How we cite our quotes: (Act.Section.Line)
Quote #1
Resolved, That California, with suitable boundaries, ought, upon her application to be admitted as one of the States of this Union, without the imposition by Congress of any restriction in respect to the exclusion or introduction of slavery within those boundaries. (Resolutions.Section 1.2)
This whole compromise business started over California wanting to become an official state, but one without slavery. Remember that it's a huge state that went across the invisible "slavery allowed" line established by the Missouri Compromise of 1820, so California was just messing up the whole super-sophisticated system. Some people argued that California should be two states. Some people still do.
Quote #2
Resolved, That as slavery does not exist by law, and is not likely to be introduced into any of the territory acquired by the United States from the republic of Mexico, it is inexpedient for Congress to provide by law either for its introduction into, or exclusion from, any part of the said territory; and that appropriate territorial governments ought to be established by Congress in all of the said territory , not assigned as the boundaries of the proposed State of California, without the adoption of any restriction or condition on the subject of slavery. (Resolutions.Section 1.3)
This resolution echoes what Daniel Webster said in his Seventh of March speech defending the Compromise plan: there's no need to regulate slavery in Utah and New Mexico, because the land isn't really suited for slave labor. How convenient.
Quote #3
[…] the said Territory, or any portion of the same, shall be received into the Union, with or without slavery, as their constitution may prescribe at the time of their admission. (Utah.Section 1.2)
The sections on the new Utah and New Mexico territories both have this clause, which leaves the "to enslave or not to enslave?" decision up to the people within the new states. It's Stephen Douglas' idea of popular sovereignty, in a nutshell. It had mixed success over the next decade—not so bad for Utah, pretty bad for Kansas later on.
Quote #4
And be it further enacted, That when a person held to service or labor in any State or Territory of the United States, has heretofore or shall hereafter escape into another State or Territory of the United States, the person or persons to whom such service or labor may be due […] may pursue and reclaim such fugitive person, either by procuring a warrant […] or by seizing and arresting such fugitive, where the same can be done without process, and by taking, or causing such person to be taken, forthwith before such court, judge, or commissioner, whose duty it shall be to hear and determine the case of such claimant in a summary manner. (Fugitive Slave Act.Section 6.1)
Here, Congress uses some alternate phrases rather than "slave" for some reason, maybe to make it sound more legitimate. It's not your slave, it's the person "held to labor" to you.
Quote #5
[…] it shall not be lawful to bring into the District of Columbia any slave whatever, for the purpose of being sold, or for the purpose of being placed in depot, to be subsequently transferred to any other State or place to be sold as merchandise. And if any slave shall be brought into the said District by its owner, or by the authority or consent of its owner, contrary to the provisions of this act, such slave shall thereupon become liberated and free. (DC Slave Trade.Section 1.1-2)
At least the Compromise ends on a somewhat happy note, if you can call outlawing the slave trade in one single city a happy note. There's some recognition that the nation's capital shouldn't also be home to a giant slave auction site.