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. [35]
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. 40
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. [45]
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, 50
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[23:1] do! [55]
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 60
With Urine the soft-flowing daughter of Fright.

[[24]]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? 65
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 70
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.

1791.

FOOTNOTES:

[21:2] First published in 1834 without a title, but tabulated as 'Mathematical Problem' in 'Contents' 1 [p. xi].

[22:1] Poetice for Angle. Letter, 1791.

[22:2] Delendus 'fere'. Letter, 1791.