# Book:Sir Thomas L. Heath/The Works of Archimedes with the Method of Archimedes

## Sir Thomas L. Heath: The Works of Archimedes with the Method of Archimedes

Published $\text {1953}$.

### Subject Matter

The works of Archimedes.

### The Works of Archimedes

Chapter $\text I$. Archimedes
Chapter $\text {II}$. Manuscripts and principal editions -- order of composition -- dialect -- Lost words
Chapter $\text {III}$. Relation of Archimedes to his predecessors
$\S 1$. Use of traditional geometrical methods
$\S 2$. Earlier discoveries affecting quadrature and cubature
$\S 3$. Conic Sections
$\S 4$. Surfaces of the second degree
$\S 5$. Two mean proportionals in continued proportion
Chapter $\text {IV}$. Arithmetic in Archimedes
$\S 1$. Greek numeral system
$\S 2$. Addition and subtraction
$\S 3$. Multiplication
$\S 4$. Division
$\S 5$. Extraction of the square root
$\S 6$. Early investigations of surds or incommensurables
$\S 7$. Archimedes' approximations to $\surd 3$
$\S 8$. Archimedes' approximations to the square roots of large numbers which are not complete squares
Note on alternative hypotheses with regard to the approximations to $\surd 3$
Chapter $\text {V}$. On the problems known as $\Nu \Epsilon \Upsilon \Sigma \Epsilon \Iota \Sigma$
$\S 1$. $\Nu \epsilon \upsilon \sigma \epsilon \iota \varsigma$ referred to by Archimedes
$\S 2$. Mechanical constructions: the conchoid of Nicomedes
$\S 3$. Pappus' solution of the $\nu \epsilon \upsilon \sigma \epsilon \iota \varsigma$ referred to in Props. $8$, $9$ On Spirals
$\S 4$. The problem of the two mean proportionals
$\S 5$. The trisection of an angle
$\S 6$. On certain plane $\nu \epsilon \upsilon \sigma \epsilon \iota \varsigma$
Chapter $\text {VI}$. Cubic equations
Chapter $\text {VII}$. Anticipations by Archimedes of the integral calculus
Chapter $\text {VIII}$. The terminology of Archimedes

The Works of Archimedes
On the Sphere and Cylinder,
Book $\text I$
Book $\text {II}$
Measurement of a Circle
On Conoids and Spheroids
On Spirals
On the Equilibrium of Planes,
Book $\text I$
Book $\text {II}$
The Sand-Reckoner
Quadrature of the Parabola
On Floating Bodies,
Book $\text I$
Book $\text {II}$
Book of Lemmas
The Cattle-Problem

### The Method of Archimedes

Introductory Note
The Method of Archimedes Treating of Mechanical Problems -- To Eratosthenes