Among the many original manuscripts in existence today which were written by Abraham Lincoln, only one dates from his boyhood. It consists of 11 leaves (22 pages) from one of his school notebooks, likely written when he was between 13 and 17 years old. The leaves are housed at 12 different locations (one of the leaves is cut in half): the Library of Congress, six university libraries, three museums, and two private collections.
While growing up on the frontier in Kentucky and Indiana, young Abraham Lincoln only attended five sessions of school, most of these lasting only about two months in the middle of winter. As Lincoln would recall many years later in a brief autobiographical account provided to newspaper editor John Locke Scripps in June 1860, writing about himself in the third person: “[Abraham] went to A.B.C. schools by littles … [he] now thinks that the agregate of all his schooling did not amount to one year.”
In those frontier schools, the students did not have textbooks. Instead, each student made for himself a copybook, which in the case of mathematics was called a ciphering (cyphering) book or a sum book. This was made by taking several sheets of paper, folding them in half, and then sewing or tying them together. The teacher would dictate quotations, mathematical rules, problems, etc. which the students would write down in their copybooks, or in the case of the youngest students, the teacher might write them down himself.
At some point, Lincoln apparently gave this ciphering book – which included his last session of formal schooling – to his stepmother, because it was she who presented it to Lincoln’s friend and law partner William Herndon after Lincoln’s death, and he in turn gifted the various leaves to different people.
As for the teachers in those frontier schools and what Lincoln learned from them, this is what he himself had to say in another autobiographical account, this one written for his friend Jesse Fell in December 1859:
There were some schools, so called; but no qualification was ever required of a teacher, beyond “readin, writin, and cipherin,” to the Rule of Three. If a straggler supposed to understand latin, happened to so-journ in the neighborhood, he was looked upon as a wizzard. There was absolutely nothing to excite ambition for education. Of course when I came of age I did not know much. Still somehow, I could read, write, and cipher to the Rule of Three; but that was all.
You’ve probably already figured out that “ciphering” refers to arithmetic and perhaps other branches of mathematics. But you probably have no clue about “the Rule of Three”; you can discover what that was by looking through Lincoln’s own ciphering book.
The first three pages contain problems of simple subtraction, multiplication, and division. Note that simple – as opposed to compound – does not necessarily mean easy! Here is one of the problems which young Abe worked out correctly: 20,254 x 4,433 = 89,785,982.
One gets the idea that Abe must have completed his work more quickly than some of his classmates, because these first few pages are also interspersed with little poems such as:
Abraham Lincoln his hand and pen he will be good but god knows When
Abraham Lincoln is my nam[e]
And with my pen I wrote the same
I wrote in both hast[e] and speed
and left it here for fools to read
The next two pages of Lincoln’s ciphering book address compound addition and multiplication, in which the quantities consist of mixed (non-decimal) denominations. For example, distance is measured in miles, furlongs, yards, feet, inches, etc.; dry goods are measured in bushels, pecks, etc.; the old English monetary system used pounds, shillings, and pence; and so on. In early 19th-century America, being able to perform arithmetic on such compound units was essential to commerce and industry. And as the primary function of schools was to prepare children for their future work, this was an important part of the curriculum.
Here’s a problem for dry measure worked out by young Abe in his copybook; to solve this you need to know that there are four pecks in a bushel, and eight bushels in a quarter: [19 quarters, 1 bushel, 1 peck] – [12 quarters, 7 bushels, 2 pecks] = [6 quarters, 1 bushel, 3 pecks].
It was after these topics of simple and compound arithmetic that a student might advance to the “Rule of Three”. An 1821 text explains the “Direct Rule of Three” as follows: “Teacheth, by three numbers given, to find out a fourth, in such proportion to the third as the second is to the first”. Thus, this is what we would call a ratio, and brings us to basic algebra. [By the way, my daughters, who went to school in Spain, knew exactly what the “Rule of Three” was when I mentioned it to them; they had been taught “la regla de tres” as the way to solve ratios!]
Here’s a problem which Lincoln worked out on the sixth page of his ciphering book: “If 3 oz. of silver cost 17 shillings, what will 48 oz. cost?” He correctly calculated the solution to be 272 shillings, or 13 pounds and 12 shillings (there were 20 shillings in a pound).
In the direct rule of three, the proportions are directly related, i.e., move in the same direction: more of one means more of the other. There was also the inverse rule of three, involving an inverse proportion, where more requires less and less requires more.
The seventh page of Lincoln’s ciphering book deals with the “double rule of three”, in which there are three instead of just two factors which vary. Here is one of the problems he solved: “If 4 men in 5 days eat 7 lb. of bread how much will be suficient for 16 men 15 days”; the answer, as he correctly worked out, is 84 lb.
Although Lincoln later claimed that he had learned to “read, write, and cipher to the Rule of Three; but that was all”, this was either a conscious or unconscious underestimate of what he had actually learned. The final four pages of his ciphering book cover the additional topics of simple interest, compound interest, and discount. Here is one of the problems on simple interest which young Abe worked out correctly: “what is the interest of £216 – 5s for one year at 5½ percent per annum?” The answer in pounds, shillings, and pence is: £11 – 17s – 10½p.
Although Lincoln’s formal education was most definitely deficient even by the standards of his day, the topics and problems in his ciphering book demonstrate that he learned as much about mathematics as some high-school graduates today. He did so without calculators, computers, or even textbooks. And most importantly, as everyone knows, he never let his lack of schooling hold him back. In the first of the autobiographical accounts cited earlier, Lincoln went on to modestly explain how he continued his education through self-study during the rest of his life:
He was never in a college or Academy as a student; and never inside of a college or accademy building till since he had a law-license. What he has in the way of education, he has picked up. After he was twentythree, and had separated from his father, he studied English grammar, imperfectly of course, but so as to speak and write as well as he now does. He studied and nearly mastered the Six-books of Euclid, since he was a member of Congress. He regrets his want of education, and does what he can to supply the want.
In this, as in so many ways, Abraham Lincoln is an example for all of us, whether we are heading back to a formal school setting this fall or not. May we all make an effort to “supply the want” in our education throughout our lives.
Kevin J. Wood
September 5, 2018