Science & Education 13: 321–332, 2004. © 2004 Kluwer Academic Publishers. Printed in the Netherlands. 321 The Treatment of the Motion of a Simple Pendulum in some Early 18th Century Newtonian Textbooks COLIN GAULD University of New South Wales, School of Education, 9 Michael Crescent, Kiama Downs, NSW, 2533; E-mail: cgauld@smartchat.net.au Abstract. The treatment of pendulum motion in early 18th century Newtonian textbooks is quite different to what we find in today’s physics textbooks and is based on presuppositions and math- ematical techniques which are not widely used today. In spite of a desire to present Newton’s new philosophy of nature as found in his Principia 18th century textbook analysis of pendulum motion appears to owe more to Galileo’s insights than to those of Newton. The following case study outlines this analysis and identifies some of its distinctive features as a resource for teachers wishing to refer to this period in the history of science. 1. Introduction Following the publication of Newton’s Principia in 1687 many other writers began to promulgate the new mathematical and experimental philosophy which Newton had presented there. That book was structured on the Euclidean model of Axioms, Propositions and Theorems (see Newton 1729/1960) and many of those who ad- opted Newton’s philosophy structured their books in the same way. Many parts of Newton’s book were complex with much detail or sketchy with important detail omitted so that one main purpose of his disciples was to present the bones of his argument as clearly as possible. Although Newton, along with Leibniz, was credited with the invention of the calculus the Principia did not use that device. Instead its arguments were often based on the use of small and vanishing quantities which preceded the introduction of the calculus. He (and others before and after) rarely used equations but instead based his arguments on proportional relation- ships. Newton did not discuss the theory behind motion of the simple pendulum (except in a very condensed form when discussing Proposition XXIV of Book II of the Principia; see Densmore 1995, pp. 317–332) but instead focused his attention, as far as pendulum motion is concerned, in Section X of Book I of the Principia, on the motion of the cycloidal pendulum under the influence of a central force. In Section VI of Book II he deals with the motion of a cycloidal pendulum in a resisting medium (Newton 1729/1960). Some of the books produced to present Newton’s philosophy were for use in university lecture halls (for example, Desaguliers 1734, 1745; Keill 1720;