The Mathematics Of Collision And The Collision Of Mathematics In The 17th Century

THE MATHEMATICS OF COLLISION AND THE COLLISION OF MATHEMATICS IN THE 17TH CENTURY Scott J. Hyslop Submitted to the faculty of the University Graduate School in partial fulfillment of the requirements for the degree Doctor of Philosophy in the Department of History and Philosophy of Science, Indiana University December 2015   ProQuest Number: 3745588 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest 3745588 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 Accepted by the Graduate Faculty, Indiana University, in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Doctoral Committee ___________________________________ Domenico Bertoloni Meli, Ph.D. ___________________________________ Amit Hagar, Ph.D. ___________________________________ William Newman, Ph.D. ___________________________________ Jordi Cat, Ph.D. August 31, 2015   ii Copyright © 2015 Scott J. Hyslop   iii To Patty & Thea   iv Acknowledgements I would like to thank, first and foremost, my adviser Domenico Bertoloni Meli, whose guidance, encouragement, and support made the realization of this project possible. I also had the great fortune and honor to have such exemplary scholars on my committee as Jordi Cat, Amit Hagar, and William Newman, who have provided much needed criticism, illuminating insight, and thoughtful instruction in dissertation reading groups, private discussion, and seminars. I aspire to the standards of precision and discipline that Professor David McCarty set in his classes on logic and the philosophy of mathematics. And I continue to be moved by the impetus that Carl Pearson impressed on his students through his enthusiasm and instruction. My interest in the history and philosophy of science and technology is inspired by Professor Gordon Brittan at Montana State University. The very best of my ideas are shaped by the unparalleled and iconoclastic Professor Lynda Sexson. I would like to thank my fellow graduate students for the conversation and camaraderie, particularly Tawrin Baker, Nicolas Bamballi, Nick Best, Stephen Friesen, Ashley Inglehart, and Patrick McNeela, as well as those early modernists who showed me the way, Karin Ekholm, Joel Klein, Evan Ragland, and Allen Shotwell. The Department of History and Philosophy of Science and Medicine, the Department of Mathematics, and the Department of Philosophy supported me throughout my time at Indiana University by providing me with opportunities to teach as an Associate Instructor. The staff of these departments have helped me in innumerable ways. I would particularly like to thank Stephanie Bennett, Becky Bledsoe, Marge Clark, and Peggy Roberts. I am very grateful for the support of the University Graduate School.   v When I first arrived at IU in the HPS MA program, Sander Gliboff, my first adviser, provided much needed guidance. Thank you. This project was born in Nico's seminar on mechanics, and was cultivated by my experiences in Ghent and Leiden, where I participated in a conference organized by Maarten Van Dyck and Albrecht Heeffer, "The Philosophical Aspects of Symbolic Reasoning in Early Modern Science," and viewed some of Huygens's manusc