On Positivism:

"The first characteristic of Positive Philosophy is that it regards all phenomena as subject ot invariable natural Laws. . . .Our real business is to analyze accurately the circumstances of phenomena, and to connect them by the natural relations of succession and resemblance" (Comte, 1830, 5-6).

"For it is only by knowing the laws of phenomena, and thus being able to foresee them, that we can . . . set them to modify one another for our advantage. . . . Whenever we effect anything great it is through a knowledge of natural laws. . . . From Science come Prevision; from Prevision comes Action" (The Positive Philosophy of Auguste Comte I, 20-21) 

"We shall find that there is no chance of order and agreement but in subjecting social phenomena, like all others, to invariable natural laws, which shall, as a whole, prescribe for each period, with entire certainty, the limits and character of social action" (I, p. 216).

"The office of science is not to govern, but to modify phenomena; and to do this it is necessary to understand their laws"  (II, p. 240). 

On Methods: 

"No social fact can have any scientific meaning till it is connected with some other social facts" (II, p. 245).

"If it is true that every theory must be based upon observed facts, it is equally true that facts cannot be observed without the guidance of some theory"  (Comte, 1830, p. 4).

"No real observation of any phenomena is possible, except in so far as it is first directed, and finally interpreted, by some theory" (Comte, 1830, p. 243). 

"Experimentation takes place whenever the regular course of the phenomenon is interfered with in any determinate manner. . . . Pathological cases are the true scientific equivalent of pure experimentation" (II, p. 245). 

[The chief method for the social scientist] "consists in a comparison of the different co-existing states of human society on the various parts of the earth's surface--these states being completely independent of each other.  By this method, the different stages of evolution may all be observed at once" (II, p. 249). 

"The historical comparison of the consecutive states of humanity is not only the chief scientific device of the new political philosophy . . . it constitutes the substratum of the science, in whatever is essential to it"  ((II, p. 251). 

On the Division of Labor: 

[Men and women are] "bound together by the very distribution of their occupations; and it is this distribution which causes the extent and growing complexity of the social organism (II, p. 292).

"The social organization tends more and more to rest on an exact estimate of individual diversities, by so distributing employments as to appoint each one to the destination he is most fit for, from his own nature. . . , from his education and his position, and, in short, from all his qualifications; so that all individual organizations, even the most vicious and imperfect . . ., may finally be made use of for the general good" (II, p. 292).

"If the separation of social functions develops a useful spirit of detail, on the one hand, it tends on the other, to extinguish or to restrict what we may call the aggregate of general spirit.  In the same way, in moral relations, while each individual is in close dependence on the mass, he is drawn away from it by the expansion of his special activity, constantly recalling him to his private interest, which he but very dimly perceives to be related to the public. . . . The inconveniences of the division of functions increase with its characteristic advantages" (II, p. 293). 

[Temporal and spiritual power should unite] "to keep up the idea of the whole, and the feeling of the common interconnection" 
(II, p. 294). 

On Functionalism: 

"There must always be a spontaneous harmony between the parts and the whole of the social system. . . . It is evident that not only must political institutions and social manners, on the one hand, and manner and ideas on the other, be always mutually
connected; but further that this consolidated whole must always be connected, by its nature, with the corresponding state of the integral development of humanity" (II, p. 222). 

Sources: 

Martineau, Harriet. (Translator) 1896.  The Positive Philosophy of Auguste Comte, Volumes I, II, and III. London:  Bell.