In his script for Hamilton, Lin-Manuel Miranda merges the American Founding with the tenor of modern America, such that history is both relived and reimagined. The characters in Hamilton recite excerpts from historical documents such as Washington’s Farewell Address and Hamilton’s History of the United States for the Year 1796, In Which the Charge of Speculation against Alexander Hamilton, Late Secretary of the Treasury, is Fully Refuted (aka The Reynolds Pamphlet). Miranda also weaves in fragments of real quotes from Hamilton and his contemporaries, effortlessly fitting them into the fabric of the whole production.
Below are a few lines that jumped out at me along with excerpts of the historic primary source documents that contain either the exact phrase or are very similar. (Note that this short list is by no means exhaustive and is entirely based on my memory from seeing the show in previews- if you think of others, add them into the comments section!)

“I wish there was a war.” (Hamilton to Burr)
“…my ambition is vigilant, so I continue the groveling condition of a clerk, or the like to which my fortune condemns me, and would willingly risk my life, though not my character, to exalt my station. … I shall conclude by saying I wish there was a war.” – Letter from Hamilton to his friend Edward “Ned” Stevens dated November 11, 1769 (reprinted in Reminisces of James A. Hamilton, available here through Google Books).
At the time of this letter, Hamilton was still in St. Croix working as a clerk. Hamilton realized that in order to rise up and advance his station in life, something dramatic would need to happen and he expressed his willingness to take any risks that would not endanger his honor.
“I’m just saying, If you really loved me, you would share him!” (Angelica to Eliza)
“…by my Amiable you know that I mean your Husband, for I love him very much and if you were as generous as the old Romans, you would lend him to me for a little while, but do not be jealous, my dear Eliza, since I am more solicitous to promote his laudable ambition, than any person in the world…” – Letter from Angelica Church to Elizabeth Hamilton, July 30, 1794 (Reprinted in the Intimate Life of Alexander Hamilton by Allan Mclane Hamilton, available on Google Books)
“Best of wives and best of women.” (Hamilton to Eliza before the duel)
“Fly to the bosom of your God and be comforted. With my last idea; I shall cherish the sweet hope of meeting you in a better world.
Adieu best of wives and best of Women. Embrace all my darling Children for me.
Ever yours. AH” – Letter from Alexander Hamilton to Eliza Hamilton written July 4, 1804
Hamilton gave this letter to Nathaniel Pendleton, his second in the duel, as part of his efforts to put his affairs in order prior to his interview with Aaron Burr at Weehawken on July 11, 1804. (Reprinted in the Papers of Alexander Hamilton, available here via Google Books). Interestingly, Hamilton and Burr had dinner together with a group of fellow former Revolutionary War officers just days before the duel.