See spherical geometry in All languages combined, or Wiktionary
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Historically, however, spherical geometry was not considered a fully fledged (non-Euclidean) geometry capable of resolving the question of whether the parallel postulate is a logical consequence of the rest of Euclid's axioms of plane geometry.", "type": "example" }, { "text": "1972, Morris Kline, Mathematical Thought from Ancient to Modern Times: Volume 1, Oxford University Press, 1990, paperback, page 119,\nSpherical trigonometry presupposes spherical geometry, for example the properties of great circles and spherical triangles, much of which was already known; it had been investigated as soon as astronomy became mathematical, during the time of the later Pythagoreans." }, { "ref": "1994, Viacheslav V. Nikulin, Igor R. Shafarevich, translated by Miles Reid, Geometries and Groups, Springer, page 194:", "text": "We start with spherical geometries. 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Whittlesey, Spherical Geometry and Its Applications, Taylor & Francis (CRC Press), unnumbered page,\nIt has been at least fifty years since spherical geometry and spherical trigonometry have been a regular part of the high school or undergraduate curriculum." } ], "glosses": [ "The geometry of the 2-dimensional surface of a sphere;" ], "id": "en-spherical_geometry-en-noun-JaO0BJ3L", "links": [ [ "geometry", "geometry" ], [ "2-dimensional", "2-dimensional" ], [ "sphere", "sphere" ] ], "raw_glosses": [ "(geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;" ], "tags": [ "uncountable", "usually" ], "topics": [ "geometry", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Geometry", "orig": "en:Geometry", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "40 60", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "21 79", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "34 66", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "29 71", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "22 78", "kind": "other", "name": "Terms with Catalan translations", "parents": [], "source": "w+disamb" }, { "_dis": "21 79", "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w+disamb" }, { "_dis": "22 78", "kind": "other", "name": "Terms with Georgian translations", "parents": [], "source": "w+disamb" }, { "_dis": "22 78", "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w+disamb" }, { "_dis": "25 75", "kind": "other", "name": "Terms with Hungarian translations", "parents": [], "source": "w+disamb" }, { "_dis": "21 79", "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w+disamb" }, { "_dis": "21 79", "kind": "other", "name": "Terms with Japanese translations", "parents": [], "source": "w+disamb" }, { "_dis": "25 75", "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" }, { "_dis": "22 78", "kind": "other", "name": "Terms with Romanian translations", "parents": [], "source": "w+disamb" }, { "_dis": "18 82", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" }, { "_dis": "22 78", "kind": "other", "name": "Terms with Tagalog translations", "parents": [], "source": "w+disamb" }, { "_dis": "33 67", "kind": "other", "langcode": "en", "name": "Non-Euclidean geometry", "orig": "en:Non-Euclidean geometry", "parents": [], "source": "w+disamb" }, { "_dis": "44 56", "kind": "other", "langcode": "en", "name": "Sphere", "orig": "en:Sphere", "parents": [], "source": "w+disamb" } ], "glosses": [ "The geometry of the 2-dimensional surface of a sphere;\n(countable) a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres.", "a given geometry of the surface of a sphere; a geometry of the surface of a given sphere, regarded as distinct from that of other spheres." ], "id": "en-spherical_geometry-en-noun-wRQLL4Hg", "links": [ [ "geometry", "geometry" ], [ "2-dimensional", "2-dimensional" ], [ "sphere", "sphere" ] ], "raw_glosses": [ "(geometry, uncountable) The geometry of the 2-dimensional surface of a sphere;" ], "related": [ { "_dis1": "42 58", "word": "spherical trigonometry" }, { "_dis1": "42 58", "word": "astrometry" }, { "_dis1": "42 58", "word": "elliptic geometry" }, { "_dis1": "42 58", "word": "great circle" }, { "_dis1": "42 58", "word": "non-Euclidean geometry" }, { "_dis1": "42 58", "word": "parallel postulate" } ], "tags": [ "countable", "usually" ], "topics": [ "geometry", "mathematics", "sciences" ], "translations": [ { "_dis1": "42 58", "code": "ca", "lang": "Catalan", "sense": "branch of geometry", "tags": [ "feminine" ], "word": "geometria esfèrica" }, { "_dis1": "42 58", "code": "fr", "lang": "French", "sense": "branch of geometry", "tags": [ "feminine" ], "word": "géométrie sphérique" }, { "_dis1": "42 58", "code": "ka", "lang": "Georgian", "roman": "speruli geomeṭria", "sense": "branch of geometry", "word": "სფერული გეომეტრია" }, { "_dis1": "42 58", "code": "de", "lang": "German", "sense": "branch of geometry", "tags": [ "feminine" ], "word": "sphärische Geometrie" }, { "_dis1": "42 58", "code": "de", "lang": "German", "sense": "branch of geometry", "tags": [ "feminine" ], "word": "Kugelgeometrie" }, { "_dis1": "42 58", "code": "de", "lang": "German", "sense": "branch of geometry", "tags": [ "feminine" ], "word": "Geometrie auf der Kugel" }, { "_dis1": "42 58", "code": "hu", "lang": "Hungarian", "sense": "branch of geometry", "word": "gömbi geometria" }, { "_dis1": "42 58", "code": "it", "lang": "Italian", "sense": "branch of geometry", "tags": [ "feminine" ], "word": "geometria sferica" }, { "_dis1": "42 58", "code": "ja", "lang": "Japanese", "sense": "branch of geometry", "word": "球面幾何学" }, { "_dis1": "42 58", "code": "pt", "lang": "Portuguese", "sense": "branch of geometry", "tags": [ "feminine" ], "word": "geometria esférica" }, { "_dis1": "42 58", "code": "ro", "lang": "Romanian", "sense": "branch of geometry", "word": "geometrie sferică" }, { "_dis1": "42 58", "code": "es", "lang": "Spanish", "sense": "branch of geometry", "tags": [ "feminine" ], "word": "geometría esférica" }, { "_dis1": "42 58", "code": "tl", "lang": "Tagalog", "sense": "branch of geometry", "word": "timbuluging sukgisan" } ] } ], "wikipedia": [ "spherical geometry" ], "word": "spherical geometry" }
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Historically, however, spherical geometry was not considered a fully fledged (non-Euclidean) geometry capable of resolving the question of whether the parallel postulate is a logical consequence of the rest of Euclid's axioms of plane geometry.", "type": "example" }, { "text": "1972, Morris Kline, Mathematical Thought from Ancient to Modern Times: Volume 1, Oxford University Press, 1990, paperback, page 119,\nSpherical trigonometry presupposes spherical geometry, for example the properties of great circles and spherical triangles, much of which was already known; it had been investigated as soon as astronomy became mathematical, during the time of the later Pythagoreans." }, { "ref": "1994, Viacheslav V. Nikulin, Igor R. Shafarevich, translated by Miles Reid, Geometries and Groups, Springer, page 194:", "text": "We start with spherical geometries. 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