Based on the following excerpt from Stephen Douglas' 1858 speech, delivered during one of the Lincoln-Douglas debates, what did Lincoln and Douglas believe about racial equality and slavery?
[Lincoln] says looks forward to a time when slavery shall be abolished [made illegal] everywhere. I look forward to a time when each State shall be allowed to do as it pleases. If it chooses to keep slavery forever, it is not my business, but its own; if it chooses to abolish slavery, it is its own business,—not mine. I care more for the great principle of self-government, the right of the people to rule, than I do for all the negroes in Christendom...I would not blot out the great inalienable rights of the white men, for all the negros that ever existed.
Just from this excerpt, you cannot know anything about Lincoln's positions other than Douglas's statement that Lincoln wants slavery abolished.
In truth, Lincoln and Douglas believed in some very similar things. Neither of them believed at all in racial equality. Douglas makes clear in this excerpt that he does not think blacks matter as much as whites. Lincoln felt much the same way.
However, Lincoln and Douglas did differ to some degree on slavery. Douglas thought (as he says in the excerpt) that any state that wanted slavery should be able to have it. Lincoln wanted slavery to be contained so that it could not spread to any new states. He did hate slavery, but he did not intend to use the power of the government to abolish it--just to keep it from spreading.