Eduard Jan Dijksterhuis

"Dijksterhuis distinguished five crucial years in the 16th and first half of the 17th century when modern science was born (Dijksterhuis 1950, p. 431):"

"Plato makes the cosmos a living being by investing the world-body with a world-soul."

"[The mathematical character of Descartes' physics lies in its methodological nature, namely, the] axiomatic structure of the whole system, in the establishment of indubitable foundations and the deduction of the phenomena."

"Classical mechanics is mathematical not only in the sense that it makes use of mathematical terms and methods for abbreviating arguments which might, if necessary, also be expressed in the language of everyday speech; it is so also in the much more stringent sense that its basic concepts are mathematical concepts, that mechanics itself is a mathematics."

"Modern science was born in the period beginning with Copernicus's work De Revolutionibus Orbium Coelestium (1543) and ending with Newton's Philosophia Naturalis Philosophiae Mathematica."

"It is pointed out convincingly by George Sarton in The Life of Science that the development of science, as contrasted with that of art, is cumulative and progressive. Every scientist is educated in the current knowledge of his age and, making use of all he has learned, attempts to add something of his own to the existing body of knowledge. For this reason it is essentially impossible to isolate his personal achievements from the total pattern of scientific development. It follows that one cannot write the scientific life story of an isolated scholar, but only the history of the branches of science in which he participated."

"In the course of the fifteenth century, the sexagesimal division of the radius, in terms of which cords and goniometrical line-segments were expressed, was generally superseded, though not immediately replaced, by a decimal system of positional notation. Instead, mathematicians sought to avoid fractions by taking the Radius equal to a number of units of length of the form {\displaystyle 10^{n}} {\displaystyle 10^{n}}...The first to apply this method was the German astronomer Regiomontanus... the second half of the sixteenth and the first decades of the seventeenth century... observed of a gradual development of this method of Regiomontanus into a complete system of decimal positional fractions. Yet none of the steps taken by... writers is comparable in importance and scope with the progress achieved by Stevin in his De Thiende."

"In opposition to Mach and his fellow positivists, Dijksterhuis felt it to be his historian's duty to regard the advance of science as an essentially continuous affair, whereas his equally firmly held conviction that the mathematical treatment of natural phenomena constitutes the essence of scientific method almost forced him to conceive of the origins of early modern science as a decisive break with the past. The inner tension that resulted from this unresolved dilemma is palpable in Dijksterhuis' pioneering Val en worp. Yet in his magisterial The Mechanization of the World Picture, written a quarter- century later, it is present in no lesser degree, although hidden much more deeply under the surface."

"The dangers inherent in the twentieth-century classifications of the ‘mechanistic’ are best illustrated by two important works from the early 1960s. Dijksterhuis’ classic work, The Mechanization of the World Picture, traces the history of the emergence of a concept by looking for antecedents of a modern notion of the ‘mechanistic’ in antiquity. His work illustrates the ways in which focus on the different senses of the term ‘mechanical’ affects the questions that are considered. Taking as a given that atomism is a ‘mechanistic’ theory, Dijksterhuis traces the prehistory, in antiquity, of ideas contributing to what came to be called a ‘mechanical’ world-view – the development of mathematical physics and corpuscular materialism – and scarcely considers the contributions made by the discipline of mechanics.6 Tellingly, he downplays the contribution of the machine analogy to the history he is writing, because of its incompatibility with atomism."

"Mechanics... was an axiomatic construction; and... its problem could be solved quantitatively by algebraic methods."