Kitap 5
10
When four magnitudes are ltcontinuouslygt proportional, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on continually, whatever be the proportion.
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11
The term corresponding magnitudes is used of antecedents in relation to antecedents, and of consequents in relation to consequents.
12
12
Alternate ratio means taking the antecedent in relation to the antecedent and the consequent in relation to the consequent.
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13
Inverse ratio means taking the consequent as antecedent in relation to the antecedent as consequent.
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14
Composition of a ratio means taking the antecedent together with the consequent as one in relation to the consequent by itself.
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15
Separation of a ratio means taking the excess by which the antecedent exceeds the consequent in relation to the consequent by itself.
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16
Conversion of a ratio means taking the antecedent in relation to the excess by which the antecedent exceeds the consequent.
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17
A ratio ex aequali arises when, there being several magnitudes and another set equal to them in multitude which taken two and two are in the same proportion, as the first is to the last among the first magnitudes, so is the first to the last among the second magnitudes;
17
Or, in other words, it means taking the extreme terms by virtue of the removal of the intermediate terms.
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