I have often been surprised that Mathematics, the quintessence of Truth, should have found admirers so few and so languid. Frequent consideration and minute scrutiny have at length unravelled the cause; viz. that though Reason is feasted, Imagination is starved; whilst Reason is luxuriating in its proper Paradise, Imagination is wearily travelling on a dreary desert. To assist Reason by the stimulus of Imagination is the design of the following production. In the execution of it much may be objectionable. The verse (particularly in the introduction of the ode) may be accused of unwarrantable liberties, but they are liberties equally homogeneal with the exactness of Mathematical disquisition, and the boldness of Pindaric daring. I have three strong champions to defend me against the attacks of Criticism: the Novelty, the Difficulty, and the Utility of the work. I may justly plume myself that I first have drawn the nymph Mathesis from the visionary caves of abstracted idea, and caused her to unite with Harmony. The first-born of this Union I now present to you; with interested motives indeed--as I expect to receive in return the more valuable offspring of your Muse. Thine ever, S. T. C. [CHRIST'S HOSPITAL], _March 31, 1791_. 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.[22:1] 5 Now let A. B. Be the given line Which must no way incline; The great Mathematician Makes this Requisition, 10 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. 15 Describe the circle B. C. D. At the distance B. A. from B. the centre The round A. C. E. to describe boldly venture.[22:2] (Third postulate see.) And from the point C. 20 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, 25 And postulate the second For Authority ye know. A. B. C. Triumphant shall be An Equilateral Triangle, 30 Not Peter Pindar carp, nor Zoilus can wrangle. III