## Introduction

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Natural Philosophy Including Mathematics, Optics, and Alchemy
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In Newton's day, the term "natural philosophy" referred to the physical sciences, and Newton's work in this area was informed by his belief in a universe which operated on mechanical principles and which was set into motion by God. His scientific study focused on identifying the nature of these mechanical principles. In the course of this study, Newton discovered, developed, and elucidated the mathematical rules by which motion is governed; the fruits of this labor are presented in *Philosophiae Naturalis Principia Mathematica* (1687). Newton also sought to examine through extensive experimentation the properties of light and color, and his findings are published in *Opticks* (1704). modern critics analyze and debate Newton's scientific and mathematical achievements as evidenced by these two works as well as by several of Newton's unpublished papers. Another area of critical discussion focuses on the historical sources that may have influenced Newton's work. Newton's interest in alchemy has proved to be a topic of controversy among critics, as many students and scholars of Newton find it difficult to reconcile his rational, scientific work with a subject deemed occult and false.

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Major Works
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Many of the calculations found in *Principia* were worked out by Newton many years earlier, after he had returned to his home in Woolsthorpe, when Trinity College closed due to the plague in 1665. In 1684 astronomer Edmund Halley approached Newton, asking him to describe the orbit of the planets. Newton responded that he had mathematically determined the orbit to be elliptical. Halley urged Newton to send him the calculations, which Newton did. With Halley's encouragement and patronage, Newton elaborated and expanded the work, which became the *Principia.* In this work, Newton explains the laws of the motion of the planets, moons, comets, the tides, and the earth. He also presents his theory of universal gravitation. The differential calculus Newton had earlier developed became a tool used for the calculations in *Principia.* In *Opticks,* Newton presents the results of his experiments with prisms, in which he had broken down white light into a spectrum of primary colors. This led to his theory that light was comprised of individual particles, or corpuscles. Also described in *Opticks* are Newton's experiments with colors of thin films. These experiments led to his theory that light could be both reflected and refracted. Additionally, *Opticks* contained a list of "Queries," in which Newton speculates not only about light and color, but other subjects of physics and philosophy as well.

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Critical Reception
**

Modern critics have continued to assess the relevance and significance of Newton's mathematical and scientific achievements. After noting the influence of Johannes Kepler and Galileo on Newton, Albert Einstein examined Newton's approach to the problem of motion and comments on the importance of Newton's findings. Einstein noted that while the theories of electromagnetic fields and relativity have limited the significance of some of Newton's work, Newton's mechanics nevertheless paved the way in other areas, making a theory of fields possible. Unlike Einstein, Brian Ellis has argued that Newton's laws of motion are more historically related to Cartesian physics than to Galileo's work in kinematics. In addition to demonstrating Newton's debt to René Descartes, Ellis also emphasizes the conceptual nature of Newton's laws of motion, arguing that they are not deduced from or supported by observation or experimentation. Rupert Hall and Marie Boas Hall center their study on Newton's theory of matter, maintaining that his unpublished manuscripts on this subject help to demonstrate the development of his theory. The critics discussed Newton's exploration of the role of aether in the movement of particles and commented on the influence of Newton's theological beliefs on his theory of matter. Critics such as Robert B. Downs and I. Bernard Cohen focus on the subject matter and significance of the *Principia.* Downs surveys the content of the three books of the *Principia* and emphasizes Newton's application of mathematics to the movement of bodies. Likewise, Cohen states that "Newton's outstanding achievement was to show how to introduce mathematical analysis into the study of nature in a new and particularly fruitful way." Cohen goes on to identify the aspects of *Principia* which may be deemed "revolutionary."

Given that Newton's achievements in mathematics made his scientific discoveries possible, it is not surprising that much, criticism has been devoted to the discussion of Newton's mathematical studies and accomplishments. E. W. Strong explores the procedure Newton identified as a method for "mathematically determining all kinds of phenomena." In particular, Strong underscores the importance to Newton of measurement, experimental investigation, and demonstration from principles. In evaluating Newton's contributions to mathematics, D. T. Whiteside states that Newton "transmuted the received theoretical bases of infinitesimal calculus, dynamics, and optics into their classical forms." Whiteside also discusses Newton's discovery of the general binomial expansion and maintains that fluxional calculus is Newton's "undivided glory."

Just as aspects of Newton's thinking on matter and motion have been supplanted by twentieth-century developments in science, so has his corpuscular theory of light. Nevertheless, his work in the area of light and color laid the foundation for future study. I. Bernard Cohen, in his examination of the content, textual history, and contemporary reception of Newton's *Opticks,* demonstrates that while the work was an exposition of the corpuscular theory of light, it also contained many basic principles of "undulation," or wave theory. The fact that Newton adopted two competing theories in one essay, Cohen explains, accounts for the negative reception the work received in the nineteenth century. In the eighteenth century, *Opticks* had gained much more popular appeal than *Principia.* Cohen compares the two works and argues that while *Principia* is "forbidding" to the nonspecialist, *Opticks* is more able to capture and retain the interest of the layperson. Additionally, Cohen observes, *Opticks* was published in English and written in an intimate style, whereas *Principia* was written in Latin, which was characteristic of its emphasis on mathematical principles. Thomas S. Kuhn analyzes the content of the papers on optical theory that Newton published in scientific journals. While Kuhn identifies the significance of Newton's findings in these papers, he also identifies problem areas in Newton's experimental procedures and presentation, such as Newton's habit of failing to fully explain the intellectual extrapolations he makes.

Critics who study Newton's interest in alchemy, evidenced by his many notebooks on the subject, write against a tradition that downplays or ignores Newton's alchemical studies. P. M. Rattansi states that many critics find Newton's interest in a subject such as alchemy completely inconsistent with his rational, scientific studies. The relationship between these two areas of study may be better understood, Rattansi contends, if Newton's interest in both biblical studies and ancient natural philosophy are further examined. Rattansi explains that the underlying assumptions of Newton's study of biblical prophesy and ancient natural philosophy was that truth about the "true system of the world," among other things, was given to man in ancient times but in a veiled and mysterious way, as in Scripture. It is Rattansi's suggestion that Newton's alchemical studies represented, like the rest of Newton's interest, his search for truth. Similarly, Betty Jo Teeter Dobbs argues that for Newton and his search for truth, no singular approach to knowledge was sufficient. For Newton, Dobbs maintains, the search for the "alchemical spirit" was one way of identifying God's action in the world. Additionally, Dobbs stresses that Newton's work in alchemy influenced his scientific thought. As Dobbs and other critics have argued, Newton sought a unified system of God and nature, and his work in mathematics, optics, motion, matter, and alchemy all supported this goal.