Euclid’s first proposition in Book I states that an equilateral triangle can be constructed from a segment AB only with a ruler and compass. Here is a poem by the British poet Samuel Taylor Coleridge on this proposition:

**A Mathematical Problem**

This is now–this was erst,

Proposition the first–and Problem the first.

I.

On a given finite Line

Which must no way incline;

To describe an equi–

–lateral Tri–

–A, N, G, L, E.

Now let A. B.

Be the given line

Which must no way incline;

The great Mathematician

Makes this Requisition,

That we describe an Equi–

–lateral Tri–

–angle on it:

Aid us, Reason–aid us, Wit!

II.

From the centre A. at the distance A. B.

Describe the circle B. C. D.

At the distance B. A. from B. the centre The round A. C. E. to describe boldly venture.

(Third Postulate see.)

And from the point C.

In which the circles make a pother

Cutting and slashing one another,

Bid the straight lines a journeying go,

C. A., C. B. those lines will show.

To the points, which by A. B. are reckon’d,

And postulate the second

For Authority ye know.

A. B. C.

Triumphant shall be

An Equilateral Triangle,

Not Peter Pindar carp, not Zoilus can wrangle.

III.

Because the point A. is the centre

Of the circular B. C. D.

And because the point B. is the centre

Of the circular A. C. E.

A. C. to A. B. and B. C. to B. A.

Harmoniously equal for ever must stay;

Then C. A. and B. C.

Both extend the kind hand

To the basis, A. B.

Unambitiously join’d in Equality’s Band.

But to the same powers, when two powers are equal,

My mind forbodes the sequel;

My mind does some celestial impulse teach,

And equalises each to each.

Thus C. A. with B. C. strikes the same sure alliance,

That C. A. and B. C. had with A. B. before;

And in mutual affiance,

None attempting to soar

Above another,

The unanimous three

C. A. and B. C. and A. B.

All are equal, each to his brother,

Preserving the balance of power so true:

Ah! the like would the proud Autocratorix do!

At taxes impending not Britain would tremble,

Nor Prussia struggle her fear to dissemble;

Nor the Mah’met-sprung Wight,

The great Mussulman

Would stain his Divan

With Urine the soft-flowing daughter of Fright.

IV.

But rein your stallion in, too daring Nine!

Should Empires bloat the scientific line?

Or with dishevell’d hair all madly do ye run

For transport that your task is done?

For done it is–the cause is tried!

And Proposition, gentle Maid,

Who soothly ask’d stern Demonstration’s aid,

Has prov’d her right, and A. B. C.

Of Angles three

Is shown to be of equal side;

And now our weary steed to rest in fine,

‘Tis rais’d upon A. B. the straight, the given line.