much acuteness and solidity of judgment, have founded the doctrine of proportionality. In order to facilitate the execution of the plan here recommended, an index has been constructed, by means of which the Geometry of this Supplement may be incorporated, as it were, with that of Euclid, and the reading of both the treatises may be made to go on together. In the demonstrations of the propositions recourse has been had to symbols. But these symbols are merely the representatives of certain words and phrases, which may be substituted for them at pleasure, so as to render the language employed strictly conformable to that of ancient Geometry. The consequent diminution of the bulk of the whole book is the least advantage which results from this use of symbols. For the demonstrations themselves are sooner read and more easily comprehended by means of these useful abbreviations, which will, in a short time, become familiar to the reader, if he is not already perfectly well acquainted with them. It appeared to be unnecessary to print the formal and logical conclusion which belongs to every geometrical demonstration, and which consists in repeating the enuntiation of the proposition which was to be proved, and in asserting that it has been proved. This last step, is, therefore, left for the reader in all cases mentally to supply. And if some omissions of a weightier kind, and some errors, be discoverable in the following pages, it is hoped that they will be found neither too great, nor too many to be forgiven, if the genéral plan of the work meet with the approbation of those who are competent to decide upon Trinity College, April 27th, 1819. it. |