"It is a maxim universally admitted in geometry, and indeed in every branch of knowledge, that, in the progress of investigation, we should proceed from known facts to what is unknown. ...In this manner, from a series of sensations, observations, and analyses, a successive train of ideas arises, so linked together, that an attentive observer may trace back to a certain point the order and connection of the whole sum of human knowledge."

“One of the most fundamental principles of Lavoisier's chemistry was the use of numbers, notably in relation to what we often call today the principle of conservation of mass... The principle implies that the experimenter must not only keep account of all the reacting solids and liquids, but also the gases—that is, all of the products. ...This rule led to quantitative experiments. Lavoisier was not the first person to use numbers in chemistry but he was a pioneer in using such numerical measurements as the basis of his system of chemistry. ...When Lavoisier first announced this law, chemists generally believed in... "phlogiston" which supposedly entered into chemical reactions but had no weight. It was a radical step, therefore, for Lavoisier to base a system of chemistry on a balance of weights and to maintain that chemistry is not concerned with weightless "substances." ...this was indeed a chemical revolution.”

“The art of concluding from experience and observation consists in evaluating probabilities, in estimating if they are high or numerous enough to constitute proof. This type of calculation is more complicated and more difficult than one might think. It demands a great sagacity generally above the power of common people. The success of charlatans, sorcerors, and alchemists—and all those who abuse public credulity—is founded on errors in this type of calculation.”

“Here, then: a revolution has taken place in an important part of human knowledge since your departure from Europe... I will consider this revolution to be well advanced and even completely accomplished if you range yourself with us. ...After having brought you up to date on what is happening in chemistry, it would be well to speak to you about our political revolution. We regard it as done and without any possibility of return to the old order.”

“The extension of Black's method by the physicist Lavoisier led to the downfall of the purely qualitative theory of phlogiston, and gave to chemistry the true methods of investigation, and its first great quantitative law—the law of conservation of matter.”

“We must trust to nothing but facts: These are presented to us by Nature, and cannot deceive. We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation.”

“Now Mayow, like Boyle, conceived the air as made up of minute particles, while he restricted himself to two varieties, those, namely, which are necessary to life, called by him "spiritus igno-aereus," and those incapable of supporting respiration or combustion, which are left after the removal of this "spiritus." Since a mixture of saltpetre and sulphur continued burning even under water, he assumed that his igno-aereal particles must also be contained in the salt. Acids too contained the new principle. ...Mayow died in 1679 at the age of thirty-four years; had he lived but a little longer, it can scarcely be doubted that he would have forestalled the revolutionary work of Lavoisier, and stifled the theory of phlogiston at its birth. As it was, his work, though rendered in one of the most luminous and convincing scientific publications of the period, was immediately forgotten, and so proved of little effect on the evolution of our modern chemical system.”