How does the fourth principle, concerning liberty, connect to the idea that certain guaranteed freedoms in American life are limited in some ways? (4th principle: Liberty consists in the freedom to do everything which injures no one else. . . .)

Liberty, in philosophy, involves free will as contrasted with determinism.[1] In politics, liberty consists of the social and political freedoms to which all community members are entitled. In theology, liberty is freedom from the effects of "sin, spiritual servitude, [or] worldly ties.

Generally, liberty is distinctly differentiated from freedom in that freedom is primarily, if not exclusively, the ability to do as one wills and what one has the power to do; whereas liberty concerns the absence of arbitrary restraints and takes into account the rights of all involved. As such, the exercise of liberty is subject to capability and limited by the rights of others.

hope this helps! :)

might be agreeing to participate ethically with other european nations in the slave trade

or notifying other european nations when taking possession   of african territories