18 Feb. 1815

Didacologia

Ch. Art & Science Division

25

IV. Sciences having for their subjects the predicaments of Number, Figure, and Quantity.

Between /Among/ these /the/ three predicaments respectively designated by these three names, the nature and intimacy of the relation that has place, has already been brought to view. Of figure, the modifications are scarcely conceivable, nor, accordingly, clearly expressible, otherwise than by means of number; whilst quantity is a predicament including both, and, therefore, still more abstract than either.

By the Greek-sprung word posology, the science of quantity, may, it is believed, and if so, now for the first time, not inappositely be distinguished.

Melomorphic, or say, morphoscopic, and amelomorphic, having regard to figure, and not having regard to figure; to the one or other of these denominations will the whole contents of the field of posology be found referable.

Of posology, the melomorphic, or morphoscopic branch has found in the word geometry (measurement of the earth) a denomination altogether familiar, but far from being co-extensively expressive. In the practice of measuring the earth may be found the origin of this branch of art and science, as well as one of its great uses. But besides the earth, it is, moreover, employed in the measuring of the rest of the visible universe. Not unfrequently, in the measuring of imaginary and unexemplified extension, i.e. in the measuring of nothing at all; and it is when thus employed, that those, by whom it is cultivated, seem most proud of it.

Oristic, and aoristic, or more expressively, oristicosemeiotic and aoristicosemeiotic, determinately and indeterminately expressed - to one or other of these denominations, will the whole contents of the field of amelomorphic posology be found referable /expressible/.

Of amclomorphic posology, the oristicosemeiotic branch has always had an appellative, no less apposite and expressive, than familiar in the word arithmetic i.e. the art and science which has numbers for its subject - the art of applying numbers to use, including the science of the properties of numbers, the aoristicosemeiotic, in the Arabic-sprung word algebra, an appellative not much less familiar, but altogether inapposite and unexpressive.

31