How do I replace text from the 3rd element of a list of 10 items?

Either the :eq() selector or the .eq() method will allow you to select the proper item. However, to replace the text, you must get the value before you set it:

// This doesn't work; text() returns a string, not the jQuery object:
$( this ).find( "li a" ).eq( 2 ).text().replace( "foo", "bar" );
 
// This works:
var thirdLink = $( this ).find( "li a" ).eq( 2 );
 
var linkText = thirdLink.text().replace( "foo", "bar" );
 
thirdLink.text( linkText );

The first example just discards the modified text. The second example saves the modified text and then replaces the old text with the new modified text. Remember, .text() gets; .text( "foo" ) sets.