"The great body of population dynamics, like those of the motion of the celestial bodies, can be solved—and what is most remarkable, there is a surprising analogy between the formulas employed in these calculations. I believe that I have achieved to some extent what I have long said about the possibility of founding a social mechanics on the model established by celestial mechanics—to formulate the motions of the social body in accordance with those of celestial bodies, and to find there again the same properties and laws of conservation."

“I have sought to determine... the different relations of bulk, subsisting between the various parts of his frame; and to ascertain how far these relations become modified during his development, what they are in the flower of his age, and in what position they remain up to the instant of decay.”

“It is of primary importance to keep out of view man as he exists in an insulated, separate, or in an individual state, and to regard him only as a fraction of the species. In thus setting aside his individual nature, we get quit of all which is accidental, and the individual peculiarities, which exercise scarcely any influence over the mass, become effaced of their own accord, allowing the observer to seize the general results.”

“As laws and the principles of religion and morality are influencing causes, I have then not only the hope, but, what you have not, the positive conviction, that society may be ameliorated and reformed.”

“I would suggest... the idea of a work which should have for its object the analytic examination of the development of our intellectual faculties for each age. Now, I have aimed to present, in the work here reproduced, only an essay, only a particular example, of such an analysis, "which tends to show that the maximum of energy of the passions occurs about the age of twenty-five." The minimum is not then determined; and even when it shall be, by a sufficient number of observations, one will no more be able to apply it to any given individual in particular, than one could make use of a table of mortality to determine the period of his decease.”

“Having for their object the Science of Man, present difficulties exceedingly great, and, to merit confidence, must be collected upon a scale far too extended to be attempted by an individual philosopher.”

“The principal artists of the era of the revival of letters, such as Leon Baptista Alberti, Michael Angelo, Leonardo da Vinci, Albert Durer, with many others who what art ought to borrow from science, felt the necessity of resorting to observation, in order to rebuild in some sort the ruined monument of ancient artistical skill. They studied nature in a philosophical manner; sought to strike out the limits within which they ought to confine themselves in order to be truthlike... and from those profound studies which kept them ever before the face of nature, they deduced original views and new models, destined to distinguish for ever that celebrated age. The proportions of the human body did not alone attract their attention: anatomy, perspective, and chemistry, formed parts of their studies; nothing was neglected; and some of these great artists even gained for themselves a first place among the geometers of their day. Their successors have not devoted themselves to such serious studies, and hence it so frequently happens that they are reduced to content themselves, either with copying from those who went before them, or with working after individual models, whose proportions they modify according to mere caprice, without having any just or proper ideas of the beautiful.”