Woman's political equality with man is the legitimate outgrowth of the fundamental principles of our government.

which two connotations does the word legitimate have in this line from the text?

valid
legal
logical
typical
official

I would say that the connotations of the word legitimate has in the line would be:

Valid and Legal 

Im not sure maybe a crying laughing emoji

Jonathan swift is using a satirical approach to make awareness to the fact that there are too many beggars (which include women and young children) on the streets. his solution? eat the children. yes this sounds like the craziest thing in the world but it's a solution. the children could be sold to landlords to pay rent and the family could have stuffed bellies. he lists the advantages, disadvantages, and the rebuttal to the disadvantages to support his claim. he also suggest what age should be the highest price and how to cook them. in the end, he excludes himself from his solution. all i all, swift uses a satirical approach to get people aware of the beggars that flood their streets.if you need more for "a modest proposal", i am here.