"There are certain cases in which a force acts for so short a time that it is difficult to estimate either its intensity or the time during which it acts. But it is comparatively easy to measure the effect of the force in altering the motion of the body on which it acts..."
"There is another maxim... which asserts "That like causes produce like effects." This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. ...there are ...cases in which a small initial variation may produce a very great change in the final state of the system..."
"The motion of a material particle which has continuous existence in time and space is the type and exemplar of every form of continuity."
"The primary property of matter was indeed distinctly announced by Descartes in what he calls the "First Law of Nature": "That every individual thing, so far as in it lies, perseveres in the same state, whether of motion or of rest."
"We shall find it more conducive to scientific progress to recognise, with Newton, the ideas of time and space as distinct, at least in thought, from that of the material system whose relations these ideas serve to co-ordinate."
"It is an observed fact that bodies of equal mass, placed in the same position relative to the earth, are attracted equally towards the earth whatever they are made of; but this is not a doctrine of abstract dynamics founded on axiomatic principles, but a fact discovered by observation, and verified by the careful experiments of Newton on the times of oscillation of hollow wooden balls suspended by strings of the same length, and containing gold, silver, lead, glass, sand, common salt, wood, water, and wheat. ...measuring the length of a pendulum which swings seconds."
"There is a maxim which is often quoted, that "The same causes will always produce the same effects." To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more than once, so that the causes and effects cannot be the same in all respects. What is really meant is that if the causes differ only as regards the absolute time or the absolute place at which the event occurs, so likewise will the effects."