By H. L. L. Busard
Euklids Hauptwerk, die Elemente, gilt als dasjenige wissenschaftliche Werk, das am häufigsten bearbeitet und benutzt wurde; es battle 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 that that the well known Euclid editor Busard has back discovered a masterly edition." Mathematical reports "àBusard's version is critical for our knowing of excessive medieval arithmetic. " Centaurus.
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Additional info for Johannes de Tinemue's Redaction of Euclid's Elements, the So-Called Adelard III Version
Example text
Proof: Let A be left invertible. Then there is an n x n matrix B such that BA = I< Then H is cogredient to a diagonal matrix (ai \ I I' \ o Since S is nonalterate, there is a nonzero diagonal element of 5, say s u ^ 0. Interchanging the first row and the i-th row of S and the first column and the i-th column of S simultaneously, we obtain a symmetric matrix which is cogredient to S and whose element at (1, 1) position is nonzero. Therefore we can assume that s u ^ 0. Write 5 = | ( 311 u V 522 / where U u — and5*22 S22= =(St*)2