Die vier Gauss'schen Beweise fur die Zerlegung ganzer algebraischer Functionen in recelle Factoren ersten odor zweiten Grades (1799-1849). Herausgegeben von E. Netto. Dritte Auflage.
1913 · Leipzig & Berlin:
by GAUSS, Johann Carl Friedrich (1777-1855).
Leipzig & Berlin:: Wilhelm Engelmann, 1913., 1913. Series: Ostwald's Klassiker der exakten Wissenschaften, Bd. 14. Sm. 8vo. 82 pp. 1 plate. Original gray black-stamped cloth. Fine copy. Former ownership signatures (ffp + title). "In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree, Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. Mathematicians including Jean le Rond d'Alembert had produced false proofs before him, and Gauss's dissertation contains a critique of d'Alembert's work. Ironically, by today's standard, Gauss's own attempt is not acceptable, owing to implicit use of the Jordan curve theorem. However, he subsequently produced three other proofs, the last one in 1849 being generally rigorous. His attempts clarified the concept of complex numbers considerably along the way." Gauss – Wikipedia. (Inventory #: BL4023)