Die griechische Logistik und die Entstehung der Algebra

Jacob Klein’s work on the difference between the transformation of the ancient concept of number in modernity, showing how the that transformation stands at the roots of modern science and philosophy, is I think the most illuminating work on modern origins that I have ever read.  Klein’s friend Strauss once wrote the following of Klein’s work:

Klein was the first to under stand the possibility which Heidegger had opened without intending it: the possibility of a genuine return to classical philosophy, to the philosophy of Aristotle and of Plato, a return with open eyes and in full clarity about the infinite difficulties which it entails. He turned to the study of classical philosophy with a devotion and a love of toil, a penetration and an intelligence, an intellectual probity and a sobriety in which no contemporary equals him. Out of that study grew his work which bears the title Greek Logistics and the Genesis of Algebra. No title could be less expressive of a man’s individuality and even of a man’s intention; and yet if one knows Klein, the title expresses perfectly his individuality, his idiosyncracy mentioned before. The work is much more than a historical study. But even if we take it as a purely historical work, there is not, in my opinion, a contemporary work in the history of philosophy or science or in “the history of ideas” generally speaking which in intrinsic worth comes within hailing distance of it. Not indeed a proof but a sign of this is the fact that less than half a dozen people seem to have read it, if the inference from the number of references to it is valid. Any other man would justly be blamed for misanthropy, if he did not take care that such a contribution does not remain inaccessible to everyone who does not happen to come across volume III of section B of Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik and in addition does not read German with some fluency. One cannot blame Klein because he is excused by his idiosyncracy.

An English translation of Klein’s masterpiece was soon made by Eva Brann, and remains readily available. And a detailed exposition of it has recently been published by Burt Hopkins. But until today the German original remained inaccessible to “everyone who does not happen to come across volume III of section B of Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik.” But today, having found a copy in the library of the University of Vienna, I made a scan, and have uploaded it here, so that now anyone with an internet connection can read Klein in the original.