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In 1870 the former vice-president of the Confederacy, Alexander H. Stephens, offered what has surely become the best-known characterization of Abraham Lincoln's nationalism. In Lincoln, Stephens suggested, the sentiment of Union "rose to the sublimity of a religious mysticism." A century later, in his entry for "nationalism" in The Abraham Lincoln Encyclopedia, Mark E. Neely, Jr., cited Stephens's famous comment but was quick to add that there was, in fact, "little that was mystical" about Lincoln's love for the Union. It was important to remember, Neely suggested, that Lincoln's political thought "never departed from the old Lockean universe of natural rights." His idea of American nationality was, therefore, not rooted in the mystical soil of nineteenth-century romanticism; it was solidly grounded in the principled bedrock of Thomas Jefferson's eighteenth-century preamble to the Declaration of Independence, and to that extent, Neely suggested, Lincoln's nationalism was "distinctly old-fashioned."  Using Neely's caveat about Stephens's observation as its point of departure, this essay seeks to explore the "old-fashioned" character of Lincoln's nationalism from an unlikely, and fresh, perspective: its connection, via the Enlightenment, to classical antiquity.
Of course when we think of Lincoln, and especially of his political thought, we tend not to think in terms of classical influences. Unlike the Revolutionary generation of American leaders whom Lincoln admired so much, he would appear to have had neither the means nor the opportunity of absorbing any significant form of a classical tradition. Had he been born even a generation earli- Page [End Page 55] er, and certainly had he been born to a higher social station, things might have been quite different. Throughout the western world during the second half of the eighteenth century, even in provincial America, the cultural imprint of the classics was ubiquitous and profound. Eighteenth-century Americans with the benefit of a formal education were steeped in the classics, and many of the Founding Fathers didn't need modern translations for access to the Greek and Roman writings that provided their philosophical and cultural anchor. And even Americans who lacked formal training in the classics could not escape the intense "social conditioning" that defined America's Augustan age. What better example, indeed, than Lincoln's hero George Washington, who never studied Greek or Latin, who had very little formal education at all, but who could understand himself, and the American republic, only in neoclassical terms?
By the time Lincoln entered the world in the early nineteenth century, however, this most intense form of classical conditioning had begun to erode. Even some of the classically trained Revolutionaries, such as Benjamin Rush, suddenly declared war on the classical canon in education; and although the defenders of the ancient languages won that battle, and Greek and Latin remained central to the academy and college curricula for some time to come, the general direction of change in the culture at large was unmistakable. With the two conspicuous exceptions of architecture and oratory, classicism retreated and became largely confined to the schools.  By Lincoln's time, fewer Americans accepted the relevance of ancient Greece and Rome to their more modern world of political experience; fewer Americans were being exposed to classical culture at all; and above all, liberally educated gentlemen were playing an increasingly less important role in politics and public life. Indeed, on the level of political leadership, a turning point was probably reached during the 1820s when, as Howard Mumford Jones once suggested, the administration of John Quincy Adams appeared to "close the era in which the classical past was a dynamic force in American public life." After "the so-called Jacksonian Page [End Page 56] revolution," Jones noted, "few presidents were literary, none was a classicist in the sense that Jefferson was, and none was portrayed, like Washington, in the character of a Roman senator nude to the waist."
Viewed in this broad context, the cultural distance between Thomas Jefferson—eighteenth-century gentleman and classical scholar—and Abraham Lincoln—nineteenth-century frontier auto-didact—appears vast indeed. I would suggest, however, that Lincoln was influenced directly, and perhaps profoundly, by one specific, largely neglected dimension of the classical tradition, and that this connection to antiquity ties Lincoln to Jefferson, especially, in suggestive and interesting ways. This connection to antiquity, and between Lincoln and Jefferson, can be fully documented. At a pivotal juncture of his life Lincoln studied with great care at least one ancient thinker, who also happened to be a particular favorite of Jefferson's. And by exploring this precise connection to antiquity we gain a fuller picture of the "old-fashioned" character of Lincoln's nationalism.
Let's begin with Jefferson, who can fairly be described as a lifelong student and lover of the classics. After receiving the rudiments of a liberal education between the ages of nine and sixteen, Jefferson entered the College of William and Mary, where the curriculum was centered on the classics.  Almost a half century later, following his retirement from public life, he reimmersed himself in the classics, and his "dialogue with the ancients," to use Karl Lehmann's phrase, entered its final, most passionate phase. Indeed, Jefferson reported that his intense classicism during these twilight years made him feel like a lonely monument of another age.  During the early years of his retirement, as he approached his seventies, he movingly described to a correspondent his efforts "to beguile the wearisomeness of declining life ... by the delights of Page [End Page 57] classical reading and mathematical truths."  He was more specific writing to John Adams a year later, in 1812: "I have given up newspapers in exchange for Tacitus and Thuycidides, for Newton and Euclid; and I find myself much the happier." Tacitus, Thuycidides, and Newton: a great Roman historian, a great Greek historian, and a modern scientific genius—no surprises here. But what about Euclid, the Greek founder of codified geometry?
We tend to forget that Euclid was absolutely central to the classical tradition that eighteenth-century Americans like Jefferson embraced. The career of Euclid's Elements, an all-time best-seller, is in many respects as mysterious as it is extraordinary. Euclid was not an original thinker—or even a great mathematician like Archimedes—and the thirteen books of his Elements are utterly lacking in color, verve, or humanity. But this book endured in a way that few other works of antiquity have. As one historian of mathematics has observed, "no work, except the Bible, has been more widely used, edited, and studied, and probably no work has exercised a greater influence on scientific thinking."  Indeed, "for twenty-one hundred years," writes another scholar, "the geometry Euclid had outlined in his Elements stood as a supreme mathematical and logical system." Specifically, Euclid's geometry had become, by Jefferson's time, a testament to the power of human reason to deduce truth. On the basis of some formal definitions of terms and five postulates and five axioms whose truth was self-evident—such as, "things that are equal to the same thing are also equal to one another," or "the whole is greater than the part"—Euclidean geometry "deduced an elaborate system of propositions that seemed both to accurately describe physical reality and to compose a flawlessly logical system."  In this sense Euclid did more than teach the principles and methods of correct reasoning in geometry; he could inspire readers of his Elements to apply reason to philosophy, economics, political theory, art, and religion, and in so Page [End Page 58] doing, to arrive at truths that were as valid as mathematical truth—as irrefutable, that is, as the propositions derived from his axioms. To this extent, Euclid not only survived the scientific revolution of the seventeenth century, he became central to the development of Newtonian science and to the Enlightenment more generally. 
Viewed in this light, Jefferson's affinity for Euclid should come as no surprise. His passion for geometry points to his more general love of mathematics, always, by his own account, his favorite subject. Jefferson's fond recourse to Euclid in old age took him back to his youth and to the education that had shaped his character and career as a Revolutionary. His principal debit in this account was to a professor at William and Mary, William Small of Scotland who, according to Jefferson in his later years, "probably fixed the destinies" of the young Virginian's life.
Jefferson had come to college eager to continue studying the classics and mathematics, and in Small he found the perfect mentor. Trained as a scientist in Scotland, where he had been taught by some of the leading lights of the Scottish Enlightenment, Small taught much of the curriculum at William and Mary, including "natural philosophy," which was comprised of "Physicks, Metaphysicks, and Mathematicks," and "moral philosophy," which included "Rhetorick, Logick, and Ethicks." Specifically, Small had studied in Scotland under William Duncan, the author of an influential book entitled Elements of Logick, which Small promptly imported into the William and Mary curriculum.  Duncan's approach relied heavily on John Locke and on the idea of self-evident truths as the key to a mathematical mode of thinking that provided the foundation of all knowledge. Teaching his young colonial charge mathematics and logic from the vantage point of Duncan's work, Small could not have avoided focusing on Euclid. Indeed, as historian of science I. Bernard Cohen has recently observed, "Small would have stressed the rigors of Euclid as the foundation of mathematics and all rigorous thought." Jefferson, the student, Page [End Page 59] in turn "would have learned and applied Euclid's system of definitions, postulates, and axioms—the 'self-evident' foundations of all sound knowledge and reasoning."  Most important in this connection, Small offered Jefferson, via Euclid, a gateway to Newtonian science and to the heart of the Enlightenment. Like Euclid's geometry, Newton's natural science was predicated on a set of axioms which, though different in kind from the axiomatic principles of Euclid's geometry, partook of the same level of self-evident validity.  Many years later, during the leisure afforded by his retirement, Jefferson explained the delight he took in mathematics (and in Euclid specifically) in very revealing terms: "We have no theories here, no uncertainties remain on the mind, but all is demonstration and satisfaction."  Indeed, from two of his four favorite authors in retirement, Newton and Euclid, Jefferson was able to savor once again the intellectual pleasures of his youth and of an approach to truth rooted in the certainty of mathematical demonstration.
As Jefferson's pleasure in Euclid deepened with age, he became increasingly ambivalent about the relevance to modern America of other dimensions of classical antiquity, including its political theory. His contemptuous dismissal of Plato (especially the Republic) is well-known; and by the second decade of the nineteenth century, Jefferson had decided that even Aristotle and Cicero—whom he had once read avidly but now saw as part of a distant, radically different past—actually had little practical wisdom to offer American republicans amid the new conditions of the early nineteenth century.  Still, the aging patriarch was intent on holding the line on educational standards at his newly founded University of Virginia. In large part because he regarded classical languages as "the foundation common to all the sciences," Jefferson endorsed his friend Thomas Cooper's proposal to exclude from the new university any prospective student who could not do three things: read classical authors "with facility"; "convert a page of English into Latin at sight"; and, finally, "demonstrate a thorough knowledge of Euclid." Page [End Page 60]
By those standards, Abraham Lincoln would have been barred from Jefferson's university. At the customary age of entrance, he would have flunked all three tests, at a time, indeed, when he was struggling to achieve basic literacy. Lincoln never would learn Latin or Greek—that accomplishment was reserved for his first-born son, Robert, whose sense of himself as the consummate Victorian gentleman would include a Harvard education—but he did work hard, well into his middle age, to teach himself Euclid. That Jefferson test he would have passed with flying colors, at age fifty, if not twenty. The thought of both Jefferson and Lincoln reading Euclid for pleasure may appear quaint, but their mutual passion for classical geometry holds considerable significance. Of course the two men had much in common that is relevant here: both were lawyers; both had at least some experience as surveyors; and they also shared a more general delight in mathematics. But the Euclid connection, in particular, is richly suggestive in ways we may have overlooked.
It is not clear when, precisely, or how, Lincoln first encountered Euclid. The presence of the classics on the mid-Western frontier may have been much greater and more visible than "Turnerian" views of the West might suggest, and it is especially interesting that among classical place names in the mid-Western states, the most common personal names for towns include—along with Homer, Seneca, and Vergil—Euclid.  But the primary domain of the classics was of course the midwestern colleges; and as Lincoln so bluntly noted of himself in an autobiographical sketch written for the 1860 presidential campaign, "he was never in a college or Academy as a student; and never inside of a college or academy building till since he had a law-license." Indeed, "what he has in the way of education," Lincoln said of himself, "he has picked up," and that homey metaphor doubtless applies to any early contact he might have had with Euclid.
We do know that Lincoln was exposed to elementary mathematics during brief stints in the pioneer schools of Indiana, and that in his mid-twenties he read up on geometry and trigonometry before trying his hand at surveying. The surveying texts he studied during the 1830's—Abel Flint's A System of Geometry and Trigonometry, With a Treatise on Surveying, and Robert Gibson's The Theory and Prac- Page [End Page 61] tice of Surveying—drew heavily on Euclid, and there is circumstantial evidence that Lincoln's study of Euclidean geometry was more or less continuous from this point on. As David Donald has recently observed of the young Lincoln, he clearly liked "the logic and precision of mathematics." Indeed, by the late 1830s he was already well-known for the logical precision of his political speeches, in which he characteristically stated propositions and proceeded to prove them, both by adducing documentary or empirical evidence and by deducing them from axioms or self-evident truths. Lincoln then turned even more seriously to Euclid at some point during the 1840s. A fellow lawyer later recalled that he began to carry Euclid with him on the circuit soon after his marriage in 1842.  Some modern scholars suggest that Congressman Lincoln devoted some of his spare time in Washington in 1847 and 1848 to the serious study of Euclid's geometry.  What we do know, with more certainty, is that during the years just after his disappointing, even disastrous, one term as a United States congressman, Lincoln set for himself the task of mastering the first six books of Euclid.
Viewed in hindsight, the years between 1849 and 1854 clearly formed a critical transitional period in Lincoln's life and career, perhaps even marking, if we accept the recent formulation of Michael Burlingame, a "mid-life crisis" of sorts. Lincoln had good reason to conclude that his political career had aborted and was now over. As his old rival Stephen Douglas rose to national prominence in Washington city, the scene of his own disappointment, Lincoln, now in his early forties, may well have brooded on his personal failures and worked hard, as Burlingame would have it, on "healing the wounds of ego deflation."  One thing seemed certain: he needed more than ever to succeed in the law, which was now the sole source of his family's support. Sensing the deficiencies of his Page [End Page 62] education—a point apparently brought home to him powerfully during his term in Congress, when he also made his first visits to New England and other parts of the East—and recognizing anew the importance of mental discipline and logical precision in the practice of law, Lincoln characteristically embarked on a fresh course of self-education. While his fellow lawyers on the eighth circuit filled the room they shared for the night at country inns with what William Herndon called "our interminable snoring," Lincoln pondered Euclid by candlelight into the wee hours of the morning, somehow managing, to the consternation of his colleagues, to "maintain his mental equilibrium" and "concentrate his thoughts on an abstract mathematical proposition." In this way, Herndon reported, Lincoln studied Euclid "until he could with ease demonstrate all the propositions in the six books."  Lincoln's report of his success was more measured. In his autobiographical sketch for the 1860 campaign, he noted with characteristic precision: "He studied and nearly mastered the Six-books of Euclid, since he was a member of Congress."
Lincoln was obviously proud of his accomplishment. Euclid's axioms may have been self-evident, but the elaborate proofs of his propositions were anything but simple or straightforward. The prevailing belief among Lincoln's countrymen was that Euclid was not for everyone—certainly not for women, for instance, who were widely assumed to be deficient in the capacity for reason that geometry demanded.  And Thomas Jefferson himself had used Euclid as a benchmark to differentiate mental capacity by race. If Lincoln ever actually read Jefferson's Notes on the State of Virginia, he would surely have noted his hero's memorable reference to Euclid in that volume, which occurred during a discussion of the Negro's innate aptitudes. In the faculty of reason, Jefferson had confidently stated, blacks were "much inferior" to whites, "as I think one could scarcely be found capable of tracing and comprehending the investigations of Euclid."  From this perspective, perhaps Lincoln's embrace and near mastery of Euclid held personal significance for Page [End Page 63] him as he negotiated the self-reckoning of his mid-life crisis. But the more significant ramifications of his self-tutorial in Euclid were surely as much public as personal.
As mental exercise, Lincoln's long hours with Euclid doubtless made him a better "close reasoner," to use Herndon's term, and hence a more effective lawyer, which was surely his conscious purpose. But they also helped prepare him, in ways he could not have known, for the unexpected resumption of his political career after 1854. Lincoln had always been noted for his ability to reduce his thought on any given subject to the simplest and plainest terms possible; and during these critical years for the republic, his mastery of that skill allowed him to argue the case against both proslavery and popular sovereignty with something close to "Euclidean coherence."  Throughout his protracted debate with Douglas between 1858 and 1860, Lincoln "appealed repeatedly to the nature of proof in Euclid" as the appropriate standard for evaluating the arguments of the two combatants. And in a larger sense, the distinctive qualities of Lincoln's mature political thought, including its content as well as its form and precision, appears to have owed a great deal to his immersion in Euclid. 
Lincoln's ability to whittle down a complex issue to one key principle, or central axiom, directly informed his political message during the second half of the 1850s, when we might say he took a vexingly complex issue, slavery, and whittled it down to a simple issue: the humanity of the slaves. Amid the acrimonious wrangling over the complex details of the politics of slavery in the territories, Lincoln's simple message became unmistakable: If the Negro is a man, then slavery is wrong, and must be disapproved of, and discouraged by all possible legal and constitutional means. In 1859, drawing an explicit connection between Euclid and the Declaration of Independence, Lincoln identified "the principles of Jefferson"—including, of course, the eighteenth-century Euclidean truth Page [End Page 64] that "all men are created equal"—as "the definitions and axioms of free society." The problem for the republic, in Lincoln's eyes, was that large numbers of Americans in the 1850s now seemed unwilling or unable to admit the truth of the axioms; they were allowing profit, or interest, or just plain sloppy thinking to obscure the self-evident truth of human equality. The challenge Lincoln accepted was to make that principle once again the focus of political debate, because the resolution of policy questions, he believed, required the prior resolution of any underlying confusion about the truth of the axioms and hence about the fundamental premises of the American regime. From his perspective, of course, Douglas's program of popular sovereignty was grounded in both bad history and specious logic. Most important, by reducing the slavery question to a matter of mere opinion and interest, Douglas and his supporters ignored the moral imperative of Jefferson's inference that no human being could justly govern another without his consent. And if James M. McPherson is correct to say that, by the 1850s, more white Americans probably agreed with Douglas than with Lincoln about the meaning of Jefferson's Declaration, we can appreciate better not only the challenge that Lincoln faced in shaping public opinion, but his heroic persistence, as McPherson puts it, "against the odds."
In sum, Lincoln can appear distant and detached from classical antiquity only if we fail to look in the right place for the relevant connection. To be sure, he was "largely ignorant" of "the classics, the great staple of the intellectual diet of Victorian gentlemen," and he considered himself uneducated—and he was so regarded by most educated people of his time—because education remained in large part synonymous with mastery of the classical languages.  That particular badge of Victorian gentility was one that Lincoln never aspired to and perhaps disdained as the purely ornamental side of classical wisdom. He was drawn instead to ancient geometry, a dimension of the classical tradition that proved vital to the shaping of not simply his character and his leadership, but his larger understanding of the American national experiment. And some of the rich connections in this vein are beautifully captured in the reminiscences in 1864 of a well-educated easterner, the Reverend J. P. Gulliver, of Norwich, Connecticut, of his personal encounter Page [End Page 65] with Lincoln four years earlier, at the height of the crisis of the American Union.
Gulliver had heard Lincoln deliver a version of his Cooper Union speech in early 1860, and the following day they rode together on the train for several hours. Gulliver reported that Lincoln was bemused that eastern sophisticates like Gulliver were treating him as some kind of master or genius in the art of public speaking. After explaining to Lincoln why he admired his speeches, Gulliver pressed the visitor from Illinois to explain how he had acquired such extraordinary power over thought and language. Surely, he insisted, it was the result of some kind of formal education. Setting Gulliver straight about his lack of much formal schooling, Lincoln instead referred to his longstanding fascination with Euclid. Gulliver said he wished that Lincoln's experience with Euclid were more widely known, especially among young people, because it demonstrated the importance of "that patient classical and mathematical culture which most minds absolutely require." "Euclid, well studied," the clergyman suggested to Lincoln "would free the world of half its calamities, by banishing half the nonsense which now deludes and curses it. I have often thought," he continued, "that Euclid would be one of the best books to put on the catalogue of the Tract Society, if they would only get people to read it. It would be," he concluded, "a means of grace." Lincoln's reply, as reported by Gulliver, was vintage Lincoln: "I think so," said he laughing; "I vote for Euclid."
That Lincoln may have seen humor and perhaps irony, as well as truth, in the notion that studying geometry was a sacred experience—indeed, for the Reverend Gulliver, nothing less than a path towards salvation!—may point us back toward Jefferson. In Lincoln's case, of course, the Euclid connection tied him not to any personal quest for salvation, but squarely to the secular heart of Page [End Page 66] the Enlightenment, to the eighteenth-century world of nature, science, and reason that Jefferson took such retrospective delight in as he savored Euclid and Newton during his declining years. And with the advantage of hindsight, we might take note of an irony that necessarily escaped Lincoln. At the time he was throwing himself into Euclid, mathematicians in Europe were already groping toward what would emerge full-blown before the end of the nineteenth century: the discovery of non-Euclidean geometries, with all of their unsettling implications for traditional notions of truth in both science and ethics.
Lincoln, however, always remained a citizen of his hero Jefferson's eighteenth-century "enlightened" world. Indeed, he shared the understanding of Euclid's Elements that Thomas Paine had sketched in The Age of Reason, the manifesto for deism that Lincoln studied as a young man on the Illinois frontier at the same time he first encountered Euclid. Echoing Jefferson's comment about the delight he took in Euclid, Paine described the Elements as "a book of self-evident demonstration, entirely independent of its author, and of every thing relating to time, place, and circumstance."  This scientific faith in abstract truth and first principles was a legacy of the eighteenth century that was fast becoming outmoded, or at least old-fashioned, amid the glow of a new romantic nationalism. But that old faith served Lincoln (and the republic) quite well during its moral and political crisis of national self-reckoning. Indeed, it provided the principal source of Lincoln's nationalism, because from his perspective, only by re-adopting Jefferson's Euclidean sense of the Declaration would Americans save, as he had put it as early as 1854, a Union "forever worthy of the saving." Page [End Page 67]
- Neely, The Abraham Lincoln Encyclopedia (New York: McGraw-Hill, 1982), 215–16.
- For elaboration of this "social conditioning," see Carl J. Richard, The Founders and the Classics: Greece, Rome, and the American Enlightenment (Cambridge, Mass.: Harvard University Press, 1994), 10, 36–37.
- Meyer Reinhold, Classica Americana: The Greek and Roman Heritage in the United States (Detroit, Mich.: Wayne State University, 1984), 108. See also Edwin A. Miles, "The Young American Nation and the Classical World," Journal of the History of Ideas 35 (1974): 259–74.
- Jones, O Strange New World: American Culture, The Formative Years (New York: Viking Press, 1964), 265, 266.
- Among recent scholars Garry Wills has attempted, not very persuasively, to link Lincoln to classical antiquity by emphasizing the extent to which he was influenced by the "Greek Revival" in ante-bellum America. See Wills, Lincoln at Gettysburg: The Words that Remade America (New York: Simon & Schuster, 1992), especially chaps. 1 and 2.
- See, in general, the useful essay by Meyer Reinhold, "The Classical World," in Thomas Jefferson: A Reference Biography, ed. Merrill D. Peterson (New York: Scribner, 1986), 135–56.
- Karl Lehmann, Thomas Jefferson: American Humanist (New York: Macmillan, 1947; Charlottesville: University Press of Virginia, 1985), 65–66.
- Cited in ibid., 144, and in Richard, Founders and the Classics, 27.
- Jefferson to Adams, Jan. 21, 1812, The Adams-Jefferson Letters: The Complete Correspondence Between Thomas Jefferson and Abigail and John Adams, ed. Lester J. Cappon (Chapel Hill: University of North Carolina Press, 1959; New York: Simon & Schuster, 1971), 291.
- Howard Whitley Eves, An Introduction to the History of Mathematics, 3d ed. (New York: Holt, Rinehart & Winston, 1969), 114.
- Edward A. Purcell, Jr., The Crisis of Democratic Theory: Scientific Naturalism and the Problem of Value (Lexington: University Press of Kentucky, 1973), 49.
- In addition to the above, see Morris Kline, Mathematics: A Cultural Approach (Reading, Mass.: Addison-Wesley Pub., 1962), esp. 17–24, 130, and Philip J. Davis and Reuben Hersh, Descartes' Dream: The World According to Mathematics (Boston: Houghton Mifflin, 1987), especially the chapter "Non-Euclidean Geometry and Ethical Relativism," 203–17.
- Dumas Malone, Jefferson the Virginian (Boston: Little, Brown, 1948), 49–61, quote on page 52.
- Wilbur Samuel Howell, "The Declaration of Independence and Eighteenth-Century Logic," in William and Mary Quarterly, 3d ser., 18 (1961): 463–84.
- Cohen, Science and the Founding Fathers: Science in the Political Thought of Jefferson, Franklin, Adams, and Madison (New York: W. W. Norton, 1995), 72.
- Ibid., 122–33.
- Jefferson to Reverend James Madison, Dec. 29, 1811, in Andrew A. Lipscomb and Albert Ellery Bergh, eds., The Writings of Thomas Jefferson (Washington, D.C.: Thomas Jefferson Memorial Association, 1903–1905), 19:183.
- Reinhold, "Classical World," 150–51.
- As cited in Richard, Founders and the Classics, 34.
- Walter R. Agard, "Classics on the Midwest Frontier," Classical Journal 51 (1955): 103–10.
- "Autobiography Written for John L. Scripps," circa June 1860, in Roy P. Basler, ed., The Collected Works of Abraham Lincoln, 9 vols. (New Brunswick, N.J.: Rutgers University Press, 1953–1955), 4:62.
- David Herbert Donald, Lincoln (New York: Simon & Schuster, 1995), 31.
- See, for instance, his "Speech on the Sub-Treasury," Dec. 26, 1839, Collected Works, 1:159–79, especially pages 160 and 166–67.
- Albert J. Beveridge, Abraham Lincoln, 1809–1858 (Boston: Houghton, Mifflin, 1928), 1:518.
- Daniel Walker Howe, The Political Culture of the American Whigs (Chicago: University of Chicago Press, 1979), 282; Harry V. Jaffa, American Conservatism and the American Founding (Durham, N.C.: Carolina Academic Press, 1984), 110; J. R. Pole, "Abraham Lincoln and the American Commitment," in Pole, Paths to the American Past (New York: Oxford University Press, 1979), 157–58.
- Michael Burlingame, The Inner World of Abraham Lincoln (Urbana: University of Illinois Press, 1994), chap. 1, quote on page 5.
- William H. Herndon and Jesse W. Weik, Life of Lincoln (1888; reprint, New York: Da Capo Press, 1983), 247–48.
- "Autobiography for Scripps," Collected Works, 4:62.
- Patricia Cline Cohen, A Calculating People: The Spread of Numeracy in Early America (Chicago: University of Chicago, 1982), 139–48.
- William Peden, ed., Thomas Jefferson, Notes on the State of Virginia (New York: Norton, 1982), 139.
- Herndon and Weik, Life of Lincoln, 248.
- Burlingame, Inner World, 5.
- Jaffa, American Conservatism, 110. For examples of Lincoln's specific references to Euclid, see "Mr. Lincoln's Rejoinder" at Charleston, Sept. 18, 1858, Collected Works, 3:186, in which Lincoln likened a Douglas position to calling Euclid a liar, eliciting "roars of laughter" from supporters, and Lincoln's "Speech at Columbus, Ohio," Sept. 16, 1859, Collected Works 3: 416–17, in which Lincoln challenged Douglas to demonstrate—"as Euclid demonstrated propositions"—his grotesque proposition that popular sovereignty was the right of one man to make a slave of another.
- "To Henry L. Pierce and Others," Apr. 6, 1859, Collected Works, 3: 375.
- McPherson, Abraham Lincoln and the Second American Revolution (New York: Oxford University Press, 1991), 51–54.
- Neely, Lincoln Encyclopedia, 34, 94.
- Gulliver's sketch first appeared in the New York Independent, Sept. 1, 1864, and was subsequently reprinted in F. B. Carpenter, The Inner Life of Abraham Lincoln: Six Months at the White House (New York: Hurd & Houghton, 1870; Lincoln: University of Nebraska Press, 1995), 313–17. Carpenter and other sources of its kind must obviously be used with great caution; see Don L. Fehrenbacher and Virginia Fehrenbacher, eds., Recollected Words of Abraham Lincoln (Stanford, Calif.: Stanford University Press, 1996), 189–90. Gulliver's rendition of Lincoln's precise words is obviously unreliable, and he also clearly got a number of details in Lincoln's story about his study of Euclid wrong. But the gist of his rendering of his conversation with Lincoln as it pertains to Euclid rings remarkably true.
- Kline, Mathematics, passim; Davis and Hersh, Descartes' Dream, 203–17; Purcell, Democratic Theory, passim.
- Eric Foner, ed., Thomas Paine: Collected Writings (New York: Library of America, 1995), 736.
- "Speech at Peoria, Illinois," Oct. 16, 1854, Collected Works, 2:276.