X 
CONTENTS 
XTX. CONTINUED. 
Book YIII (continued) 
The inclined plane .... pages 433-434 
Construction of a conic through five points . . 434-437 
Given two conjugate diameters of an ellipse, to find 
the axes <■. . . 437-438 
Problem of seven hexagons in a circle . . . 438-439 
Construction of toothed wheels and indented screws 439 
XX. ALGEBRA; DIOPHANTUS OF ALEXANDRIA 
. 440-517 
Dio- 
Beginnings learnt from Egypt .... 
‘ Hau ’-calculations ...... 
Arithmetical epigrams in the Greek Anthology 
Indeterminate equations of first degree . 
Indeterminate equations of second degree before 
phantus ....... 
Indeterminate equations in Heronian collection* 
Numerical solution of quadratic equations 
Works of Diophantus ..... 
The Arithmetica 
The seven lost Books and their place . 
Relation of ‘ Porisms ’ to Arithmetica 
Commentators from Hypatia downwards 
Translations and editions .... 
Notation and definitions .... 
Sign for unknown (= x) and its origin 
Signs for powers of unknown &c. 
The sign (/j\) for minus and its meaning . 
The methods of Diophantus .... 
I. Diophantus’s treatment of equations 
(A) Deter-minate equations 
(1) Pure determinate equations 
(2) Mixed quadratic equations . 
(3) Simultaneousequationsinvolvingquadratics 
(4) Cubic equation 
(B) Indeterminate equations 
(a) Indeterminate equations of the second degree 
(1) Single equation 
(2) Double equation . . . . . 
1. Double equations of first degree 
2. Double equations of second degree 
{}>) Indeterminate equations of degree higher 
than second 
(1) Single equations . 
(2) Double equations . 
II. Method of limits 
III. Method of approximation to limits 
Porisms and propositions in the Theory of Numbers 
(a) Theorems on the composition of numbers as the 
sum of two squares 
(/3) On numbers which are the sum of three squares . 
(y) Composition of numbers as the sum of four squares 
Conspectus of Arithmetica, with typical solutions 
The treatise on Polygonal Numbers . . 
440 
440 441 
441-443 
443 
443- 444 
444- 447 
448 
448- 450 
449- 514 
449-450 
451-452 
453 
453-455 
455- 461 
456- 457 
458- 459 
459- 460 
462-479 
462-476 
462- 463 
463- 465 
465 
465 
466-473 
466-468 
468- 473 
469- 472 
472- 473 
473- 476 
473-475 
475- 476 
476- 477 
477- 479 
479-484 
481-483 
483 
483- 484 
484- 514 
514-517 
XXI. COMMI 
Seren 
Theon 
Con 
Edil 
Edil 
Hypat 
Porph 
Proclu 
Con 
(« 
•■(/s 
Hjp 
Coir 
Marin 
Domn 
Simpli 
Exti 
Eutoc; 
An the: 
On 1 
The Pi 
Gtodat 
Micha 
Georgi 
Maxin 
Exti 
Two 
Man ut 
. Nicola 
Ruh 
ni 
Ioannt 
Barlaa 
Isaac I 
APPENDIX, 
of a spirai 
INDEX OF ( 
ENGLISH TN