Editing Spherical geometry (section)

==History==

=== Greek antiquity===

The earliest mathematical work of antiquity to come down to our time is ''On the rotating sphere'' (Περὶ κινουμένης σφαίρας, ''Peri kinoumenes sphairas'') by [[Autolycus of Pitane]], who lived at the end of the fourth century BC.<ref>{{cite book|last1=Rosenfeld|first1=B.A|title=A history of non-Euclidean geometry : evolution of the concept of a geometric space|date=1988|publisher=Springer-Verlag|location=New York|isbn=0-387-96458-4|page=2}}</ref>

Spherical trigonometry was studied by early [[Greek mathematics|Greek mathematicians]] such as [[Theodosius of Bithynia]], a Greek astronomer and mathematician who wrote ''[[Theodosius' Spherics|Spherics]]'', a book on the geometry of the sphere,<ref>{{cite web|url=http://www.encyclopedia.com/doc/1G2-2830904281.html|title=Theodosius of Bithynia – Dictionary definition of Theodosius of Bithynia |work=[[HighBeam Research]]|access-date=25 March 2015}}</ref> and [[Menelaus of Alexandria]], who wrote a book on spherical trigonometry called ''Sphaerica'' and developed [[Menelaus' theorem]].<ref>{{MacTutor|id=Menelaus|title=Menelaus of Alexandria}}</ref><ref>{{cite web|url=http://www.encyclopedia.com/topic/Menelaus_of_Alexandria.aspx#1|title=Menelaus of Alexandria Facts, information, pictures |work=[[HighBeam Research]]|access-date=25 March 2015}}</ref>

===Islamic world===
{{See also|Mathematics in medieval Islam}}
''The Book of Unknown Arcs of a Sphere'' written by the Islamic mathematician [[Al-Jayyani]] is considered to be the first treatise on spherical trigonometry. The book contains formulae for right-handed<!--angled?--> triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle.<ref>[http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Al-Jayyani.html School of Mathematical and Computational Sciences University of St Andrews]</ref>

The book ''On Triangles'' by [[Regiomontanus]], written around 1463, is the first pure trigonometrical work in Europe. However, [[Gerolamo Cardano]] noted a century later that much of its material on spherical trigonometry was taken from the twelfth-century work of the [[Al-Andalus|Andalusi]] scholar [[Jabir ibn Aflah]].<ref>{{Cite web |url=http://press.princeton.edu/chapters/i8583.html |title=Victor J. Katz-Princeton University Press |access-date=2009-03-01 |archive-date=2016-10-01 |archive-url=https://web.archive.org/web/20161001214903/http://press.princeton.edu/chapters/i8583.html |url-status=dead }}</ref>

===Euler's work===
[[Leonhard Euler]] published a series of important memoirs on spherical geometry:
* L. Euler, Principes de la trigonométrie sphérique tirés de la méthode des plus grands et des plus petits, Mémoires de l'Académie des Sciences de Berlin 9 (1753), 1755, p.&nbsp;233–257; Opera Omnia, Series 1, vol. XXVII, p.&nbsp;277–308.
* L. Euler, Eléments de la trigonométrie sphéroïdique tirés de la méthode des plus grands et des plus petits, Mémoires de l'Académie des Sciences de Berlin 9 (1754), 1755, p.&nbsp;258–293; Opera Omnia, Series 1, vol. XXVII, p.&nbsp;309–339.
* L. Euler, De curva rectificabili in superficie sphaerica, Novi Commentarii academiae scientiarum Petropolitanae 15, 1771, pp.&nbsp;195–216; Opera Omnia, Series 1, Volume 28, pp.&nbsp;142–160.
* L. Euler, De mensura angulorum solidorum, Acta academiae scientiarum imperialis Petropolitinae 2, 1781, p.&nbsp;31–54; Opera Omnia, Series 1, vol. XXVI, p.&nbsp;204–223.
* L. Euler, Problematis cuiusdam Pappi Alexandrini constructio, Acta academiae scientiarum imperialis Petropolitinae 4, 1783, p.&nbsp;91–96; Opera Omnia, Series 1, vol. XXVI, p.&nbsp;237–242.
* L. Euler, Geometrica et sphaerica quaedam, Mémoires de l'Académie des Sciences de Saint-Pétersbourg 5, 1815, p.&nbsp;96–114; Opera Omnia, Series 1, vol. XXVI, p.&nbsp;344–358.
* L. Euler, Trigonometria sphaerica universa, ex primis principiis breviter et dilucide derivata, Acta academiae scientiarum imperialis Petropolitinae 3, 1782, p.&nbsp;72–86; Opera Omnia, Series 1, vol. XXVI, p.&nbsp;224–236.
* L. Euler, Variae speculationes super area triangulorum sphaericorum, Nova Acta academiae scientiarum imperialis Petropolitinae 10, 1797, p.&nbsp;47–62; Opera Omnia, Series 1, vol. XXIX, p.&nbsp;253–266.