A mathematical problem, a poem by Coleridge [1791]
Channel: Classic Poetry
Date: 2021-03-29

A mathematical problem. A poem by Coleridge.

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, nor 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 Autocratrix 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 proved 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.