During the century which has nearly elapsed since Dr Matthew Stewart published his General Theorems, many eminent geometers, both English and Foreign, have attempted to discover their solutions. Those attempts have, however, been rewarded with but limited success, and by far the most general and the most difficult of them remain still without a single published remark in the way of discussion or solution. Dr Stewart did not, as far as I know, make allusion to them himself in any of his subsequent writings, though he describes them as “of considerable use in the higher parts of mathematics;” and we learn from the preface to Mr Glenie's Demonstration of the 42d Proposition (Tract, 1813), that in conversation, Professor Dugald Stewart, in 1805, stated that, “he had not been able to find amongst his father's posthumous papers one word respecting them; that he had, oftener than once, observed mention made of them, in terms of admiration and respect, by some of the first mathematicians on the continent of Europe; but that as both they and the geometers in this country had tried their strength on them without success, and they had so long remained without demonstrations, he never expected to see them demonstrated.” This circumstance, of neither any demonstrations nor even memoranda, on the subject being found amongst Dr Stewart's papers, is readily accounted for by Professor Playfair, in his biography of that distinguished geometer (Edin. Trans. vol. i. p. 74), in the description which he gives of the habits of study of Dr Stewart. “He rarely wrote down any of his investigations till it became necessary to do so for the purpose of publication. When he discovered any proposition, he would put down the enunciation with great accuracy, and on the same piece of paper would construct very neatly the figure to which it referred. To these he trusted for recalling to his mind, at any future period, the demonstration or the analysis, however complicated it might be.”