Lincoln and Euclid Elements...

5fish

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Did you know Lincoln was a self taught mathematician in Euclid's Geometry...

The Elements” of Euclid taught Abraham Lincoln the art of reason and logic, which he used as a power tool throughout his life, to win cases in court, to debate against slavery and to guide our country through the civil war

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When Abraham Lincoln debated slavery against Stephen Douglas in 1858, Douglas gave a long list of reasons why slavery was justified. But following Euclid, Lincoln made his most powerful argument by starting from the most basic ideas, by going back to the postulates of morality.
Lincoln asked Douglas: “Are you a Christian?” Douglas replied, “Yes.” Lincoln asked, “Do you know and practice the Golden Rule?” Douglas replied, “Of course: Do unto others as you would have them do unto you.” Then Lincoln asked one simple question: “Would you like to be a slave?”


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"He 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." Abraham Lincoln from Short Autobiography of 1860.

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"Euclid wrote thirteen books," says Dan Van Haften, co-author of Abraham Lincoln and the Structure of Reason. "The first six books covered plane geometry," Van Haften says, "and that's what Lincoln studied."

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Van Haften's book, written with David Hirsch, isn't the first to prove Lincoln's fascination with Euclidean geometry. But it is the first to draw a direct connection to how Lincoln used Euclid in his Cooper's Union Address, the Gettysburg Address, and other speeches pivotal to his career -- and the nation

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they have a copy of Proclus's commentaries on Euclid. And on page 159, it says that a proposition, if it has all its parts, has six elements -- an enunciation, exposition, specification, a construction, proof and conclusion."
 

5fish

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Here a good article... about Lincoln lessons from Euclid... its a great little short article... from Lincoln thoughts on Euclid...


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Lincoln wrote about why he decided to study Euclid:

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
 

5fish

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here is a bit of news...


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Abraham Lincoln (1809–1865), the 16th president of the United States of America, came from a rural background. It was long believed that he was self-educated and received little formal schooling; however, some emerging documents point to the fact that, indeed, Lincoln did have a formal education. Pages of a cipher book belonging to Abraham Lincoln have been discovered in various library collections, including Columbia University, Harvard University, and the Lilly Library of Indiana University. Here are two pages of this book concerning the computation of simple interest
 

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Based on the problems involved and dates on some of the pages – 1824 and 1826 – Lincoln probably worked in the book intermittently over several years. The professors think he could have started as early as the age of 10. "Most people say he went to school for anything between three months and nine months" over the course of his life, Professor Clements said. "We think he went to school [for up to] two years." And very little of the work is wrong, he added

Here the Lincoln Society putting in their two cents... good details

https://quod.lib.umich.edu/j/jala/2...d-the-abbaco-tradition?rgn=main;view=fulltext
 

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here a another take...


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The professors’ find suggests Lincoln may have gone to school over as many as three to five winters, said historian Daniel Stowell, director of the Papers of Abraham Lincoln project at the Abraham Lincoln Presidential Library in Springfield. The library owns one previously identified page of the book.

“They are arguing with some merit that a cyphering book would have been created in a school setting,” Stowell said. “It does at least open the possibility that he may have had more formal schooling than originally thought — not a whole lot more, but still more.”

The pages — attached as a single leaf — include word problems that are the equivalent of eighth-grade modern work, Clements said.

“If 100 dollars in one year gain 3½ dollars interest, what sum will gain $38.50 cents in one year and a quarter?” one reads.

Any student doing such work in the 1820s would have been more advanced than most on the frontier in Indiana, Clements said.
 
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