Download Johannes de Tinemue's Redaction of Euclid's Elements, the by H. L. L. Busard PDF
By H. L. L. Busard
Euklids Hauptwerk, die Elemente, gilt als dasjenige wissenschaftliche Werk, das am häufigsten bearbeitet und benutzt wurde; es warfare ueber 2000 Jahre lang nicht nur das mathematische Lehrbuch schlechthin, sondern es beeinfluáte auch die Entwicklung anderer wissenschaftlicher Disziplinen. Das Werk wurde im 12. Jahrhundert aus dem Arabischen ins Lateinische uebersetzt, u.a. von Adelhard von bathtub. Diese Übersetzung wurde der Ausgangspunkt fuer zahlreiche weitere Bearbeitungen, wie die Redaktion, die um 1200 wahrscheinlich von Johannes de Tinemue angefertigt wurde. Campanus, der in den Jahren 1255/59 die fuer Jahrhunderte maágebende Euklid-Ausgabe besorgte, hat diese Redaktion sehr wahrscheinlich auch gekannt. "It is remember the fact that that the well known Euclid editor Busard has back discovered a masterly edition." Mathematical experiences "àBusard's version is critical for our figuring out of excessive medieval arithmetic. " Centaurus.
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Extra resources for Johannes de Tinemue's Redaction of Euclid's Elements, the So-Called Adelard III Version
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In this article, we denote a complete simply connected complex m-dimensional complex space form of constant holomorphic sectional curvature 4c ˜ m (4c). -Y. Chen ˜ m (4c) satisfies The curvature tensor R˜ of a complex space form M ˜ R(U, V, W ) = c{ V, W U − X, W V + J V, W JU − JU, W J V + 2 U, J V J W }. 7) ˜ m (4c) is holomorphically isometric to the complex projective It is well-known that M m m-space CP (4c), the complex Euclidean m-space Cm , or the complex hyperbolic m-space CH m (4c) according to c > 0, c = 0, or c < 0, respectively.
Sahin proved the following. 21 ([42]) There do not exist doubly warped product CR-submanifolds which are not (singly) warped product CR-submanifolds in the form f1 MT ×f2 M⊥ , where MT is a holomorphic submanifold and M⊥ is a totally real submanifold of a ˜ Kaehler manifold M. -Y. 7 CR-Warped Products with Compact Holomorphic Factor When the holomorphic factor NT of a CR-warped product NT ×f N⊥ is compact, we have the following sharp results. 22 ([24]) Let NT ×f N⊥ be a CR-warped product in the complex projective m-space CPm (4) of constant holomorphic sectional curvature 4.
And dim N⊥ > 1, then ||σ||2 = 2p ||∇ T ln λ||2 (3) If M is anti-holomorphic in M holds identically if and only if NT is a totally geodesic submanifold and N⊥ is a ˜ totally umbilical submanifold of M. For mixed foliate twisted product CR-submanifolds of Kaehler manifolds, we have the following result. 36 ([11]) Let M = NT ×λ N⊥ be a twisted product CR-submanifold of ˜ such that N⊥ is a totally real submanifold and NT is a holoa Kaehler manifold M ˜ If M is mixed totally geodesic, then we have morphic submanifold of M.