil. Mag. 64(315), 35–39 (1824).
  https://books.google.com/books?id=xk0wAAAAIAAJ&pg=PA35
  https://doi.org/10.1080/14786442408644549
  Errata: Phil. Mag. 65(324), 249–250 (1825).
  https://books.google.com/books?id=_UwwAAAAIAAJ&pg=PA249
  https://doi.org/10.1080/14786442508628431
• 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 & 67(337), 340–352 (1826).
  https://books.google.com/books?id=PkwwAAAAIAAJ&pg=PA241
  https://books.google.com/books?id=PkwwAAAAIAAJ&pg=PA340
  https://doi.org/10.1080/14786442608674051
  https://doi.org/10.1080/14786442608674069
  Mr. Ivory's mode of finding the length of the geodetic curve, Quart. Jour. Roy. Inst. 21(42), 361–363 (1826).
  https://books.google.com/books?id=ei1GAAAAcAAJ&pg=PA361
  F. W. Bessel, Über einen Aufsatz von Ivory im Philosophical Magazine [Comments on a paper by Ivory in the Philosophical Magazine], Astron. Nachr. 5(108), 177–180 (1927).
  https://ui.adsabs.harvard.edu/abs/1826AN......5..177B
  https://doi.org/10.1002/asna.18270051202
• 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 (2nd ser.), 30–34 & 114–117 (misprinted as 134–137) (1830).
  https://books.google.com/books?id=j4EqAAAAYAAJ&pg=PA30
  https://books.google.com/books?id=j4EqAAAAYAAJ&pg=PA114
  https://doi.org/10.1080/14786443008675355
  https://doi.org/10.1080/14786443008675378
• F. T. Poselger,
  Anleitung zu Rechnungen der Geodäsie [Guide to the Calculations of Geodesy] (Dümmler, Berlin, 1831), Chap. 4.
  https://books.google.com/books?id=OVkOAAAAYAAJ&pg=PA39
• C. F. Gauss,
  Allgemeine Auflösung der Aufgabe: die Theile einer gegebnen Fläche auf einer andern gegebnen Fläche so abzubilden, daß die Abbildung dem Abgebildeten in den kleinsten Theilen ähnlich wird [The general solution of the problem of mapping one surface to another so that small shapes are preserved], Schumacher's Astron. Abhandlungen 3, 1–30 (Altona, 1825) Reprint: edited by A. Wangerin, Ostwald's Klass. ex. Wiss., No. 55 (Engelmann, Leipzig, 1894).
  https://books.google.com/books?id=odTPAAAAMAAJ&pg=RA2-PA1
  https://books.google.com/books?id=O4AOAAAAYAAJ&pg=PA57 (pdf)
• C. F. Gauss,
  Conforme Abbildung des Sphäroids in der Ebene (Projectionsmethode der Hannoverschen Landesvermessung) [Conformal mapping of the spheroid to the plane (The projection for the survey of Hannover)], König. Ges. Wiss., Göttingen (1828), in Carl Friedrich Gauss Werke, Vol. 9 (Ges. Wiss., Göttingen, 1903), pp. 142–194.
  https://books.google.com/books?id=ICwPAAAAIAAJ&pg=PA141 (pdf)
  Remarks by Krüger: https://books.google.com/books?id=ICwPAAAAIAAJ&pg=PA195
  Letters to Schumacher: https://books.google.com/books?id=ICwPAAAAIAAJ&pg=PA205
• C. F. Gauss,
  Disquisitiones generales circa superficies curvas (Dieterich, Göttingen, 1828).
  https://books.google.com/books?id=bX0AAAAAMAAJ&pg=PA3
  In Carl Friedrich Gauss Werke, Vol. 4 (Ges. Wiss., Göttingen, 1873), pp. 217–258.
  https://gdz.sub.uni-goettingen.de/id/PPN236005081?tify={"pages":[221]}
  French translation: Recherches générales sur les surfaces courbes, by E. Roger (Grenoble, 1855).
  https://books.google.com/books?id=PxcOAAAAQAAJ
  German translation: Allgemeine Flächentheorie, by A. Wangerin, Ostwald's Klass. ex. Wiss., No. 5 (Engelmann, Leipzig, 1889).
  https://books.google.com/books?id=W2UEAAAAYAAJ (pdf)
  English translation: General Investigations of Curved Surfaces of 1827 and 1825, by J. C. Morehead and A. M. Hiltebeitel (Princeton Univ. Lib., 1902).
  https://www.gutenberg.org/files/36856/36856-pdf.pdf
• 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).
  https://gdz.sub.uni-goettingen.de/id/PPN236005081?tify={"pages":[263]}
  https://gdz.sub.uni-goettingen.de/id/PPN236005081?tify={"pages":[305]}
  https://geographiclib.sourceforge.io/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.
  https://books.google.com/books?id=ICwPAAAAIAAJ&pg=PA65 (pdf)
  alt: https://gdz.sub.uni-goettingen.de/id/PPN23601515X?tify={"pages":[71]}
• A. Galle,
  Über die geodätischen Arbeiten von Gauss [The Geodetic Works of Gauss], in Carl Friedrich Gauss Werke, Vol. 11 (Ges. Wiss., Göttingen, 1924), Part 2, 1–161.
  https://gdz.sub.uni-goettingen.de/id/PPN236059505?tify={"pages":[7]}
• C. G. J. Jacobi,
  Fundamenta nova theoriae functionum ellipticarum [A Fundamental New Theory of Elliptic Functions] (Borntraeger, Könisberg, 1829).
  https://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).
  https://books.google.com/books?id=2qrxAAAAMAAJ&pg=PA344
  https://doi.org/10.1515/crll.1837.16.344
• C. G. J. Jacobi,
  Zur Theorie der Variations Rechnung und der Differential Gleichungen [The theory of the calculus of variations and of differential equations], Jour. Crelle 17, 68–82 (1837).
  https://books.google.com/books?id=FKvxAAAAMAAJ&pg=PA68
  https://doi.org/10.1515/crll.1837.17.68
• 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).
  https://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002141973
  https://doi.org/10.1515/crll.1839.19.309
  French translation: Jour. Liouville 6, 267–272 (1841).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1841_1_6_A20_0.pdf
  Letter to Bessel, Dec. 28, 1838: https://books.google.com/books?id=_09tAAAAMAAJ&pg=PA385 (pdf)
  Announcement: Comptes Rendus 8, 284 (1839).
  https://gallica.bnf.fr/ark:/12148/bpt6k2967c/f290
• C. G. J. Jacobi,
  Bestimmungen der geodätischen Linie auf einem dreiaxiges Ellipsoid [Determining geodesics on a triaxial ellipsoid], König. Preuss. Ak. d. Wiss. Berlin 8, 351–355 (1846).
  https://books.google.com/books?id=ZipJAAAAcAAJ&pg=PA351
• 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).
  https://ui.adsabs.harvard.edu/abs/1855AN.....41..209J
  https://ui.adsabs.harvard.edu/abs/1856AN.....42..337J
  https://doi.org/10.1002/asna.18550411401
  https://doi.org/10.1002/asna.18550422201
  also in Jour. Crelle 53, 335–365 (1857).
  https://books.google.com/books?id=vc0GAAAAYAAJ&pg=PA335
  https://doi.org/10.1515/crll.1857.53.335
• C. G. J. Jacobi,
  Vorlesungen über Dynamik [Lectures on Dynamics], edited by A. Clebsch (Reimer, Berlin, 1866), Secs. 6 & 26–28.
  https://books.google.com/books?id=ryEOAAAAQAAJ&pg=PA43
  https://books.google.com/books?id=ryEOAAAAQAAJ&pg=PA198
  English translation: by K. Balagangadharan (Hindustan Book Agency, 2009)
  https://www.worldcat.org/oclc/440645889
  https://books.google.com/books?id=s9o0QwAACAAJ
  Errata: https://geographiclib.sourceforge.io/jacobi-errata.html
• 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.
  https://books.google.com/books?id=_09tAAAAMAAJ&pg=PA72 (pdf)
• F. Minding,
  Über die Curven des kürzesten Perimeters auf krummen Flächen [Curves of minimum perimeter on curved surfaces], Jour. Crelle 5, 297–304 (1830).
  https://books.google.com/books?id=Y6wGAAAAYAAJ&pg=PA297
  https://doi.org/10.1515/crll.1830.5.297
• F. Minding,
  Beiträge zur Theorie der kürzesten Linien auf krummen Flächen [Contributions to the theory of shortest lines on curved surfaces], Jour. Crelle 20, 323–327 (1840).
  https://books.google.com/books?id=bLwGAAAAYAAJ&pg=PA323
  https://doi.org/10.1515/crll.1840.20.323
• 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).
  https://books.google.com/books?id=85HxAAAAMAAJ&pg=PA279 (pdf)
  https://doi.org/10.1515/crll.1879.86.279
• F. J. Joachimsthal,
  Observationes de lineis brevissimis et curvis curvaturae in superficiebus secundi gradus [Observations on the shortest lines on curved surfaces of the second degree], Jour. Crelle 26, 155–171 (1843).
  https://books.google.com/books?id=8ptGAAAAcAAJ&pg=PA155
  https://doi.org/10.1515/crll.1843.26.155
• F. J. 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.
  https://books.google.com/books?id=BvQoAAAAYAAJ&pg=PA131
• P.Q.R. (W. Thomson, Lord Kelvin),
  Elementary demonstration of Dupin's theorem, Camb. Math. Jour. 4(20), 62–64 (1844).
  https://gdz.sub.uni-goettingen.de/id/PPN600493016_0004?tify={"pages":[70]}
• J. Liouville,
  De la ligne géodésique sur un ellipsoïde quelconque [The geodesic on an arbitrary ellipsoid], Jour. Liouville 9, 401–408 (1844).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1844_1_9_A37_0.pdf
• J. Liouville,
  Démonstration géométrique relative à l'équation des lignes géodésiques sur les surfaces du second degré [Geometrical demonstration of the equation for geodesic lines on the surfaces of the second degree], Jour. Liouville 11, 21–24 (1846).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1846_1_11_A3_0.pdf
• J. Liouville,
  Sur quelques cas particuliers où les équations du mouvement d'un point matériel peuvent s'intégrer [Special cases where the equations of motion are integrable], Jour. Liouville 11, 345–378 (1846).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1846_1_11_A45_0.pdf
• J. Liouville,
  Notes on G. Monge, Application de l'Analyse à la Géometrie (5th edition, Bachelier, Paris, 1850), pp. 547–600.
  https://books.google.com/books?id=Nf5zhlffjd0C&pg=PA547
• J. Liouville,
  Sur la théorie générale des surfaces [On the general theory of surfaces], Jour. Liouville 16, 130–132 (1851).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1851_1_16_A4_0.pdf
• M. Roberts,
  Géométrie, Communication verbale de M. Liouville [Geometry, Verbal communication of J. Liouville], Comptes Rendus 21, 1410–1411 (1845).
  https://gallica.bnf.fr/ark:/12148/bpt6k64491361/f20
• 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://sites.mathdoc.fr/JMPA/PDF/JMPA_1846_1_11_A1_0.pdf
• M. Roberts,
  On the lines of curvature of the surface of an ellipsoid, Proc. Roy. Irish Acad. 3, 383–385 (1847).
  https://www.jstor.org/stable/20489620
• M. Roberts,
  Nouvelles propriétés des lignes géodésiques et des lignes de courbure sur l'ellipsoïde [New properties of geodesics and lines of curvature on an allispoid], Jour. Liouville 13, 1–11 (1848).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1848_1_13_A1_0.pdf
• M. Roberts,
  Theorems on the lines of curvature of an ellipsoid, Camb. Dublin Math. Jour. 3, 159–163 (1848).
  https://gdz.sub.uni-goettingen.de/id/PPN600493962_0003?tify={"pages":[185]}
• M. Roberts,
  Mémoire sur la géométrie de courbes tracées sur la surface d'un ellipsoïde [The geometry of curves on the surface of an ellipsoid], Jour. Liouville 15, 275–295 (1850).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1850_1_15_A16_0.pdf
• M. Roberts,
  Sur quelques applications de la théorie des surfaces [Some applications of the theory of surfaces], Nouvelles Annales de Mathématiques 14, 268–271 (1855).
  http://www.numdam.org/item/NAM_1855_1_14__268_1.pdf
• M. Chasles,
  Sur les lignes géodésiques et les lignes de courbure des surfaces du second degré [Geodesic lines and the lines of curvature of the surfaces of the second degree], Jour. Liouville 11, 5–20 (1846).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1846_1_11_A2_0.pdf
• M. Chasles,
  Nouvelles démonstrations des deux équations relatives aux tangentes communes à deux surfaces du second degré homofocales; Et propriétés des lignes géodésiques et des lignes de courbure de ces surfaces [New demonstration of two equations for the common tangents to two confocal surfaces of the second degree; and properties of the geodesic lines and the lines of curvature of these surfaces], Jour. Liouville 11, 105–119 (1846).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1846_1_11_A14_0.pdf
• L. Schläfli,
  Bemerkungen über confocale Flächen zweiten Grades und die geodätische Linie auf dem Ellipsoid [Confocal surfaces of the second degree and the geodesic line on the ellipsoid], Mittheilungen Nat. Gesell. Bern 99–100, 97–101 (1847).
  https://books.google.com/books?id=mq8AAAAAYAAJ&pg=PA97
• 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).
  https://books.google.com/books?id=VGo_AAAAcAAJ&pg=PA1
• P. O. Bonnet,
  Sur quelques propriétés des lignes géodésiques [Some properties for geodesic lines], Comptes Rendus 40, 1311–1313 (1855).
  https://gallica.bnf.fr/ark:/12148/bpt6k29976/f1308
• P. O. Bonnet,
  [Note sur la courbure géodésique [A note on geodesic curvature], Comptes Rendus 42, 1137–1139 (1856).
  https://gallica.bnf.fr/ark:/12148/bpt6k2999t/f1135
• P. O. Bonnet,
  Démonstration du théorème de Gauss relatif aux petits triangles géodésiques situés sur une surface courbe quelconque [Demomstration of Gauss' theorem on small geodesic triangles for arbitrary surfaces], Comptes Rendus 58, 183–188 (1864).
  https://gallica.bnf.fr/ark:/12148/bpt6k3015d/f185
• J. Bertrand,
  Démonstration géométrique de quelques théorèmes relatifs à la théorie des surfaces [Geometric proof of some theorems for surfaces], Jour. Liouville 13, 78–79 (1848).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1848_1_13_A11_0.pdf
• J. Bertrand,
  Démonstration d'un théorème de M. Gauss [Proof of a theorem of C. F. Gauss], Jour. Liouville 13, 80–82 (1848).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1848_1_13_A11_0.pdf
• C.-F. Diguet,
  Note à l'occasion de l'article précédent [Note on the preceding article], Jour. Liouville 13, 83–86 (1848).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1848_1_13_A12_0.pdf
• A. S. Hart,
  On the form of geodesic lines through the umbilic of an ellipsoid, Proc. Roy. Irish Acad. 4, 274 (1849).
  https://www.jstor.org/stable/20520288
• A. S. Hart,
  Geometrical demonstration of some properties of geodesic lines, Camb. Dublin Math. Jour. 4, 80–84 (1849).
  https://gdz.sub.uni-goettingen.de/id/PPN600493962_0004?tify={"pages":[84]}
• A. S. Hart,
  On geodesics lines traced on a surface of the second degree, Camb. Dublin Math. Jour. 4, 192–194 (1849).
  https://gdz.sub.uni-goettingen.de/id/PPN600493962_0004?tify={"pages":[196]}
• C. Graves,
  On geodetic lines in surfaces of the second order, Proc. Roy. Irish Acad. 4, 283–287 (1850).
  https://www.jstor.org/stable/20520292
• C. Graves,
  Elementary geometrical proof of Joachimsthal's theorem, Jour. Crelle 42, 279 (1851).
  https://books.google.com/books?id=gKBGAAAAcAAJ&pg=PA279
  https://doi.org/10.1515/crll.1851.42.279
• G. Piobert,
  De la forma mejor que conviene dar á los triángulos geodésicos [The most convenient form for geodesic triangles], Revista Cien. Fís. Madrid 1, 373–380 (1850).
  https://books.google.com/books?id=nMXOAAAAMAAJ&pg=PA373
• G. Piobert,
  Sur la rectification des angles dans le calcul des triangles géodésiques [Rectifying angles in the solution of geodesic triangles], Comptes Rendus 31, 409–418 (1850).
  https://gallica.bnf.fr/ark:/12148/bpt6k29887/f409
• A. R. Clarke,
  On the measurement of azimuths on a spheroid, Mem. Roy. Astron. Soc. 20, 131–136 (1851).
  https://books.google.com/books?id=8GtaAAAAYAAJ&pg=RA1-PA131
• A. R. Clarke,
  On the course of geodetic lines on the earth's surface, Phil. Mag. 39 (4th ser.), 352–363 (1870).
  https://books.google.com/books?id=i2swAAAAIAAJ&pg=PA352
  https://doi.org/10.1080/14786447008640325
• A. R. Clarke,
  Geodesy (Clarendon Press, Oxford, 1880), Chap. 6.
  https://books.google.com/books?id=lfIoAAAAYAAJ&pg=PA124 (pdf)
• B. Tortolini,
  Sulla determinazione della linea geodesica descritta sulla superficie di un'ellissoide a tre assi ineguali [The determination of geodesics on the surface of a triaxial ellipsoid], Accad. d. Lincei 4, 287-324 (1851).
  https://books.google.com/books?id=Ht8cAQAAMAAJ&pg=PA287
  https://books.google.com/books?id=FICcJDc809AC
• B. Tortolini,
  Sulla espressione dei raggi delle due curvature di una linea geodesica tracciata sulla superficie di un'ellissoide [The two radii of curvaturefor a geodesic line drawn on the surface of an ellipsoid], Ann. Sci. Mat. Fis. 2, 345–357 (1851).
  https://books.google.com/books?id=xZkfAQAAIAAJ&pg=PA345
• C. Gudermann,
  Fundamenta trigonometriae sphaeroïdicae exacta; imprimis de lineis brevissimis, vulgo dictis geodaeticis, in superficie sphaeroïdica [Foundations of exact spheroidal trigonometry, in particular, concerning geodesic lines on a spheroidal surface], Jour. Crelle 43, 294–339 (1852).
  https://books.google.com/books?id=ygVCAAAAcAAJ&pg=PA294
  https://doi.org/10.1515/crll.1852.43.294
• A. Terrero,
  Memoria sobre la forma mas conveniente de los triángulos geodésicos [A convenient treatment of geodesic triaganles], Mem. Real Acad. Cien. Madrid 1(1), 77–84 (1853).
  https://books.google.com/books?id=RUGcoYhxhoUC&pg=PA77
• F. Brioschi,
  Sulla integrazione della equaziono delle linea geodetiche [On the integration of the equation for geodesics], Ann. Sci Mat. Fis. 4, 133-135 (1853).
  https://books.google.com/books?id=iRhm-BQ9YEoC&pg=PA133
• F. Brioschi,
  Intorno al movimento di un punto materiale sopra una superficie qualsivoglia [The movement of a material point on any surface], Mem. Mat. Fis. Modena '25(2)',155–167 (1860).
  https://books.google.com/books?id=VaYgAQAAMAAJ&pg=PA155
• W. Roberts,
  Sur une ligne géodésique de l'ellipsoïde [The geodesic line of the ellipsoid], J. Math. Pures Appl. (Ser. 2) 2, 213–216 (1857).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1857_2_2_A18_0.pdf
• H. Molins,
  Sur les lignes de courbure et les lignes géodésiques des surfaces développables dont les génératrices sont parallèles a celles d'une surface réglée quelconque [The lines of curvature and geodesic lines on developable surfaces whose generatrices are parallel to those of an ruled surface], Jour. Liouville 4, 347–365 (1859).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1859_2_4_A31_0.pdf
• H. Molins,
  Sur les lignes gèodésiques tracées sur une surface développable donnée [Geodesics on a given developable surface], Mém. de l'Acad. Toulouse (Ser. 5) 5, 401–412 (1861).
  https://books.google.com/books?id=5mkmAQAAIAAJ&pg=PA401
• O. Böklen,
  Über die geodätischen Linien auf dem Ellipsoid [Geodesics on the ellipsoid], Arch. d. Math. Phys. 35, 101–103 (1860).
  https://books.google.com/books?id=rJ9EAAAAcAAJ&pg=PA101
• O. Böklen,
  Zur Theorie der geodätischen Linien [The theory of geodesics], Arch. d. Math. Phys. 39, 189–198 (1862).
  https://books.google.com/books?id=_6AbAQAAMAAJ&pg=PA189
• O. Böklen,
  Über geodätischen Linien [Geodesic lines], Z. Math. Phys. 26, 254–269 (1881).
  https://books.google.com/books?id=X9g4AAAAIAAJ&pg=PA264 (pdf)
• L. Aoust,
  Sur une forme de l'équation de la ligne géodésique ellipsoïdale et de ses usages pour trouver les propriétés communes aux lignes ellipsoïdales et à des courbes planes correspondantes [A form of the equation for ellipsoidal geodesics and its use to determine the properties common to ellipsoidal lines and the corresponding plane curves], Comptes Rendus 50, 484–489 (1860).
  https://gallica.bnf.fr/ark:/12148/bpt6k3007r/f488
• K. T. W. Weierstrass,
  Über die geodätischen Linien auf dem dreiaxigen Ellipsoid [Geodesic lines on a triaxial ellipsoid], Monat. König. Akad. Wiss. 986–997 (Berlin, 1861), in Mathematische Werke, Vol. 1 (Berlin, 1894), pp. 257–266.
  https://books.google.com/books?id=9O4GAAAAYAAJ&pg=PA257 (pdf)
• O. Staude,
  Über geodätische Bogenstücke von algebraischer Längendifferenz auf dem Ellipsoid [Geodesic arcs of algebraic longitude difference on the ellipsoid], Math. Ann. 20(2), 185–186 (1862).
  https://gdz.sub.uni-goettingen.de/id/PPN235181684_0020?tify={"pages":[199]}
  https://doi.org/10.1007/BF01446520
• A. Allégret,
  Essai sur le Calcul des Quaternions de M. W. Hamilton [Essay on Hamilton's Quaternions]] (Leiber, Paris, 1862), Sec. 3.
  https://books.google.com/books?id=rYEYtcwcIJoC&pg=PT12
• A. Allégret,
  Mémoire sur la flexion des lignes géodésiques tracées sur une même surface quelconque [The bending of geodesics on an arbitrary surface], Comptes Rendus 66, 342–344 (1868).
  https://gallica.bnf.fr/ark:/12148/bpt6k30232/f344
• P. A. Gordan,
  De linea geodetica [On geodesic lines] (Berolini, 1862).
  https://gdz.sub.uni-goettingen.de/id/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.
  https://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).
  https://ui.adsabs.harvard.edu/abs/1864AN.....61..225V
  https://doi.org/10.1002/asna.18640611502
• 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).
  https://ui.adsabs.harvard.edu/abs/1868AN.....71..289V
  https://doi.org/10.1002/asna.18680711902
• 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).
  https://books.google.com/books?id=ggRCAAAAcAAJ&pg=PA160
  https://doi.org/10.1515/crll.1863.62.160
• J. Weingarten,
  Über 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).
  https://ui.adsabs.harvard.edu/abs/1869AN.....75...91W
  https://doi.org/10.1002/asna.18690750604
• P. A. Hansen,
  Geodätische Untersuchungen [Geodetic investigations] (Hirzel, Leipzig, 1865), Sec. 1.
  https://books.google.com/books?id=WlsOAAAAYAAJ&pg=PA1
• C. A. H. Bachoven von Echt,
  Die Kürzeste auf dem Erdsphäroid nebst den Hauptaufgaben der Geodäsie in neuer Darstellung [Shortest lines on the spheroid together with the geodesic problems in a new representation], (Istwann, Coesfeld, 1865).
  https://books.google.com/books?id=l35aAAAAcAAJ
  https://sammlungen.ulb.uni-muenster.de/hd/content/titleinfo/1012467
• B. Price,
  A Treatise on Infinitesimal Calculus, Vol. 2 (2nd edition, Oxford, 1865), Chap. 14, Sec. 2.
  https://books.google.com/books?id=fho1AAAAIAAJ&pg=PA475
• G. Salmon,
  A Treatise on the Analytic Geometry of Three Dimensions (2nd Edition, Dublin, 1865), Chap. 12, Sec. 4.
  https://books.google.com/books?id=Y54LAAAAYAAJ&pg=PA305
• 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).
  https://books.google.com/books?id=dfgEAAAAYAAJ&pg=PA185
  https://doi.org/10.1007/BF03198517
• 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.
  https://books.google.com/books?id=c48vHvLN--kC&pg=PA366 (pdf)
• F. Faà de Bruno,
  Démonstration élémentaire du théorème fondamental des lignes géodésiques [Elementary demonstration of the fundamental theorem of geodesics], Les Mondes 8, 739–740 (1865).
  https://books.google.com/books?id=nf4CAAAAYAAJ&pg=PA739
• O. Schreiber,
  Theorie der Projectionsmethode der Hannoverschen Landesvermessung [Theory of the projection for the survey of Hannover] (Hahn, 1866).
  https://books.google.com/books?id=rIQ_AAAAcAAJ
• A. F. J. Yvon Villarceau,
  De la limite des erreurs que l'on peut commettre en appliquant la théorie des lignes géodésiques aux observations des angles des triangles [A limit on the errors applying the theory of geodesic lines to triangulation], Comptes Rendus 62, 850–851 (1866).
  https://gallica.bnf.fr/ark:/12148/bpt6k3019n/f850
• 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).
  https://books.google.com/books?id=EEtFAAAAcAAJ&pg=PA119
• U. Dini,
  Sopra un problema che si presenta nella teoria generale delle rappresentazioni geografiche di una superficie su di un altra [The general theory of mapping one geographical surface to another], Ann. Mat. Pura App. 3 (2nd ser.), 269–293 (1869).
  https://books.google.com/books?id=FvkEAAAAYAAJ&pg=PA269
  https://doi.org/10.1007/BF02422982
• 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.
  https://books.google.com/books?id=Zk0wAAAAIAAJ&pg=PA329
  https://books.google.com/books?id=4XGIOoCMYYAC&pg=PA15 (pdf)
  https://doi.org/10.1080/14786447008640411
• A. Cayley,
  Note on the geodesic lines on an ellipsoid, Phil. Mag. 41 (4th ser.), 534–535 (1871), in The Collected Mathematical Papers of Arthur Cayley, Vol. 7 (Cambridge Univ. Press, 1894), paper 425, pp. 34–35.
  https://books.google.com/books?id=oHUvAQAAIAAJ&pg=PA534
  https://books.google.com/books?id=4XGIOoCMYYAC&pg=PA34 (pdf)
  https://doi.org/10.1080/14786447108640519
• A. Cayley,
  On the geodesic lines on an ellipsoid, Mem. Roy. Astron. Soc. 39, 31–53 & plate 2 (1872), in The Collected Mathematical Papers of Arthur Cayley, Vol. 7 (Cambridge Univ. Press, 1894), paper 478, pp. 493–510.
  https://rcin.org.pl/dlibra/publication/178304/edition/148111
  https://books.google.com/books?id=S4znAAAAMAAJ&pg=PA31 (pdf)
  https://books.google.com/books?id=4XGIOoCMYYAC&pg=PA493 (pdf)
• A. Cayley,
  On geodesic lines, in particular those of a quadric surface, Proc. London Math. Soc. 4, 191–211 & 368–380 (1871–1873), in The Collected Mathematical Papers of Arthur Cayley, Vol. 8 (Cambridge Univ. Press, 1895), papers 508 & 511, pp. 156–178 & 188–199.
  https://books.google.com/books?id=4gWd3fZi4zIC&pg=PA156 (pdf)
  https://books.google.com/books?id=4gWd3fZi4zIC&pg=PA188
  https://doi.org/10.1112/plms/s1-4.1.191
  https://doi.org/10.1112/plms/s1-4.1.368
• 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).
  https://books.google.com/books?id=6GMSAAAAIAAJ&pg=PR3 (pdf)
  https://books.google.com/books?id=xmMSAAAAIAAJ&pg=PP7 (pdf)
• I. Todhunter,
  Spherical Trigonometry, for the use of Colleges and Schools, (5th edition, Macmillan, 1886).
  https://books.google.com/books?id=aVgNAQAAMAAJ (pdf)
  retypeset: https://www.gutenberg.org/ebooks/19770
• H. Levret,
  Détermination des positions géographiques sur un ellipsoïde quelconque [Determinations of geographic positions on an arbitrary ellipsoid], Comptes Rendus 76, 410–413 (1873).
  https://gallica.bnf.fr/ark:/12148/bpt6k3033b/f410
• H. M. Jeffery,
  On the duals of geodesics and lines of curvature on an ellipsoid and on its pedal surfaces, Quart. J. Pure and Appl. Math. 12, 322–345 (1873).
  https://books.google.com/books?id=ink_AQAAIAAJ&pg=PA322
• C. Trepied,
  Sur le calcul des coordonnées géodésiques [On the calculation of geodesic coordinates], Comptes Rendus 80, 36–40 (1875).
  https://gallica.bnf.fr/ark:/12148/bpt6k3037k/f36
• F. R. Helmert,
  Einfache Ableitung Gaussischen Formeln für die Auflösung einer Hauptaufgabe der sphärischen Geodäsie [A simple derivation of the Gaussian formulas for the solving a principal problem in spherical geodesy], Z. f. Vermess. 4, 153–156 (1875).
  https://books.google.com/books?id=wpJIAAAAMAAJ&pg=153 (pdf)
• F. R. Helmert,
  Einfache Ableitung eines bekannten Satzes für die Krümmung des Rotationsellipsoids [A simple derivation of the known formula for the curvature of an ellipsoid of revolution], Z. f. Vermess. 6(1), 26–28 (1877).
  https://books.google.com/books?id=WKxIAAAAMAAJ&pg=PA26 (pdf)
• F. R. Helmert,
  Die geodätische Übertragung geographischer Coordinaten [The geodesic applied to geographic coordinates], Astron. Nachr. 94(2252), 313–320 (1879).
  https://ui.adsabs.harvard.edu/abs/1879AN.....94..313H
  https://doi.org/10.1002/asna.18790942003
• F. R. Helmert,
  Nochmals der Fundamentalsatz für die geodätische Linie auf Umdrehungsflächen [Revisiting the fundamental theorem for the geodesic line on surfaces of revolution], Z. f. Vermess. 9(8), 338–339 (1880).
  https://books.google.com/books?id=r5RIAAAAMAAJ&pg=PA338 (pdf)
• 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.
  https://books.google.com/books?id=qt2CAAAAIAAJ&pg=PA212 (pdf)
  English translation: by Aeronautical Chart and Information Center (St. Louis, 1964).
  https://doi.org/10.5281/zenodo.32050
  https://www.worldcat.org/oclc/17273288
• F. R. Helmert,
  Entwicklung der ersten Glieder für die Reduction eines sphäroidischen Dreiecks auf ein sphärisches mit denselben Seiten [Development of the first terms for the reduction of a spheroidal triangle to a spherical one with the same sides], Z. f. Vermess. 18(9), 257–268 (1889).
  https://books.google.com/books?id=L5xIAAAAMAAJ&pg=257 (pdf)
• M. Levy,
  Sur les intégrales rationnelles du problème des lignes géodésiques [On the rational integrals of geodesic lines], Comptes Rendus 85, 1065–1068 (1877).
  https://gallica.bnf.fr/ark:/12148/bpt6k30429/f1060
• K. Schwering,
  Neue geometrische Darstellung der geodätischen Linie auf dem Rotationsellipsoid [New geometric representation of the geodesic on an ellipsoid of revolution], Z. Math. Phys. 24, 405–407 (1879).
  https://books.google.com/books?id=bNk4AAAAIAAJ&pg=PA405 (pdf)
• C. Wiener,
  Zusatz zu der elementaren Begründung des Fundamentalsatzes über die geodätische Linie auf einer Umdrehungsfläche von Professor Jordan [Addendum to Jordan's paper], Z. f. Vermess. 9(8), 337–338 (1880).
  https://books.google.com/books?id=r5RIAAAAMAAJ&pg=PA337 (pdf)
• 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).
  https://books.google.com/books?id=CycYAAAAYAAJ&pg=PA353 (pdf)
• 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).
  https://ui.adsabs.harvard.edu/abs/1877AN.....89..103W
  https://ui.adsabs.harvard.edu/abs/1877AN.....89..113W
  https://doi.org/10.1002/asna.18770890703
  https://doi.org/10.1002/asna.18770890802
• 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).
  https://ui.adsabs.harvard.edu/abs/1877AN.....91..113W
  https://doi.org/10.1002/asna.18780910803
• 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).
  https://ui.adsabs.harvard.edu/abs/1879AN.....95..223W
  https://ui.adsabs.harvard.edu/abs/1879AN.....95..239W
  https://ui.adsabs.harvard.edu/abs/1879AN.....95..271W
  https://doi.org/10.1002/asna.18790951502
  https://doi.org/10.1002/asna.18790951602
  https://doi.org/10.1002/asna.18790951802
• T. Craig,
  The motion of a point upon the surface of an ellipsoid, American J. Math. 1(4), 359–364 (1878).
  https://doi.org/10.2307/2369380
  https://www.jstor.org/stable/2369380
• 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), 207–220 (1879).
  https://ui.adsabs.harvard.edu/abs/1879AN.....95..207S
  https://doi.org/10.1002/asna.18790951402
• A. v. Braunmühl,
  Über Enveloppen geodätischer Linien [The envelopes of geodesic lines], Math. Ann. 14(4), 557–566 (1879).
  https://gdz.sub.uni-goettingen.de/id/PPN235181684_0014?tify={"pages":[583]}
  figures: https://gdz.sub.uni-goettingen.de/id/PPN235181684_0014?tify={"pages":[604]}
  https://doi.org/10.1007/BF01445142
  
• 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(4), 557–586 (1882).
  https://gdz.sub.uni-goettingen.de/id/PPN235181684_0020?tify={"pages":[580]}
  figures: https://gdz.sub.uni-goettingen.de/id/PPN235181684_0020?tify={"pages":[630]}
  https://doi.org/10.1007/BF01540145
• A. v. Braunmühl,
  Über die reducirte Länge eines geodätischen Bogens und die Bildung jener Flächen deren Normalen eine gegebene Fläche berühren [The reduced length of a geodesic and the formation of surfaces whose normals touch a given surface], Abhand. König. Bay. Akad. der Wiss. 14(3), 93–110 (1883).
  https://publikationen.badw.de/de/003083004
• A. v. Braunmühl,
  Notiz über geodätische Linien auf den dreiaxigen Flächen zweiten Grades welche durch elliptische Functionen dargestellen lassen [Note on geodetic lines on the triaxial surfaces of the second degree which can be represented by elliptic functions], Math. Ann. 26(n), 151–153 (1886).
  https://gdz.sub.uni-goettingen.de/id/PPN235181684_0026?tify={"pages":[157]}
• H. Bruns,
  Bemerkung über die geodätische Linie [A remark about the geodesic line], Z. f. Vermess. 10(7), 298–301 (1881).
  https://books.google.com/books?id=spZIAAAAMAAJ&pg=298 (pdf)
• J. Lüroth,
  Notiz über die Rectification eines Ellipsenbogens [The rectification of an elliptical arc], Z. f. Vermess. 10(5), 225–226 (1881).
  https://books.google.com/books?id=spZIAAAAMAAJ&pg=PA225 (pdf)
• J. Lüroth,
  Eine Gleichung zwischen den Längen, Breiten und Azimuten dreier Erdorte [An equation between the longitudes, latitudes, and azimuths for three points on the earth], Z. f. Vermess. 15(21), 529–535 (1886).
  https://books.google.com/books?id=m5hIAAAAMAAJ&pg=529 (pdf)
• 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).
  https://ui.adsabs.harvard.edu/abs/1880AN.....96..209A
  https://doi.org/10.1002/asna.18790961402
• C. T. Albrecht,
  Formeln und Hülfstafeln für geographische Ortsbestimmungen [Formulas and tables for geographic calculations] (3rd edition, Engelmann, Leipzig, 1894).
  https://books.google.com/books?id=muYRAAAAYAAJ (pdf)
• H. v. Mangoldt,
  Über diejenigen Punkte auf positiv gekrümmten Flächen, welche die Eigenschaft haben, dass die von ihnen ausgehenden geodätischen Linien nie aufhören, kürzeste Linien zu sein [The points on positively curved surfaces, which have the property that the geodesic lines emanating from them never cease to be shortest lines], Jour. Crelle 91, 23–53 (1881).
  https://books.google.com/books?id=vQYPAAAAIAAJ&pg=PA23 (pdf)
  https://doi.org/10.1515/crll.1881.91.23
• W. Jordan,
  Über die Bestimmung des mittleren Winkelmessungsfehlers einer nach der Bessel'schen Methode ausgeglichenen Triangulirung [The average error in angle measurments with Bessel's method of balanced triangulation], Astron. Nachr. 89(2114), 27–30 (1877).
  https://ui.adsabs.harvard.edu/abs/1877AN.....89...27J
  https://doi.org/10.1002/asna.18770890204
• W. Jordan,
  Elementare Begründung des Fundamentalsatzes über die geodätische Linie auf einer Umdrehungsfläche [Elementary derivation of the fundamental theorem for the geodesic line on a surface of revolution], Z. f. Vermess. 9(7), 297–298 (1880).
  https://books.google.com/books?id=r5RIAAAAMAAJ&pg=PA297 (pdf)
• W. Jordan,
  Bemerkungen zur Rectification eines Meridianbogens [Comment on the rectification of an elliptical arc], Z. f. Vermess. 11(23), 622–625 (1882).
  https://books.google.com/books?id=fK9IAAAAMAAJ&pg=PA622 (pdf)
• W. Jordan,
  Neue Auflösung der geodätischen Hauptaufgabe und ihrer Umkehrung [A new solution for the principal geodesic problem and its inverse], Z. f. Vermess. 12(3), 65–82 (1883).
  https://books.google.com/books?id=QrBIAAAAMAAJ&pg=PA65 (pdf)
• W. Jordan,
  Elementare Begründung der Beziehungen zwischen der Linie und den Normalschnitten [Elementary derivation of the relationship between the line and the normal sections], Z. f. Vermess. 13(10), 238–241 (1884).
  https://books.google.com/books?id=7YNNAAAAYAAJ&pg=238 (pdf)
• W. Jordan,
  Handbuch der Vermessungskunde [Handbook of Surveying], Vol. 3 (4th edition, Metzler, Stuggart, 1896), Chaps. 6–10.
  https://books.google.com/books?id=4KgRAAAAYAAJ&pg=PA361 (pdf)
  English translation (of 8th edition, 1941): Jordan's Handbook of Geodesy, by M. W. Carta (Army Map Service, 1962), Vol. 3, 2nd half, Chaps. 1–5.
  https://www.worldcat.org/oclc/34429043
  https://doi.org/10.5281/zenodo.35316
• C. H. Kummell,
  Solution of Problem 155, Tha Analyst 4(4), 117–120 (1877).
  https://books.google.com/books?id=eKYEAAAAQAAJ&pg=RA1-PA117 (pdf)
• C. H. Kummell,
  Alignment of curves on any surface, with special application to the ellipsoid, Bull. Phil. Soc. Washington 6, 123–132 (1883).
  https://books.google.com/books?id=z6kWAAAAQAAJ&pg=RA2-PA123 (pdf)
• C. H. Kummell,
  On the determination of the shortest distance between two points on a spheroid, Astron. Nachr. 112(2671), 97–108 (1885).
  https://ui.adsabs.harvard.edu/abs/1885AN....112...97K
  https://doi.org/10.1002/asna.18851120702
• S. Lie,
  Untersuchungen über geodätischen Curben [On geodesic curves], Math. Ann. 20(3), 357–454 (1882).
  https://gdz.sub.uni-goettingen.de/id/PPN235181684_0020?tify={"pages":[376]}
  https://doi.org/10.1007/BF01443601
• A. Brill,
  Zur Theorie der geodätischen Linie und des geodätischen Dreiecks [The theory of geodesic lines and geodesic trangles], Abhand. König. Bay. Akad. der Wiss. 14(2), 111–140 (1883).
  https://publikationen.badw.de/de/003082996
• 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).
  https://geographiclib.sourceforge.io/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.
  https://doi.org/10.2312/GFZ.b103-krueger28
• C. Haupt,
  Die Ausgleichung grosser geodätischer Dreiecke [The adjustment of large geodesic triangles], Astron. Nachr. 107(2549–2550), 65–84 (1883).
  https://ui.adsabs.harvard.edu/abs/1883AN....107...65H
  https://doi.org/10.1002/asna.18841070501
• P. Frost,
  Solid Geometry (3rd edition, Macmillan, 1886), Chap. 23.
  https://books.google.com/books?id=ym1LAAAAMAAJ&pg=PA305 (pdf)
• C. M. Schols,
  La courbure de la projection de la ligne géodésique [The curvature of the projection of a geodesic], Ann. l'École Poly. Delft 2, 179–230 (1886).
  https://books.google.com/books?id=Rw1HAQAAMAAJ&pg=RA1-PA179 (pdf)
• H. Resal,
  Note sur la courbure des lignes géodésiques d'une surface de révolution [On the curvature of geodesics on a surface of revolution], Nouv. Ann. de Math. (Ser. 3) 6, 57–60 (1887).
  https://books.google.com/books?id=QNw_AQAAMAAJ&pg=PA57 (pdf)
• G. H. Halphen,
  Traité des Fonctions Elliptiques et de leurs Applications [A Treatise on Elliptic Functions and their Applications], Vol. 2 (Gauthier-Villars, 1888), Chaps. 6–7.
  https://books.google.com/books?id=7C3vAAAAMAAJ&pg=PA237 (pdf)
• A. Voss,
  Über diejenigen Flächen auf denen zwei Schaaren geodätischer Linien ein conjugirtes System bilden [Surfaces on which two sets of geodesics make a conjugate system], Sitz. König. Akad. der Wiss. München 18, 95–102 (1888).
  https://books.google.com/books?id=5zoEAAAAIAAJ&pg=RA1-PA95 (pdf)
• 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.
  https://books.google.com/books?id=zPdMAAAAMAAJ&pg=PA137 (pdf)
• O. Börsch,
  Geodätische Literatur [Geodetic Bibliography] (Internationale Erdmessung, 1889).
  https://books.google.com/books?id=AZUZAAAAMAAJ (pdf)
• J. H. Gore,
  A Bibliography of Geodesy (US Coast and Geodetic Survey, 1889).
  https://books.google.com/books?id=K38hAAAAMAAJ (pdf)
  1903 edition: https://archive.org/stream/bibliographyofge00gorerich#page/431
• J. H. Gore,
  Elements of Geodesy (3rd edition, Wiley, 1893), Chap. 1.
  https://books.google.com/books?id=h-8ZAAAAYAAJ&pg=PA1 (pdf)
• J. G. Darboux,
  Sur une série de lignes analogues aux lignes géodésiques [A series of lines analogous to geodesics], Ann. l'École Norm. 7, 175–180 (1870).
  https://books.google.com/books?id=PHZFAAAAcAAJ&pg=PA175
• J. G. Darboux,
  Leçons sur la Théorie Générale des Surfaces [Lessons on the General Theory of Surfaces], Vol. 2 (Gauthier-Villars, 1889), Book 4, Chap. 14.
  https://gallica.bnf.fr/ark:/12148/bpt6k77831k/f296
• J. G. Darboux,
  Leçons sur la Théorie Générale des Surfaces [Lessons on the General Theory of Surfaces], Vol. 3 (Gauthier-Villars, 1894), Book 6, Chaps. 1–3.
  https://gallica.bnf.fr/ark:/12148/bpt6k778307/f9
• M. F. Khandrikov,
  Odno iz resheniy osnovnogo voprosa geodezii [One solution to the fundamental problem of geodesy], Matematicheskiy sbornik 17(3), 575–586 (1894).
  http://mi.mathnet.ru/msb7284
  https://books.google.com/books?id=34_xAAAAMAAJ&pg=PA575 (pdf)
• G. N. Shebuev,
  Geometricheskiye osnovaniya geodezii na trekhosnom ellipsoide, ves'ma malo otlichayushchemsya ot sferoida [Geometric bases of geodesy on a triaxial ellipsoid, very little different from a spheroid], Trudy Topografo-geodezicheskoy komissii 5, 70–97 (1896).
  https://geographiclib.sourceforge.io/geodesic-papers/shebuev96.pdf
• G. N. Shebuev,
  Rasstoyaniya, azimuty i treugolniki na trekhosnom ellipsoide, malo otlichayushchemsya ot sfery Geometricheskiye osnovaniya geodezii na trekhosnom ellipsoide, ves'ma malo otlichayushchemsya ot sferoida [Distances, azimuths, and triangles on a triaxial ellipsoid, little different from a sphere], Trudy Topografo-geodezicheskoy komissii 8, 1–72 (1898).
  https://geographiclib.sourceforge.io/geodesic-papers/shebuev98.pdf
• A. R. Forsyth,
  Geodesics on quadrics, not of revolution, Proc. London Math. Soc. 27, 250–280 (1896).
  https://books.google.com/books?id=vUOcAAAAMAAJ&pg=PA250 (pdf)
  https://doi.org/10.1112/plms/s1-27.1.250
• 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).
  https://books.google.com/books?id=YsAKAAAAIAAJ&pg=PA81 (pdf)
  https://books.google.com/books?id=YsAKAAAAIAAJ&pg=PA161
  unreadable page: https://geographiclib.sourceforge.io/geodesic-papers/forsyth96b-add.pdf
• A. R. Forsyth,
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  https://archive.org/details/cu31924060289141
• A. Klingatsch,
  Zur Identität der kürzesten mit der geodätischen Linie [On the indentity of the shortest line with the geodesic], Z. f. Vermess. 26(21), 614–615 (1897).
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• J. S. Hadamard,
  Sur certaines propriétés des trajectoires en Dynamique [On certain properties of trajectories in dynamics], J. Math. Pures Appl. (Ser. 5) 3, 331–388 (1897).
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• J. S. Hadamard,
  Les surfaces à courbures opposées et leurs lignes géodésiques [Surfaces with negative curvature and their geodesics], J. Math. Pures Appl. (Ser. 5) 4, 27–74 (1898).
  http://sites.mathdoc.fr/JMPA/PDF/JMPA_1898_5_4_A3_0.pdf
• J. S. Hadamard,
  Sur la forme des lignes géodésiques à l'infini et sur les géodésiques des surfaces réglées du second ordre [On geodesics at infinity and on geodesics on ruled surfaces of second order], Bull. Soc. Math. France 26, 195–216 (1898).
  http://www.numdam.org/item?id=BSMF_1898__26__195_0
• 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.
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• L. Crawford,
  The general equation of a geodesic on a surface of revolution applied to the sphere, Proc. Edinburgh Math. Soc. 19, 57–61 (1900).
  https://doi.org/10.1017/S0013091500032624
• L. Bianchi,
  Lezioni di Geometria Differenziale [Lessons in Differential Geometry], Vol. 1 (2nd edition, Spoerri, Pisa, 1902), Chap. 6.
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  German translation: Vorlesungen über Differentialgeometrie, by M. Lukat, (Teubner, Leipzig 1899), Chap. 6.
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• F. N. Krasovsky,
  Opredeleniye razmerov zemnogo trekhosnogo ellipsoida iz rezultatov russkikh gradusnykh izmereniy [Determination of the size of the Earth triaxial ellipsoid from the results of the Russian arc measurements], Memorial Book of the Konstantinovsky Mezhevoy Institute for 1900–1901 (Russian Association of Printing and Publishing, Moscow, 1902), pp. 19–54, in Selected Works, Vol 1 (Geodezizdat, Moscow, 1953), pp. 23–49.
  https://geographiclib.sourceforge.io/geodesic-papers/krasovsky02.pdf
  https://www.geokniga.org/bookfiles/geokniga-krasovskiy-fnizbrannye-sochineniyav-4-h-tomahtom-imgeodezizdat1953.pdf
• F. N. Krasovsky,
  Obzor i rezultaty sovremennykh gradusnykh izmereniy [Review and results of modern arc measurements], Geodezist, No. 6-12 (1936), in Selected Works, Vol 1 (Geodezizdat, Moscow, 1953), pp. 82–178.
  https://www.geokniga.org/bookfiles/geokniga-krasovskiy-fnizbrannye-sochineniyav-4-h-tomahtom-imgeodezizdat1953.pdf
• F. N. Krasovsky,
  Rukovodstvo po Vysshei Geodezii [Guide to Higher Geodesy], Part 2 (Geodezizdat, Moscow, 1942), 560 pp., in Selected Works, Vol 4 (Geodezizdat, Moscow, 1955), pp. 4–549.
  https://www.geokniga.org/bookfiles/geokniga-krasovskiy-fnizbrannye-sochineniyav-4-h-tomahtom-ivmgeodezizdat1955.pdf
• P. Sager,
  Übersicht über die Entwickelung der Theorie der geodätischen Linien seit Gauss [Overview of the development of the theory of geodesic lines since Gauss], Dissertation, Rostock Univ. (1903).
  https://books.google.com/books?id=eKILAAAAYAAJ
  Includes some 247 citations.
• J. H. Poincaré,
  Sur les lignes géodésiques des surfaces convexes [Geodesics lines on convex surfaces], Trans. AMS 6(3), 237–274 (1905).
  https://doi.org/10.2307/1986219
  https://www.jstor.org/stable/1986219
• J. Frischauf,
  Zur Berechnung sphäroidischer Dreiecke [Calculating spheroidal triangles], Z. f. Vermess. 37(20), 534–539 (1908).
  https://books.google.com/books?id=EKJIAAAAMAAJ&pg=534 (pdf)
• L. P. Eisenhart,
  A Treatise on the Differential Geometry of Curves and Surfaces (Ginn & Co., Boston, 1909).
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• O. S. Adams,
  Latitude developments connected with geodesy and cartography, Spec. Pub. 67 (US Coast and Geodetic Survey, 1921), Appendix.
  https://geodesy.noaa.gov/library/pdfs/Special_Publication_No_67.pdf
• L. A. Lyusternik and L. G. Schnirelmann,
  Sur le problème de trois géodésiques fermées sur les surfaces de genre 0 [The problem of three closed geodesics on surfaces of genus 0], Comptes Rendus 189, 269–271 (1929).
  https://gallica.bnf.fr/ark:/12148/bpt6k3142j/f269
• L. E. Ward,
  Geodesics and plane arcs on an oblate spheroid, American Math. Monthly 50(7), 423–429 (1943).
  https://doi.org/10.2307/2303665
• P. D. Thomas,
  Conformal projections in geodesy and cartography, Spec. Pub. 251 (US Coast and Geodetic Survey, 1952), pp. 63–66.
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• P. D. Thomas,
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• P. D. Thomas,
  Spheroidal geodesics, reference systems, and local geometry, SP-138 (US Naval Oceanographic Office, 1970).
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• M. S. Molodensky,
  Novyy metod resheniya geodezicheskikh zadach [A new method for solving geodetic problems], Trudy TsNIIGAiK 103, 3–21 (1954), in Selected Works, Gravitational Field (Nauka, Moscow, 2001), pp. 250–268.
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• T. Harada,
  Formula for calculating latitude of a point when meridian length from equator to it is given (in Japanese), J. Geodetic Soc. Jap. 6(3), 75–77 (1960).
  https://doi.org/10.11366/sokuchi1954.6.75
• T. Harada,
  A solution of the second problem on the long geodesic line on an oblate spheroid (in Japanese), J. Geodetic Soc. Jap. 8(1), 23-28 (1962).
  https://doi.org/10.11366/sokuchi1954.8.23
• G. V. Bagratuni,
  Kurs Sferoidicheskoi Geodezii [Course in Spheroidal Geodesy] (Moscow, 1962).
  https://www.worldcat.org/oclc/37391023
  English translation: FTD-MT-64-390 (US Air Force, Feb. 1967).
  https://apps.dtic.mil/sti/citations/AD0650520
  https://www.worldcat.org/oclc/6150611
  clean copy: https://doi.org/10.5281/zenodo.32371
• E. M. Sodano and T. A. Robinson,
  Direct and inverse solutions of geodesics, Tech. Rep. 7 Rev. (Army Map Service, 1963).
  https://apps.dtic.mil/sti/citations/AD0657591
• E. A. Lewis,
  Parametric formulas for geodesic curves and distances on a slightly oblate Earth, AFCRL-63-485 (US Air Force, Apr. 1963).
  https://apps.dtic.mil/sti/citations/AD0412501
• W. Köhnlein,
  Geodesics on an equipotential surface of revolution, Special Report 144, Smithsonian Astrophysical Observatory (1964).
  https://ui.adsabs.harvard.edu/abs/1964SAOSR.144.....K
• V. N. Gan'shin,
  Geometriya Zemnogo Ellipsoida [Geometry of the Earth Ellipsoid] (Moscow, 1967), Chaps. 5–7.
  https://www.worldcat.org/oclc/78077777
  English translation: by J. M. Willis, ACIC-TC-1473, Aeronautical Chart and Information Center (St. Louis, 1969).
  https://doi.org/10.5281/zenodo.32854
  https://apps.dtic.mil/sti/citations/AD0689507
  https://www.worldcat.org/oclc/493553
• Y. G. Ostromukhov and I. I. Radimov,
  Printsipy Resheniya Pryamoy i Obratnoy Geodezicheskikh Zadach pri pomoshchi Tsifrovykh Vychislitelnykh Mashin [Principles of Solving Direct and Inverse Geodetic Problems using Digital Computers], (Sudostroenie, Leningrad, 1973), 85 pp.
  https://doi.org/10.5281/zenodo.495727
• E. J. Krakiwsky and D. B. Thomson,
  Geodetic position computations, Dept. of Geodesy and Geomatics Engineering, Lecture Notes 39, Univ. of New Brunswick (1974), Secs. 3–4.
  https://www2.unb.ca/gge/Pubs/LN39.pdf
• 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).
  https://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
  https://doi.org/10.1179/sre.1975.23.176.88
  https://doi.org/10.1179/sre.1976.23.180.293
• T. Vincenty,
  Geodetic inverse solution between antipodal points, unpublished report, DMAAC (Aug. 28, 1975).
  https://doi.org/10.5281/zenodo.32999
• V. P. Morozov,
  Kurs Sferoidicheskoy Geodezii [A Course in Spheroidal Geodesy] (2nd edition, Nedra, Moscow, 1979) 296 pp.
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• N. A. Bespalov,
  Metody Resheniya Zadach Sferoidicheskoy Geodezii [Methods for Solving Problems of Spheroidal Geodesy] (Nedra, Moscow, 1980), 287 pp.
  https://doi.org/10.5281/zenodo.495726
• B. R. Bowring,
  The Direct and Inverse Problems for Short Geodesic Lines on the Ellipsoid, Surveying and Mapping 41(2), 135–141 (1981).
  https://books.google.com/books?id=eEI4AAAAIAAJ&pg=PA135
• B. K. Meade,
  Comments on Formulas for the Solution of Direct and Inverse Problems on Reference Ellipsoids Using Pocket Calculators, Surveying and Mapping 41(1), 35–41 (1981).
  https://books.google.com/books?id=eEI4AAAAIAAJ&pg=PA35
• J. P. Snyder,
  Map projections: a working manual, Professional Paper 1395 (US Geological Survey, 1987).
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• R. Bourbon,
  Geodesic line on the surface of a spheroid, J. Navigation 43(1), 132–135 (1990).
  https://doi.org/10.1017/S0373463300013886
• R. H. Rapp,
  Geometric geodesy, Part I, Dept. of Geodetic Science and Surveying, Ohio State Univ. (1991), Chaps. 4 & 6.
  https://hdl.handle.net/1811/24333
• R. H. Rapp,
  Geometric geodesy, Part II, Dept. of Geodetic Science and Surveying, Ohio State Univ. (1993), Chap. 1.
  https://hdl.handle.net/1811/24409
• K. Borre,
  Ellipsoidal geometry and conformal mapping (Mar. 2001); these notes, with some modifications, constitute Chaps. 11 & 12 of K. Borre and W. G. Strang, Algorithms for Global Positioning (Wellesley-Cambridge Press, 2012)
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• R. Sinclair,
  On the last geometric statement of Jacobi, Experimental Math. 12(4), 477–485 (2003).
  https://projecteuclid.org/euclid.em/1087568023
  https://doi.org/10.1080/10586458.2003.10504515
• R. J. Mathar,
  Geodetic line at constant altitude above the ellipsoid (May 2008).
  https://arxiv.org/abs/0711.0642
• R. J. Mathar,
  Two Integrals of Geodetic Lines in Oblate Ellipsoidal Coordinates (May 2010).
  https://arxiv.org/abs/1005.3790
• C. F. F. Karney,
  GeographicLib, version 2009-03 (Mar. 2009).
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• C. F. F. Karney,
  Test set for geodesics (2010).
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• C. F. F. Karney,
  Geodesics on an ellipsoid of revolution (Feb. 2011).
  https://arxiv.org/abs/1102.1215
  Errata: https://geographiclib.sourceforge.io/geod-addenda.html#geod-errata
• C. F. F. Karney,
  Algorithms for geodesics, J. Geodesy 87(1), 43–55 (2013).
  https://doi.org/10.1007/s00190-012-0578-z
  https://arxiv.org/abs/1109.4448
  Addenda: https://geographiclib.sourceforge.io/geod-addenda.html
• C. F. F. Karney,
  Geodesics on an arbitrary ellipsoid of revolution, J. Geodesy 98(1), 4:1–14 (2024).
  https://doi.org/10.1007/s00190-023-01813-2
  https://arxiv.org/abs/2208.00492
• C. F. F. Karney,
  Geodesic intersections, J. Surveying Eng. 150(3), 04024005:1–9 (2024).
  https://doi.org/10.1061/JSUED2.SUENG-1483
  https://arxiv.org/abs/2308.00495
• C. F. F. Karney,
  Test set of geodesics on a triaxial ellipsoid (2024).
  https://doi.org/10.5281/zenodo.12510796
• C. F. F. Karney,
  Jacobi's solution for geodesics on a triaxial ellipsoid, J. Geodesy 100(2), 17:1–23 (2026).
  https://doi.org/10.1007/s00190-026-02030-3
  https://arxiv.org/abs/2511.01621
• C. M. Rollins,
  An integral for geodesic length, Survey Review 42(315), 20–26 (2010).
  https://earth-info.nga.mil/php/download.php?file=coord-geodesic
  https://doi.org/10.1179/003962609X451663
• Y. C. Lee,
  The accuracy analysis of methods to solve the geodetic inverse problem (in Korean), J. Korean Soc. Surveying, Geodesy, Photogrammetry and Cartography 29(4), 329–341 (2011).
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• A. S. Lenart,
  Solutions of direct geodetic problem in navigational applications, TransNav 5(4), 527–532 (2011).
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• A. S. Lenart,
  Solutions of inverse geodetic problem in navigational applications, TransNav 7(2), 253–257 (2013).
  https://doi.org/10.12716/1001.07.02.13
• L. E. Sjöberg and M. Shirazian,
  Solving the direct and inverse geodetic problems on the ellipsoid by numerical integration, J. Surveying and Engineering 138(1), 9–16 (2012).
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• L. E. Sjöberg,
  Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration, J. Geodetic Science 2(3), 162–171 (2012);
  Errata: J. Geodetic Science 3(2), 110 (2013).
  https://doi.org/10.2478/v10156-011-0037-4
  https://doi.org/10.2478/jogs-2013-0014
• G. Panou, D. Delikaraoglou, and R. Korakitis,
  Solving the geodesics on the ellipsoid as a boundary value problem, J. Geodetic Science 3(1), 40–47 (2013).
  https://doi.org/10.2478/jogs-2013-0007
• G. Panou,
  The geodesic boundary value problem and its solution on a triaxial ellipsoid, J. Geodetic Science 3(3), 240–249 (2013).
  https://doi.org/10.2478/jogs-2013-0028
• G. Panou and R. Korakitis,
  Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid, J. Geodetic Science 7(1), 31–42 (2017).
  https://doi.org/10.1515/jogs-2017-0004
  https://arxiv.org/abs/1612.01357
• G. Panou and R. Korakitis,
  Geodesic equations and their numerical solution in Cartesian coordinates on a triaxial ellipsoid, J. Geodetic Science 9(1), 1–12 (2019).
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  https://arxiv.org/abs/1811.03513
• W.-K. Tseng,
  An algorithm for the inverse solution of geodesic sailing without auxiliary sphere, J. Navigation 67(5), 825–844 (2014);
  Publisher's notice: J. Navigation 68(1), 215–216 (2015);
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  https://doi.org/10.1017/S0373463314000228
  https://doi.org/10.1017/S0373463314000745
  https://doi.org/10.1017/S0373463314000733
• V. A. Botnev and S. M. Ustinov,
  Methods for direct and inverse geodesic problems solving with high precision (in Russian), Comput. Telcomm. Control 3(198), 49-58 (2014).
  https://infocom.spbstu.ru/en/article/2014.39.5
• V. A. Botnev and S. M. Ustinov,
  A method for finding the distance between a point and a line in geodesy (in Russian), Comput. Telcomm. Control 6(234), 33–44 (2015).
  https://doi.org/10.5862/JCSTCS.234.4 (broken)
  https://infocom.spbstu.ru/en/article/2015.47.4
• V. A. Botnev and S. M. Ustinov,
  Distance finding method between a point and a segment in navigation (in Russian), Comput. Telcomm. Control 12(2), 68–79 (2019).
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• C. Jekeli,
  Geometric reference systems in geodesy, Division. of Geodetic Science, Ohio State Univ. (2016), Chap. 2.
  https://hdl.handle.net/1811/77986
• C. Marx,
  Performance of a solution of the direct geodetic problem by Taylor series of Cartesian coordinates, J. Geodetic Science 11(1), 122–130 (2021).
  https://doi.org/10.1515/jogs-2020-0127
• E. Nowak and J. Nowak Da Costa,
  Theory, strict formula derivation and algorithm development for the computation of a geodesic polygon area, J. Geodesy 96(4), 20:1–23 (2022).
  https://doi.org/10.1007/s00190-022-01606-z

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