CONTENTS.
INTRODUCTION.
page Chapter I. Archimedes................................................................................................................................................................................................................................................................................................................................................................................................xv Chapter II. Manuscripts and principal editions—order of composition—dialect—lost works................................................................................................................................................................................................................................................................................................................................................................................................xxiii Chapter III. Relation of Archimedes to his predecessors................................................................................................................................................................................................................................................................................................................................................................................................xxxix §1. Use of traditional geometrical methods................................................................................................................................................................................................................................................................................................................................................................................................xl §2. Earlier discoveries affecting quadrature and cubature................................................................................................................................................................................................................................................................................................................................................................................................xlvii §3. Conic Sections................................................................................................................................................................................................................................................................................................................................................................................................lii §4. Surfaces of the second degree................................................................................................................................................................................................................................................................................................................................................................................................liv §5. Two mean proportionals in continued proportion................................................................................................................................................................................................................................................................................................................................................................................................lxvii Chapter IV. Arithmetic in Archimedes................................................................................................................................................................................................................................................................................................................................................................................................lxviii §1. Greek numeral system................................................................................................................................................................................................................................................................................................................................................................................................lxix §2. Addition and subtraction................................................................................................................................................................................................................................................................................................................................................................................................lxxi §3. Multiplication................................................................................................................................................................................................................................................................................................................................................................................................lxxii §4. Division................................................................................................................................................................................................................................................................................................................................................................................................lxxiii §5. Extraction of the square root................................................................................................................................................................................................................................................................................................................................................................................................lxxiv §6. Early investigations of surds or incommensurables................................................................................................................................................................................................................................................................................................................................................................................................lxxvii §7. Archimedes' approximations to √3................................................................................................................................................................................................................................................................................................................................................................................................lxxx §8. Archimedes' approximations to the square roots of large numbers which are not complete squares................................................................................................................................................................................................................................................................................................................................................................................................lxxxiv - Note on alternative hypotheses with regard to the approximations to √3................................................................................................................................................................................................................................................................................................................................................................................................
xc
