“The Bible is not my book nor Christianity my profession. I could never give assent to the long, complicated statements of Christian dogma.”— Abraham Lincoln (c.1865), in FSM app
“My earlier views of the unsoundness of the Christian scheme of salvation and the human origin of the scriptures have become clearer and stronger with advancing years, and I see no reason for thinking I shall ever change them.”— Abraham Lincoln (c.1865), in FSM app
“Lincoln read hard works—was philosophical—logical—mathematical—never read generally.”— John Stuart (c.1870), “Comment on Lincoln” by his first law partner
“If A can prove, however conclusively, that he may, of right, enslave B — why may not B snatch the same argument, and prove equally, that he may enslave A?– You say A is white, and B is black. It is color, then; the lighter, having the right to enslave the darker? Take care. By this rule, you are to be slave to the first man you meet, with a fairer skin than your own. You do not mean color exactly?–You mean the whites are intellectually the superiors of the blacks, and, therefore have the right to enslave them? Take care again. By this rule, you are to be slave to the first man you meet, with an intellect superior to your own. But, say you, it is a question of interest; and, if you can make it your interest, you have the right to enslave another. Very well. And if he can make it his interest, he has the right to enslave you.”— Abraham Lincoln (1854), “Personal Notes”, Unpublished [4]
“If you have ever studied geometry, you remember that by a course of reasoning, Euclid proves that all the angles in a triangle are equal to two right angles. Euclid has shown you how to work it out. Now, if you undertake to disprove that proposition, and to show that it is erroneous, would you prove it to be false by calling Euclid a liar?”— Abraham Lincoln (1858), “Fourth Lincoln-Douglas Debate”, Sep 18 [5]
“There are two ways of establishing a proposition. One is by trying to demonstrate it upon reason, and the other is, to show that great men in former times have thought so and so, and thus to pass it by the weight of pure authority. Now, if Judge Douglas will demonstrate somehow that this is popular sovereignty,—the right of one man to make a slave of another, without any right in that other, or anyone else to object,—demonstrate it as Euclid demonstrated propositions,—there is no objection. But when he comes forward, seeking to carry a principle by bringing it to the authority of men who themselves utterly repudiate that principle, I ask that he shall not be permitted to do it.”— Abraham Lincoln (1860), “Speech”, Columbus, Ohio [4]
“In the course of my law reading I constantly came upon the word “demonstrate”. I thought at first that I understood its meaning, but soon became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof? I consulted Webster’s Dictionary. They told of ‘certain proof,’ ‘proof beyond the possibility of doubt’; but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have defined blue to a blind man. At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies.”— Abraham Lincoln (c.1863) [4]
“Lincoln studied and nearly mastered the six-books of Euclid (geometry) since he was a member of Congress. He began a course of rigid mental discipline with the intent to improve his faculties, especially his powers of logic and language. Hence his fondness for Euclid, which he carried with him on the circuit till he could demonstrate with ease all the propositions in the six books; often studying far into the night, with a candle near his pillow, while his fellow-lawyers, half a dozen in a room, filled the air with interminable snoring.”— William Herndon (c.1870) [4]
The "Euclid scene" from the 2012 film Lincoln, wherein Lincoln ruminates on Eulid's first common axiom: "things which are equal to the same thing are equal to each other" as the basis of his "decision" that he is going all for none in respect to passing a law (Amendment #13) that ends slavery, once and for all, whatever the cost. |
1. Things which equal the same thing also equal one another.
2. If equals are added to equals, then the wholes are equal.
3. If equals are subtracted from equals, then the remainders are equal.
4. Things which coincide with one another equal one another.
5. The whole is greater than the part.
Lincoln: Euclid's first common notion is this: "Things which are equal to the same thing are equal to each other."
Scene: Homer doesn't get it; neither does Sam.
Lincoln: That's a rule of mathematical reasoning. It's true because it works; has done and always will do. In his book, Euclid says this is "self-evident."
Lincoln: D'you see? There it is, even in that two-thousand year old book of mechanical law: it is a self-evident truth that things which are equal to the same thing are equal to each other. We begin with equality. That's the origin, isn't it? That balance, that's fairness, that's justice.
Section 1. Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction. Section 2. Congress shall have power to enforce this article by appropriate legislation.
A depiction of “sparing the circle”, a problem proposed by ancient geometers, the goal of which is to constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. It was proven impossible to do, in a finite number of steps, in 1882. |
Herndon (reflection): “I say Lincoln so deeply absorbed in study he scarcely looked up when I entered. He was surrounded by a quantity of blank paper, large heavy sheets, a compass, a ruler, numerous pencils, several bottles of ink of various colors, and a profusion of stationery. He was apparently struggling with a calculation of some magnitude, for scattered about were sheet after sheet of paper covered with an unusual array of figures.”
Herndon: (speaking): “What are you doing?”
Lincoln: “I am trying to solve the difficult problem of squaring the circle. I have devoted the better part of two days, almost to the point of exhaustion.”
“Much of Lincoln’s unhappiness, the melancholy that ‘dripped from him as he walked’, was due to his want of religious faith. When the black fit was on him, he suffered as much mental misery as Bunyan or Cowper in the deepest anguish of their conflicts with the evil one.”— Ward Lamon (1872), Life of Lincoln [9]
“Towering genius disdains a beaten path. It seeks regions hitherto unexplored.”— Abraham Lincoln (1838), “Lyceum Address”, Jan 27 (Ѻ)
“Stand with anybody that stands RIGHT. Stand with him while he is right and PART with him when he goes wrong.”— Abraham Lincoln (1854), “Speech at Peoria, Illinois”, in reply to Senator Douglass, Oct 6 (Ѻ)
“I walk slowly, but never walk backwards.”— Abraham Lincoln (c.1860) (Ѻ)
“Nearly all men can stand adversity, but if you want to test a man’s character, give him power.”— Abraham Lincoln (c.1860) (Ѻ)
“In great contests each party claims to act in accordance with the will of god. Both may be, and one must be, wrong. God cannot be for and against the same thing at the same time.”— Abraham Lincoln (1862), “Mediation on the Will of God”, Sep (Ѻ)
“It is best not to swap horses while crossing the river.”— Abraham Lincoln (1864), “Reply to Nation Union League”, Jun 9 (Ѻ)