Rhetoric refers to any language that is used to influence or persuade people. There are many different types of rhetorical devices ("Glossary of Rhetorical Terms"), but the most commonly referred to are ethos, logos, and pathos ("A General Summary of Aristotle's Appeals"). Ethos is the Greek word for ethics and is an ethical appeal. Essentially ethos is used to establish the credibility of the speaker. If we see the person as an ethical, just, upright person, then we are more likely to listen to and be persuaded by the speaker. Pathos is the Greek word for emotions and is an emotional appeal. Pathos refers to any words, phrases, or ideas that stir up a listener's emotions. Finally, logos is Greek for logic and is a logical appeal. Logos refers to any argument that is logical and rational. While we can certainly find many examples of all three rhetorical devices in both speeches, below are a couple of ideas to help get you started.
One thing both speeches have in common is that they both contain a great deal of ethos, or ethical appeals. One example is seen in the very first paragraph of The Declaration of Independence, particularly in the final clause, "...a decent respect to the opinion of mankind requires that they should declare the causes which impel them to the separation." Essentially, what the writer is saying in this opening paragraph is that when a polity, or organized group of people, decide it is time to break away from a government, then that group is morally obligated to declare the reasons for why they are breaking away from the government. Since the writer is appealing to the listener's sense of ethics, this is certainly an ethical appeal.
We see many ethical appeals also in The Gettysburg Address. One of the best can be seen in the passage:
But, in a larger sense, we can not dedicate--we can not consecrate--we can not hallow--this ground.
It is rather for us to be here dedicated to the great task remaining before us--that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion...
In other words, what Lincoln is saying here is that, while they have gathered to dedicate the battlefield of Gettysburg as a memorial cemetery, what those who are gathered there truly need to do is dedicate themselves to creating a free nation under which "all men are [truly] created equal." Since Lincoln is appealing to his audience's sense of ethics by appealing to their sense of duty, we can clearly see how this statement is an example of ethos.