=1839.= All such reasonings [natural philosophy, chemistry, agriculture, political economy, etc.] are, in comparison with mathematics, very complex; requiring so much _more_ than that does, beyond the process of merely deducing the conclusion logically from the premises: so that it is no wonder that the longest mathematical demonstration should be much more easily constructed and understood, than a much shorter train of just reasoning concerning real facts. The former has been aptly compared to a long and steep, but even and regular, flight of steps, which tries the breath, and the strength, and the perseverance only; while the latter resembles a short, but rugged and uneven, ascent up a precipice, which requires a quick eye, agile limbs, and a firm step; and in which we have to tread now on this side, now on that--ever considering as we proceed, whether this or that projection will afford room for our foot, or whether some loose stone may not slide from under us. There are probably as many steps of pure reasoning in one of the longer of Euclid’s demonstrations, as in the whole of an argumentative treatise on some other subject, occupying perhaps a considerable volume.--WHATELY, R. _Elements of Logic, Bk. 4, chap. 2, sect. 5._ =1840.= [Geometry] that held acquaintance with the stars, And wedded soul to soul in purest bond Of reason, undisturbed by space or time. --WORDSWORTH. _The Prelude, Bk. 5._