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
Circular library stamp from Lesley College with the number 1105 inside.	§ 2. Earlier discoveries affecting quadrature quadrature: the process of finding a square equal in area to a given surface and cubature cubature: the process of finding the volume of a solid . . . . . . . .	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 surds: irrational numbers or roots 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