Fig. 6. The algebraic properties of the Roman system can be made palpable by considering the equivalent geometric properties based on the interrelation of the proportions: 1, Ö2, and q. For example, if S is either removed or added to SR, this results in RR, as Figure 6a illustrates. This is equivalent to Properties 2 and 3. That 2S +RR = RR is equivalent to Property 1 (see Figure 6b). Finally, if SR is cut in half it forms two SR at a smaller scale (Figure 6c), while two SR added together form an enlarged SR (see Figure 6d) as predicted by Property 4, the doubling property of Table 8.  top of page  back to text 
