Rechnungsmethoden, die sich auf Eine Erweiterung des Grössenbegriffes Grunden. Dissertation zur Erlangung der Venia Docendi bei der Philosophiscehn Fakultät in Jena

Jena: Friederich Fromann, 1874 First edition of Frege's qualifying dissertation for his job teaching at the University of Jena. Very scarce. Self-wrapper, with reinforcement strip at spine. Quarto. This item is printed on acidic paper , which is lightlybrowned around the edges. The last leaf is beginning to chip at the top, with notext loss. A very good copy of an extremely fragile pamphlet. This is one of the rarest of Frege items. We have been able to locate only the Smithsonian copy and the copy at Brown. "In 1873 Frege received his doctorate in philosophy at Göttingen with the thesis Ueber eine geometrische Darstellung der imäginaren Gebilde in der Ebene. The following year at Jena he obtained the venia docendi in the Faculty of Philosophy with a dissertation entitled "Rechunsmethoden, die sich auf eine Erweitung des Grössenbegriffes gründen," which concerns one-parameter groups of functions and was motivated by his intention to give such a definition of quantity as gives maximal extension to the applicability of the arithmetic based upon it. The idea presented in the dissertation of viewing the system of an operation f and its iterates as a system of quantities, which in the introduction to his Grundlagen der Arithmetik (1884) Frege essentially ascribes to Herbart, hints at the notion of f-sequence expounded in his Begriffschrift (1879)" (B. Van Rootselaar, writing in the D.S.B.)