What purpose does each quote serve in paragraphs 6-8 of Gould's essay "Women's Brains"?
Considering that paragraph eight of Gould's essay is one line, "Sound familiar?" I assume you are speaking of three three quotes within paragraphs 5-7. Just those two words from paragraph eight do a lot to explain these quotes, but let's look at them in turn, just to show that they are meant to show the antiquated and erroneous thoughts about men's brains being superior to women's brains according to the mistaken Topinard and Le Bon.
In short, if you haven't read the essay yet, be ready to get angry. Or perhaps I should say, get ready to see the reasoning as to why American women couldn't vote until 1920. Then again, maybe you will laugh at these quotations.
Here is the first quote from paragraph five by Topinard:
The man who fights for two or more in the struggle for existence, who has all the responsibility and the cares of tomorrow, who is constantly active in combating the environment and human rivals, needs more brain than the woman whom he must protect and nourish, the sedentary woman, lacking any interior occupations, whose role is to raise children, love, and be passive.
In the most intelligent races, as among the Parisians, there are a large number of women whose brains are closer in size to those of gorillas than to the most developed male brains. This inferiority is so obvious that no one can contest it for a moment; only its degree is worth discussion. All psychologists who have studied the intelligence of women, as well as poets and novelists, recognize today that they represent the most inferior forms of human evolution and that they are closer to children and savages than to an adult, civilized man. They excel in fickleness, inconstancy, absence of thought and logic, and incapacity to reason.
A desire to give them the same education, and, as a consequence, to propose the same goals for them, is a dangerous chimera. The day when, misunderstanding the inferior occupations which nature has given her, women leave the home and take part in our battles; on this day a social revolution will begin, and everything that maintains the sacred ties of the family will disappear.
The opening quote in paragraphs 6 to 8 illustrates the fallacy that function follows size. Gustave Le Bon says women's brains mirror the size of gorilla brains. That this illustrates female inferiority falls flat when Le Bon says "some distinguished women, very superior to the average man," should be considered as extraordinary as a gorilla born with two heads. One side of the argument says that women have the intelligence of a lesser being because of similarity in brain size; but, considering that there are many intelligent women, we must conclude that here exact science is taking a back seat to deformed fantasy.
Le Bom presents a logical puzzle in his second quote by claiming that a "social revolution" will take place in which "the sacred ties of the family will disappear" if women leave their "inferior occupations." If women are only suited for inferior aspects of society, how could changes in those "inferior occupations" lead to total disruption of the family? Another view (inference) might be that "sacred" family ties require substantial female intelligence as bulwarks of society.