Abstract

This is a translation of Jacob Klein's study "Die Griechische Logistik und die Entstehung der Algebra" which appeared in 1934-1936. His principal thesis is that the Renaissance mathematicians of the sixteenth century did not simply continue the work of the Greek and Arab mathematicians but in the process of developing ancient mathematics introduced a radically new conception of number which has since guided modern mathematical thought. The central figure in this revolution is Vieta. Klein traces the influence of Vieta's ideas upon Stevin, Descartes, Wallis, and other figures of the scientific revolution, after discussing the conception of number and arithmetic in Plato, Aristotle, and other Greek sources. Persons reading this book with a primary interest in the philosophical ideas involved will be frustrated by the mass of historical detail which often obscures rather than illuminates the philosophical issues. But the book deserves its reputation as an important historical study.--R. H. K.