If as many numbers as we please beginning from an unit be in continued proportion, the less measures the greater according to some one of the numbers which have place among the proportional numbers.
若从单位开始任意多个数成连比例,则最小数依比例数中的某个数来量最大数。
从单位 A 开始的连比例数 B、C、D、E,最小数 B 依比例数中的某项量度最大数 E:B 量 E 的次数等于单位 A 量 D 的次数。
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Let there be as many numbers as we please, B, C, D, E, beginning from the unit A and in continued proportion; I say that B, the least of the numbers B, C, D, E, measures E according to some one of the numbers C, D. For since, as the unit A is to B, so is D to E, therefore the unit A measures the number B the same number of times as D measures E; therefore, alternately, the unit A measures D the same number of times as B measures E.
设从单位A开始有连比例数B、C、D、E,则A比B等于D比E。
[VII. 15] But the unit A measures D according to the units in it; therefore B also measures E according to the units in D; so that B the less measures E the greater according to some number of those which have place among the proportional numbers.
因此单位A量B的次数等于D量E的次数,由VII.15,交替得A量D的次数等于B量E的次数。
— PORISM.
但A量D依其单位数,故B量E也依D的单位数。
And it is manifest that, whatever place the measuring number has, reckoned from the unit, the same place also has the number according to which it measures, reckoned from the number measured, in the direction of the number before it.
所以最小数B量最大数E依比例数中的某个数。推论:量数从单位起的位置,与被量数从被量数起向前数的位置相同。