A Line Divided into Equal Multiples (Series 151)
Line c as three eights (24) and d as three fours (12), bracketed as multiplici
Series 151 shows line c divided into three equal parts of 8, totalling 24, and line d into three parts of 4, totalling 12, the pair bracketed under the heading multiplici (multiples); the short lines a and b give the single units 8 and 4. The figure demonstrates a multiple ratio, one magnitude containing another an exact number of times. Ruled segments with interior tick-marks realise the division.
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A multiple ratio: 24 as three eights
Line c holds 24 built from three parts of 8, and line d holds 12 built from three parts of 4, both bracketed as multiplici. Set against the units a 8 and b 4, the figure shows one magnitude that is an exact multiple of another.
Line cut into three equal parts
The right-hand lines are ruled and ticked into three equal sub-segments — 8, 8, 8 on c and 4, 4, 4 on d — while the left-hand a and b give the corresponding single lengths. The tick-marks make the equal division of the line explicit.