What did Lincoln say about equality triangle linked with maths and

[matthew]

slavery in the film? I watched Lincoln the movie last night and in the movie he said something about equality in a triangle or something in maths and linked it with Black and White humans being equal, but what exactly did Lincoln say about the maths triangle thing?

[Mark]

LINCOLN
I never had much of schooling, but
I read Euclid, in an old book I
borrowed. Little enough ever found
its way in here -
(touching his cranium)
- but once learnt it stayed learnt.
75.Euclid’s first common notion is
this: “Things which are equal to
the same thing are equal to each
other.”

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.”

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.

............................

At first he basically says that :
If A=B, and B=C, then A=C, which he learned by reading Ellucid.

The argument that follows about equality is not as clear to me, but I believe he is saying:
If (equality)balance = fairness, and fairness = justice, then equality = justice.

[Jim]

Things which are equal to the same thing are equal to each other