All language conſiſts of repreſentative ſigns, and thoſe ſigns are the beſt which effeƈt their purpoſes with the greateſt preciſion and diſpatch. Such for all common purpoſes are the audible ſigns called words, which are ſtill conſidered as audible, whether addreſſed immediately to the ear, or through the medium of letters to the eye. Geometrical diagrams are not ſigns, but the materials of geometrical ſcience, the objeƈt of which is to ſhow the relative quantities of their parts by a proceſs of reaſoning called Demonſtration. This reaſoning has been generally carried on by words, letters, and black or uncoloured diagrams; but as the use of coloured ſymbols, ſigns, and diagrams in the linear arts and ſciences, renders the proceſs of reaſoning more preciſe, and the attainment more expeditious, they have been in this inſtance accordingly adopted.
Such is the expedition of this enticing mode of communicating knowledge, that the Elements of Euclid can be acquired in leſs than one third the time uſually employed, and the retention by the memory is much more permanent; theſe facts have been aſcertained by numerous experiments made by the inventor, and ſeveral others who have adopted his plans. The particulars of which are few and obvious; the letters annexed to points, lines, or other parts of a diagram are in faƈt but arbitrary names, and repreſent them in the demonſtration; inſtead of theſe, the parts being differently coloured, are made to name themſelves, for their forms in correſponding colours repreſent them in the demonſtration.
In order to give a better idea of this ſyſtem, and of the advantages gained by its adoption, let us take a right
