The Contents of the Fifth and Sixth Books of Euclid With a Note on Irrational Numbers

First published in 1908 as the second edition of a 1900 original, this book explains the content of the fifth and sixth books of Euclid's Elements, which are primarily concerned with ratio and magnitudes. Hill furnishes the text with copious diagrams to illustrate key points of Euclidian reasoning. This book will be of value to anyone with an interest in the history of education.

1. Propositions 1-8. On magnitudes, their multiples and their measures; 2. Propositions 9-12. Commensurable magnitudes; 3. Propositions 13, 14. On ratio; 4. Propositions 15-26. The simpler propositions in the theory of ratios with geometrical applications; 5. Propositions 27-34. Similar figures; 6. Propositions 35, 36. Miscellaneous propositions; 7. Proposition 37. An important proposition in the theory of ratio; 8. Propositions 38-50. On areas; 9. Propositions 51-56. Miscellaneous geometrical propositions; 10. Propositions 57-64. The remaining important theorems in the theory of ratio; 11. Propositions 65, 66. Other propositions in the theory of ratio.