"Squaring the Circle": a History of the Problem

by Ernest William Hobson

 

"SQUARING THE CIRCLE"

A HISTORY OF THE PROBLEM

 

 

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"SQUARING THE CIRCLE"

A HISTORY OF THE PROBLEM

 

BY

E. W. HOBSON, Sc.D., LL.D., F.R.S.

Sadleirian Professor of Pure Mathematics, and Fellow of Christ's College, in the University of Cambridge

 

Cambridge:

at the University Press

1913

 

Cambridge:
Printed by John Clay, M.A.
At the University Press

 

PREFACE

IN the Easter Term of the present year I delivered a short course of six Professorial Lectures on the history of the problem of the quadrature of the circle, in the hope that a short account of the fortunes of this celebrated problem might not only prove interesting in itself, but might also act as a stimulant of interest in the more general history of Mathematics. It has occurred to me that, by the publication of the Lectures, they might perhaps be of use, in the same way, to a larger circle of students of Mathematics.

The account of the problem here given is not the result of any independent historical research, but the facts have been taken from the writings of those authors who have investigated various parts of the history of the problem.

The works to which I am most indebted are the very interesting book by Prof. F. Rudio entitled "Archimedes, Huygens, Lambert, Legendre. Vier Abhandlungen über die Kreismessung" (Leipzig, 1892), and Sir T. L. Heath's treatise "The works of Archimedes" (Cambridge, 1897). I have also made use of Cantor's "Geschichte der Mathematik," of Vahlen's "Konstruktionen und Approximationen" (Leipzig, 1911), of Yoshio Mikami's treatise "The development of Mathematics in China and Japan" (Leipzig, 1913), of the translation by T. J. McCormack (Chicago, 1898) of H. Schubert's "Mathematical Essays and Recreations," and of the article "The history and transcendence of $\pi$" written by Prof. D. E. Smith which appeared in the "Monographs on Modern Mathematics" edited by Prof. J. W. A. Young. On special points I have consulted various other writings.

E. W. H.

Christ's College, Cambridge.
October, 1913.

CONTENTS

CHAPTER I
	Page
General Account of the Problem	1
CHAPTER II
The First Period	13
CHAPTER III
The Second Period	36
CHAPTER IV
The Third Period	43