Whatever else he was to be, there was work enough before him for a while in translation from the German and in commentary on the great German writers for the behoof of the British public. There were but three or four men in Britain competent for that business, and he was one of them. The translation of _Legendre’s Geometry_ for Brewster deserves a passing notice. Though not published till 1824,—when it appeared, from the press of Oliver and Boyd of Edinburgh, as an octavo of nearly 400 pages, with the title _Elements of Geometry and Trigonometry; with Notes. Translated from the French of A. M. Legendre, Member of the Institute, etc. Edited by David Brewster, LL.D., etc. With Notes and Additions, and an Introductory Essay on Proportion_,—it was begun by Carlyle in 1822, and continued to occupy him through the whole of that year. His authorship of this Translation remained such a secret, or had been so forgotten, that the late Professor De Morgan, specially learned though he was in the bibliography of mathematics, did not know the fact, and would hardly believe it, till I procured him the evidence. It was one day in or about 1860, if I remember rightly, and in the common room of University College, London, that De Morgan, in the course of the chats on all things and sundry which I used to have with him there, adverted to the Legendre book. He knew, he said, that Brewster himself could not have done the translation; but he had always been under the impression that the person employed by Brewster had been a certain Galbraith, a noted teacher of mathematics in Edinburgh. Recently, however, he had heard Carlyle named as the man; and, being very doubtful on the point, he wanted very much to be certain. To back my own statement, I undertook to obtain an _affidavit_ from head-quarters. “Tell De Morgan,” said Carlyle, when I next saw him, “that every word of the book is mine, and that I got £50 for the job from Brewster; which was then of some consideration to me.” He went on to speak, very much as he does in the _Reminiscences_, of the prefixed little Essay on Proportion, retaining a fond recollection of that section of the book,—begun and finished, he says, on “a happy forenoon (Sunday, I fear)” in his Edinburgh lodgings, and never seen again since he had revised the proof. De Morgan, who had some correspondence on the subject with Carlyle after I had conveyed Carlyle’s message, paid it a compliment afterwards in his _Budget of Paradoxes_, by calling it “as good a substitute for the Fifth Book of Euclid as could be given in speech”; and a glance at the Essay in the volume itself will confirm the opinion. It fills but eight printed pages, and consists of but four definitions and three theorems, wound up with these concluding sentences:—“By means of these theorems, and their corollaries, it is easy to demonstrate, or even to discover, all the most important facts connected with the Doctrine of Proportion. The