Newton Quotes - page 5
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 method applied by Newton to the grounding of the Infinitesimal Calculus, and which since the beginning of this century has been recognised by the best mathematicians as the only one that furnishes sure results, is the method of limits. The method consists in this, viz., instead of considering a continuous transition from one value of a quantity to another, from one position to another, or, speaking generally, from one determination of a concept to another, one considers in the first place a transition through a finite number of intervals and then allows the number of these intervals to increase so that the distances of two successive points of division all decrease infinitely.
Bernhard Riemann
Gradually... during the second half of the nineteenth century, the uncomfortable feeling of dislike of the action at a distance, which had been so strong in Huygens and other contemporaries of Newton, but had subsided during the eighteenth century, began to emerge again, and gained strength rapidly.
This was favoured by the purely mathematical transformation (which can be compared in a sense with that from the Ptolemaic to the Copernican system), replacing Newton's finite equations by the differential equations, the potential becoming the primary concept, instead of the force, which is only the gradient of the potential. These ideas, of course, arose first in the theory of electricity and magnetism or perhaps one should say in the brain of Faraday.
Willem de Sitter
The word hypothesis has now a somewhat different significance from that given it by Newton. We are now accustomed to understand by hypothesis all thoughts connected with the phenomena.
Newton was far from the crude thought that explanation of phenomena could be attained by abstraction.
Bernhard Riemann
I remember from my school days Archimedes jumping into his bath and displacing water and coming up with his famous principle, and of course Isaac Newton being hit on the head with an apple. In other words, this realm of human knowledge - which is mathematical, essentially - can have a playful visual element to it.
James Marsh
Newton's own motto, "hypotheses non fingo" was, in a sense, disregarded by Newton himself: he rejected hypotheses only where they violated his own "regula philosophandi", that is to say, his principle of their strict parsimony. In terms of present-day methodology, we reject hypotheses as scientifically meaningless if they are incapable even of indirect test; and we reject them as superfluous or as implausible if they are too complex and artificial to conform with well established canons of inductive probability. But freedom of scientific theorizing must be preserved wherever the conditions of meaningfulness and of economy appear to be satisfied.
Arthur Beer
Let me close by reminding you of what Newton actually did on the day that he conceived G = k \frac{mm'}{r^2}. ...Newton did not have any subsidies, grants, funds, Secret Service money. But he had the moon. He said, "... I cannot throw a ball round the world, but let me picture the moon as if it were a ball which has been flung around the world... How long will it take to go round the world?" ...He knew the value of gravity at the earth's surface ...but he did not know the value of the earth's gravity for the moon. He said, "Let us suppose that it is given by an inverse square law. Now, how long will it take the moon to go around?"
Jacob Bronowski
Let me end with... man's ageless fantasy, to fly to the moon.... Plutarch and Lucian, Ariosto and Ben Jonson wrote about it, before the days of Jules Verne and H. G. Wells and science fiction. The seventeenth century was heady with... fables about voyages to the moon. Kepler wrote one full of deep scientific ideas... wrote... The Discovery of a New World. They did not draw a line between science and fancy... they all tried to guess where... earth's gravity would stop. Only Kepler understood that gravity has no boundary, and put a law to it-... the wrong law.
All this was a few years before Isaac Newton was born, and it was all in his head that day in 1666, when he... came to conceive... that the moon is like a ball... thrown so hard that it falls exactly as fast as the horizon... he went on to calculate how long... the distant moon would take to round the earth... [T]he imagination that day chimed with nature, and made a harmony.
Jacob Bronowski
