of Salt Lake City, who read the first part of my work in manuscript, I desire to express my hearty thanks. But in acknowledging their kindness, I trust that I shall not seem to lay upon them any share in the responsibility for errors which I may have introduced in subsequent revision of the text.

FLORIAN CAJORI.

COLORADO COLLEGE, December, 1893.

BOOKS OF REFERENCE.

The following books, pamphlets, and articles have been used in the preparation of this history. Reference to any of them is made in the text by giving the respective number. Histories marked with a star are the only ones of which extensive use has been made.

1. Günther, S. Ziele und Resultate der neueren Mathematisch-historischen Forschung. Erlangen, 1876.

2. CAJORI, F. The Teaching and History of Mathematics in the U. S. Washington, 1890.

3. CANTOR, MORITZ. Vorlesungen über Geschichte der Mathematik. Leipzig. Bd. I., 1880; Bd. II., 1892.

4. EPPING, J. Astronomisches aus Babylon. Unter Mitwirkung von P. J. R. STRASSMAIER. Freiburg, 1889.

5. BRETSCHNEIDER, C. A. Die Geometrie und die Geometer vor Euklides. Leipzig, 1870.

6. *Gow, JAMES. A Short History of Greek Mathematics. Cambridge, 1884.

7. *HANKEL, HERMANN. Zur Geschichte der Mathematik im Alterthum und Mittelalter. Leipzig, 1874.

8. *ALLMAN, G. J. Greek Geometry from Thales to Euclid. Dublin, 1889.

9. DE MORGAN, A.

"Euclides" in Smith's Dictionary of Greek and

Roman Biography and Mythology.

10. HANKEL, HERMANN. Theorie der Complexen Zahlensysteme. Leipzig, 1867.

11. WHEWELL, WILLIAM. History of the Inductive Sciences.

12. Zeuthen, H. G. Die Lehre von den Kegelschnitten im Alterthum.

Kopenhagen, 1886.

ix

13. *CHASLES, M. Geschichte der Geometrie. Aus dem Französischen übertragen durch DR. L. A. SOHNCKE. Halle, 1839.

14. MARIE, MAXIMILIEN. Histoire des Sciences Mathématiques et Physiques. Tome I.-XII. Paris, 1883-1888.

15. COMTE, A. Philosophy of Mathematics, translated by W. M. GIL

LESPIE.

16. HANKEL, HERMANN. Die Entwickelung der Mathematik in den letzten Jahrhunderten. Tübingen, 1884.

17. GÜNTHER, SIEGMUND und WINDELBAND, W. Geschichte der antiken Naturwissenschaft und Philosophie. Nördlingen, 1888.

18. ARNETH, A. Geschichte der reinen Mathematik. Stuttgart, 1852. 19. CANTOR, MORITZ. Mathematische Beiträge zum Kulturleben der Völker. Halle, 1863.

20. MATTHIESSEN, LUDWIG. Grundzüge der Antiken und Modernen Algebra der Litteralen Gleichungen. Leipzig, 1878.

21. OHRTMANN und MÜLLER. Fortschritte der Mathematik.

22. PEACOCK, GEORGE. Article " Arithmetic," in The Encyclopædia of Pure Mathematics. London, 1847.

23. HERSCHEL, J. F. W. Article "Mathematics," in Edinburgh Ency

clopædia.

24. SUTER, HEINRICH.

Zürich, 1873-75.

Geschichte der Mathematischen Wissenschaften.

25. QUETELET, A. Sciences Mathématiques et Physiques chez les Belges. Bruxelles, 1866.

26. PLAYFAIR, JOHN. Article "Progress of the Mathematical and Physical Sciences," in Encyclopædia Britannica, 7th edition, continued in the 8th edition by SIR JOHN LESLIE.

27. DE MORGAN, A. Arithmetical Books from the Invention of Printing to the Present Time.

28. NAPIER, MARK.

burgh, 1834.

Memoirs of John Napier of Merchiston. Edin

29. HALSTED, G. B. “Note on the First English Euclid," American Journal of Mathematics, Vol. II., 1879.

30. MADAME PERIER. The Life of Mr. Paschal. Translated into English by W. A., London, 1744.

31. MONTUCLA, J. F. Histoire des Mathématiques. Paris. 1802. 32. DÜHRING E. Kritische Geschichte der allgemeinen Principien der Leipzig, 1887.

Mechanik.

33. BREWSTER, D.

34. BALL, W. W. R.

The Memoirs of Newton. Edinburgh, 1860.

A Short Account of the History of Mathematics. London, 1888, 2nd edition, 1893.

35. DE MORGAN, A. "On the Early History of Infinitesimals," in the Philosophical Magazine, November, 1852.