Final answer:
The phrase that most clearly shows an imperialistic attitude in the excerpt is 'the furtherance of the British Empire and the bringing of the whole uncivilized world under British rule.'
Step-by-step explanation:
The phrase that most clearly shows an imperialistic attitude in the excerpt is 'the furtherance of the British Empire and the bringing of the whole uncivilized world under British rule.' This phrase demonstrates a desire to expand British control over other territories and populations, reflecting an imperialistic mindset. The speaker envisions a single Anglo-Saxon empire and expresses disappointment in the loss of the United States as a colony. This language exemplifies an attitude of superiority and a desire for dominance.