The elements of non-Euclidean plane geometry and trigonometry, by H. S. Carslaw.

CONTENTS
CHAPTER 1.
THE PARALLEL POSTULATE, AND THE WORK
OF SACCHERI, LEGENDRE AND GAUSS.
PAGE
~ 1. Euclid's treatment of parallels - - 1
~ 2. The principle of continuity - - - 2
~ 3. Some problems of construction - - - - - 5
~ 4. Two theorems independent of the Parallel Postulate - - 8
~ 5. The controversy regarding the Parallel Postulate - - 10
~ 6. The work of Saccheri - --- 12
~ 7. The work of Legendre -- - 15
~ 8. The Postulate of Archimedes and the Parallel Postulate 18
~ 9. The work of Gauss - -- 19
~ 10. Gauss and Schweikart - - 21
~ 11. Gauss and Taurinus 23
~ 12. Gauss and Schumacher - 25
CHAPTER II.
THE WORK OF BOLYAI, LOBATSCHEWSKY, AND RIEMANN,
THE FOUNDERS OF THE NON-EUCLIDEAN GEOMETRIES.
~ 13. John Bolyai, and his father Wolfgang - - 27
~ 14. Bolyai's Appendix - --- 28
~ 15. Bolyai's later years - - - 30
~ 16. The work of Lobatschewsky - - -- 32
~ 17. Lobatschewsky's Principles of Geometry 33
~ 18. Gauss, Bolyai, and Lobatschewsky - - - 36
~~ 19-20. The work of Riemann - --- 38