Principia Quotes
Newton was born during Cromell's revolution in the troubled 1640s; he was eighteen at the Restoration in 1660; and he published the Principia during the intrigues which ended by bringing William of Orange to England in the revolution of 1688. These are the moments when the powerful or the forceful character feels the ferment of the times, when his thoughts quicken...
Jacob Bronowski
Isaac Newton's Philosophae Naturalis Principia Mathematica abstracted time from events, establishing its tractability to scientific calculation. Conceived as pure, absolute duration, without qualities, it conforms perfectly to its mathematical idealization (as the real number line). Since time is already pure, its reality indistinguishable from its formalization, a pure mathematics of change – the calculus – can be applied to physical reality without obstruction. The calculus can exactly describe things as they occur in themselves, without straying, even infinitesimally, from the rigorous dictates of formal intelligence. In this way natural philosophy becomes modern science.
Nick Land
So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.
Bertrand Russell
Of the many references to Newton in 18th-century electrical writings only a small number were to the Principia, the greater part by far were to the Opticks. This was true not alone of the electrical writings but also in other fields of experimental enquiry.... [The Opticks] would allow the reader to roam, with great Newton as his guide, through the major unresolved problems of science and even the relation of the whole world of nature to Him who had created it.... in the Opticks Newton did not adopt the motto... -Hypotheses non fingo; I frame no hypotheses-but, so to speak, let himself go, allowing his imagination full reign and by far exceeding the bounds of experimental evidence.
I. Bernard Cohen
The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of Newton, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier's Descriptio.
James Whitbread Lee Glaisher
The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with the general method of Frege, Whitehead and Russell. Following these authorities, I hold that mathematics is part of logic, and so belong to what may be called the logical school as opposed to the formalist and intuitionist schools. I have therefore taken Principia Mathematica as a basis for discussion and ammendment; and believe myself to have discovered how, by using the work of Mr Ludwig Wittgenstein, it can be rendered free from the serious objections which have caused its rejection by the majority of German authorities, who have deserted altogether its line of approach.
Frank P. Ramsey
But to return to the Newtonian Philosophy: Tho' its Truth is supported by Mathematicks, yet its Physical Discoveries may be communicated without. The great Mr. Locke was the first who became a Newtonian Philosopher without the help of Geometry; for having asked Mr. Huygens, whether all the mathematical Propositions in Sir Isaac's Principia were true, and being told he might depend upon their Certainty; he took them for granted, and carefully examined the Reasonings and Corollaries drawn from them, became Master of all the Physics, and was fully convinc'd of the great Discoveries contained in that Book.
John Theophilus Desaguliers
A particle moving with a uniform velocity would be denoted by Wallis by the formula s = vt, ...while previous writers would have denoted the same relation by stating what is equivalent to the proposition s1 : s2 = v1t1 : v2t2 (see e.g. Newton's Principia, bk. I. sect. I., lemma 10 or 11).
John Wallis
