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Ciphering Book, [1819-1826]
In the winter months between his tenth and seventeenth birthdays, Abraham Lincoln attended four 3-month terms of school in Spencer County, Indiana. At different pioneer schools operated by different teachers, Lincoln was instructed in the Abbaco method common to the early 19th-century United States. In this business-oriented curriculum, which focused on commerce, weights, and measures, students learned calculations like interest and discount before being introduced to decimals or common fractions. Abraham procured the paper, prepared the pages at different times throughout those four school terms, and stitched the sheets together himself. Abraham Lincoln’s ciphering book not only provides the earliest example of his handwriting, it also represents the entirety of his twelve months of formal schooling.
Book ownership was rare on the frontier: students instead created workbooks by copying problems, questions, and quotations from a text owned by their teacher. For example, leaf 6 (images 11 and 12) of Lincoln’s ciphering book were copied from Thomas Dilworth’s popular textbook The Schoolmaster’s Assistant.
There are eleven known sheets from Lincoln’s ciphering book; likely, there were originally more. These eleven pages were given by family members to Lincoln’s law partner and biographer William H. Herndon after Lincoln’s death in 1865. Currently, the eleven sheets are owned by twelve different individuals or institutions. The Papers of Abraham Lincoln presents them arranged in the order in which the calculations were taught in Abbaco schools and textbooks. We have also digitally stitched together leaf 6, whose upper and lower halves have become separated and now reside in separate repositories.
Nerida F. Ellerton, Valeria Aguirre Holguin, and M. A. Clements, “He would be Good: Abraham Lincoln’s Early Mathematics, 1819-1826,” in Nerida F. Ellerton and M. A. Clements, Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books (Cham, Switzerland: Springer, 2014), 123-186; McKenzie A. Clements and Nerida F. Ellerton, “Abraham Lincoln’s Cyphering Book and the Abbaco Tradition,” Journal of the Abraham Lincoln Association 36 (Winter 2015), 1-17; Douglas L. Wilson and Rodney O. Davis, eds., Herndon’s Informants: Letters, Interviews, and Statements about Abraham Lincoln (Urbana, IL: University of Illinois Press, 1998), 111-12, 120-21, 128, 532; William H. Herndon and Jesse W. Weik, Herndon’s Life of Lincoln (Cleveland: World Publishing, 1949), 36-37.
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Abraham
Abramham
Abraham Lincoln his hand and pen he will be good but god knows When1Time What2 an emty vaper tis and days how swift3 they are swift as an indian ar[row] fly on like a shooting star the presant moment Just . . .then slides away in [haste] that we [can n]ever say they[‘re ours] but [only say theyre] past4
<Page 2>
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<Page 3>
Multiplication 1824
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<Page 4>
Multiplication Continued
Examples
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Abraham Lincoln Book
<Page 5>
Long Division C. . .
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Abraham
Book 		Abraham Lincoln is my ^nam[e]^
And with my pen I wrote the same
I wrote in both hast and speed
and left it here for fools to read
<Page 6>
Division 1824
Examples
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Abraham Lincolns
Book
<Page 7>
Subtraction of Long Meas[ure]
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of Land Measure
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of Dry Measure
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Abraham Lincoln
his hand and pen
he will be good but
[god?] knows When
<Page 8>
Long Measure &c &c[etc etc]
Q[Question] Which are the Denominations of long measure
A[Answer] 3 Barley corns or BC[Barley Corns] makes 1 InchIn[Inch]
4 Inches 1 handhd[hand]
12 Inches 1 footft[foot]
3 feet 1 yardyd[yard]
6 feet 1 fathomfa[fathom]
5 yards and 1 half 1 Rod pole or pearch
408 poles 1 furlongfu[furlong]
8 furlongs 1 mileM[mile]
3 miles 1 leaguel[league]
60 miles 1 DegreeDeg[Degree]
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<Page 9>
To Exercise Multiplication
There were 40 men Concerned in payment [of?] a sum of money and each man paid 1271£
how much was paid in all—
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If 1 foot contain 12 inches I demand ^many^ how there are in 126 feet—
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of Compound Division
Q What is compound Division
A When several numbers of Divers Denomination are given to be divided by 1 common divisor this called Compound Division—
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Abraham Lincoln His Book
<Page 10>
[Co]mpound Multiplication
Q What is Compound Multiplication
A When several numbers of divers Denomination are given to be multiplied by one common multiplier this is called Compound multiplication
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An army of a 10000 men having plundered a City; took so much money that when it w[as] shared among them each man had ^£^27. I dem[and] how much money was taken in all
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<Page 11>
The Single Rule of Three
If 3 oz of silver Cost 17 S what will 48- oz Cost
[Calculations not transcribed.]		 If 1 gallon of ale Cost 8 d what Cost 36 gallons answer ^£^1-4-S
[Calculations not transcribed.]
If 3 lb of ginger Cost 3 S what Cost 26 lb
[Calculations not transcribed.]5		 If 1 lb sugar Cost 4½ what Cost 48 lb answer 18 Shillings
[Calculations not transcribed.]
If 2 oz of silk Cost 2 S-6 D what Cost 7 LB Answer 7 C
[Calculations not transcribed.]		 If 1 lb of Sugar Cost . . . what Cost 1 Cwt[Hundredweight] ans[wer]
1 £ 17 S & 4 d—
[Calculations not transcribed.]
If an Cwt[Hundredweight] of sugar Cost 2 £ 12 S what Costs 1C— 2 £ 12 S 1 lb
[Calculations not transcribed.]
<Page 12>
Q What do you observe Concerning the 1st & 3rd term.
A they must be of the same name and kind
Q What do you observe Concerning the 4th term
A it must be of the same name and kind of the 2nd
Q What do you observe of three given terms taken togethe[r]
A that the two first are suposeition the last is a demand
Q how is the third term known
A it is know by these or like the words what Cost how m. . . how much
Q how many sorts of proportion are there
A two direct and inverse of Direct proportion
. . .rportion
[Direct] proportion is when more requires more or [less re]quires less
[Wha]t do you mean by more requires more—
[Mo]re requires more is when the third is greater
[than] the first and therefore requires the fourth term
[to be] greater than the second in the same proportio[n]
[W]hat do you mean by less requires less
[Less] requires less is when third term is less than
[the] first and therefore requires the fourth
[term] to be less than the second in the like [pro]portion
[H]ow is the fourth term found in [direc]t proportion
. . . multipliing the 2nd and 3rd together and dividing that . . .by the first term
<Page 13>
Double Rule of three
if 100£ in 12 months gain 7£ interest what principal will gain 3£-18-9d in 9 months ans[answer] £75
[Calculations not transcribed.]		 if 100£ in 12 months gain 8. . . interest what sum will g[ain] £8-12S-in 5 months
[Calculations not transcribed.]
if 145 men can make a [wall?] 32 feet hig[h]. . . long in 8 days in how [m]any days can 68 Men build a wall 28 feet high of the length
[Calculations not transcribed.]
if 200 lb be carried 40 miles for 40 Cents how far may 20200 lb be carried for $60-60 cts An[Answer] 60 miles
[Calculations not transcribed.]
if a footman travel 240 miles in 12 days when the days are 12 hours long how many days will he require to travel 720 miles when the days are 16 hours long
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Double Rule of three
Aplication.
if 4 men in 5 days eat 7 lb of bread how much will be suficient for 16 men 15 days
[Calculations not transcribed.]		 if 100 dollars in one year gain 3½ dollars interest what sum will gain $38-50 cts in one year and a quarter
[Calculations not transcribed.]
if 360 lb of beef serve 340 men 15 days how many lb will serve 130 men 25 days
[Calculations not transcribed.]		 if the tuition of 3 boys for two quarters of a year be $40-20 cts. how much will the tuition of 60 boys, amount to for 4½ years
ans $72[.]36
[Calculations not transcribed.]
<Page 15>
Simple interest
what is the amount of a bond for 387 dollars 50 cents for 1 year at 6 percent per annum
[Calculations not transcribed.]		 what is the interest of 428 doll[ars] for one year at 6¾ per cent p[er] annum
[Calculations not transcribed.]
Case 2
when there is a fraction as ¼ ½ ¾ &c[etc] in the rate per cent
Rule
multiply the principal by the rate per cent to the product add ¼ ½ or ¾ of said principal and divide by 100 for the interest required
Examples
what is the interest of £ 526-10s for 1 year at 5 ½ per cent per annum
[Calculations not transcribed.]
^£^ 28-19-1s an[answer] 		what is the interest of £216-5s for one year at 5½ percent per annum
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what is the interest [of] £400 for one year at . . . cent per annum
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Simple Interest
what is the interest of £855-17-6 for one year at 5¾ per cent per annum
[Calculations not transcribed.]		 Case 3
when the interest of a sum given for several years is required
Rule
Multiply the interest of the given for one year by the number of
years
Examples
what is the interest of ^£^246-18^s^ for 5 years at 4¼ per cent per annum.
[Calculations not transcribed.]
what is the interest of . . . for one year at 6¼ [per]cent per annum
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what is the interest of $426-18 [fo]r one year at 4½ per cent [p]erannum
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<Page 17>
Simple Interest
Examples6
What principal at interest for 5 year at 6 per Cent per anum will amount to £650
[Calculations not transcribed.]		 Case S[?]
to find the rate per cent when the amount time and principal are given
Rule
As the product of the [time and] principal is to the interest for the whole time So is 100 pound[s] or dollars to the rate per cent
Examples
at what rate per cent per annum will £500 amount to £650 in 5 years
[Calculations not transcribed.]
What principle at inter[est] for 10 years at 6 percent per anum will amounto[amount to] £1300—
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What principal at interest for 4 years at 7 per cent peranum will amount to $57
[Calculations not transcribed.]		 at what rate per cent per annum will £500 amount to £725 in 9 years
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<Page 18>
Simple Interest
At what rate persent[percent] peranum will $600 amount to $856—50 Cts in 9 years and 6 months
[Calculations not transcribed.]		 In what time will £540 amt[amount] to £734— 8s at 4 persent per an[num]
[Calculations not transcribed.]
Case 7
to find the time when the principal amount and rate persent are given
Rule
as the intrust of the principal for one year is to one yeare so is the whole interest to the time required
Examples
In what time will £500 per amount to £725— at 5 persent
[Calculations not transcribed.]		 at what time will $837— amount to $10-20-51- cts at 5¾ persent peranum
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A testator left his son besides providing for his education &c $1500 to receive the amount thereof at 6 percent per an[num] when he should arrive at the age of 21 years which his guardian then found to be $2332-50 Cents how old was the Boy at his fathers decease
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<Page 19>
Compound Interest.
. . .interest is that which arises from [the?] principal and its interest put together as the [interest?] becomes due and for this reason it is Called Compound
Rule—
. . . the amount of the . . . interest . . . which will . . . for the second year. . .principal for the second year and . . . principal for the [third?] year and . . .number of years from the last. . .the given principal and the [remainder?]. . .Compound Interest
Examples
what is the Compound intrust of £500 . . . 5 per cent
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what is the compound interest of £450 for 5years at 5 percent perannum
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<Page 20>
Compound Intru[st]
What is the amount of £550 10s for 3 years at 7 per Cent per anum Compound interest
[Calculations not transcribed.]		 what will $1200 ammoun[t to in] 4 years at 4¼ percent compound interest
[Calculations not transcribed.]
What is the Compound interest of $500 for 4 years at 6 persent per annum
[Calculations not transcribed.]		 How much will £400 amount to in 4 years at 6 per cent per annum
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<Page 21>
Discount 1826
Bought goods to the value of £109-10s to be paid at 9 months what present money will discharge the same if I am allowed 6 per cent per annum discount
[Calculations not transcribed.]		 What is the present worth of $430-67 Cts for 19 months Discount at 5 percent—
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what is the present worth of £161-10s for 19 months discount at 5 per cent per annum
[Calculations not transcribed.]		 What is the Rebate of £112— 12s for 20 months at 7 percent per annum
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<Page 22>
Discount march 1st 1826
Discount is an allowance made for the payment of a sum of money before it becomes due according to a certain rate per cent agreed on between the parties concerned the preasant worth of any sum or debt due some time hence is such a sum as if put to interest for that time at a certain rate per cent would amount to the sum or debt (See Case 5 Simple interest)
Rule
As the ammount of 100 pounds or dollars at the rate and time given is to 100 pounds or dollars so is the whole debt to the presant worth
Proof
Find the amount of the present worth for the time and rate proposed which must equal the sum or debt
Examples
what is the present worth and what the discount of £500 payable in 10 months at 5 per cent per annum
Ans { persen £480
Discount 20
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1A version of this verse, which appears again on page 7 of the copybook, was also inscribed in a dictionary belonging to Mordecai Lincoln, Thomas Lincoln’s brother and thus Abraham’s uncle. The verse may have been traditional in the Lincoln family.
Roy P. Basler, ed., Collected Works of Abraham Lincoln (New Brunswick, NJ: Rutgers University Press, 1953), 1:2; Albert J. Beveridge, Abraham Lincoln, 1809-1858 (Boston: Houghton Mifflin, 1928), 64.
2“when” and “T C” are written between the lines at this point.
3“George” is written between the lines at this point.
4Supplied text is taken from Herndon’s handwritten copy of the verse, which was made before the original became badly damaged.
Roy P. Basler, ed., Collected Works of Abraham Lincoln, 1:2.
5“(No 2)” is written to the right of the calculations, and William H. Herndon signed his name, “W. H. Herndon,” below it.
6William H. Herndon wrote “Genuine” and signed his name, “W H Herndon”, on the page at this point.

Handwritten Document, 22 page(s), Leaf 1 (Simple Subtraction): Handwritten Document (recto), Copy of Handwritten Document (verso), Private Collection, Shapell Manuscript Foundation (Los Angeles, CA); Leaf 2 (Simple Multiplication): Handwritten Document, Plimpton Collection, Columbia University (New York, NY); Leaf 3 (Simple Division): Handwritten Document, Taper Collection, Lincoln Presidential Foundation (Springfield, IL); Leaf 4 (Compound Addition): Handwritten Document, Core Collection, Library of Congress Core Collection [Washington, DC] ; Leaf 5 (Compound Multiplication): Handwritten Document, Box 1, Folder 1, Lincoln Papers, Indiana Historical Society (Indianapolis, IN); Leaf 6 (Single Rule of Three): Handwritten Document, Upper portion: Lincoln Collection, LA02, Brown University (Providence, RI); Lower portion: Lincoln Collection, Lincoln Miscellaneous Manuscripts, Box 4, Folder 21, University of Chicago (Chicago, IL) ; Leaf 7 (Double Rule of Three): Handwritten Document, Harvard University [Cambridge, MA]; Leaf 8 (Simple Interest): Lincoln Manuscripts, Lilly Library, Handwritten Document, Indiana University (Bloomington, IN); Leaf 9 (Simple Interest Examples): , Handwritten Document, Yale University, The Beinecke Rare Book and Manuscript Library (New Haven, CT); Leaf 10 (Compound Interest): Handwritten Document, Private Collection, Seth Kaller Inc. (Westchester County, NY); Leaf 11 (Discount): Handwritten Document, Folder X.2324.2004, Chicago Historical Society (Chicago, IL).