A Mathematical Problem

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.