# Euclid and Coleridge: A Poem

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