2011 David Hirsch Speech at National Archives II (video).

2010 Virtual Book Signing (at Abraham Lincoln Book Shop). December 10 (Part 1) December 10 (Part 2) December 10 (Part 3) December 10 (Part 4)

    The six elements are simple to express:[1] They were nearly lost in the dust bin of history. This is how Euclid proved geometric propositions (though, as far as is known, Euclid never explicitly described the technique). It his also how Lincoln, starting in 1854, tried cases and gave speeches. He too did not directly explain how his speeches mean. Lincoln's words did the speaking --- with their ancient structure just beneath the surface. Thomas Jefferson also studied Euclid. If Aristotle's Madison Avenue rhetoric is based on deception, Euclid's geometric technique is rock solid beauty, based on honesty.

    Hirsch and Van Haften are presently working on a Jefferson book.

Enunciation: “The enunciation states what is given and what is being sought from it.”

Exposition: “The exposition takes separately what is given and prepares it in advance for use in the investigation.”

Specification: “The specification takes separately the thing that is sought and makes clear precisely what it is.”

Construction: “The construction adds what is lacking in the given for finding what is sought.”

Proof: “The proof draws the proposed inference by reasoning scientifically from the propositions that have been admitted.”

Conclusion: “The conclusion reverts to the enunciation, confirming what has been proved.”


[1] Proclus, A Commentary on the First Book of Euclid’s Elements, Translated, with Introduction and Notes, by Glenn R. Morrow [Princeton, NJ: Princeton University Press, 1970], 159.

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