54

LIFE OF COLONEL MACERONI.

of simplicity. The Romans had begun by finding itnecessary to relieve the eye from the fatigue and embarrass-ment of counting vertical strokes, all absolutely similar, inthe instance above shown of making the first and the laststroke in Ini vir, and Iiml vir, longer than the intermediateones. Another improvement followed; in order to repre-sent the half of each corporation complete. The V., wasevidently the half of the X.; they, therefore, made it repre-sent the fifth unity. The letter C., was originally formedthus, E.; they took the half of this sign representing ahundred, and so L. became the representative of the halfhundred, or fifty. In like manner they haired the sign ofCIq., a thousand, and If).; i.e., the D. became equivalentto the half thousand, or five hundred.

At length, in order to abridge anti condense, as well asto render more clear to ocular perception their numericalexpressions, the Romans established the rule that every signof an inferior value when placed before, that is, to the left ofanother of superior value, should indicate that such inferioramount was to be deducted from the superior; and, on thecontrary, that the inferior value was to be added to the su-perior, when the latter was written first, thus it was, thatafter having expressed four by IIII, and nine by VIIII, theyafterwards expressed them by IV, and IX.

It is not in my power to assign the dates to each of theabove modifications and improvements in the numerical sys-tem of the Romans. But it would not be difficult to provethat they occurred progressively, and at pretty long intervalsof time. With respect, however, to the fractional sign D,it would appear that it was not introduced into the Romansystem by the Romans themselves, but only about thefifteenth century, when their language had again become inEurope the language of theologians, of literature, and ofthe sciences.