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- Study the Lesson carefully.
- Complete the lesson Assessment.
Lesson
The second and composite number, is indeed itself odd, because it is formed by the same property of the odd number, but it retains in itself no principal essence; is composed from other numbers; and has parts which are denominated both from itself and a foreign word; but the part alone which is denominated from itself, will always in these numbers be found to be unity. The parts however, which are denominated from a foreign word, are sometimes many, and sometimes only one. Of this kind are the numbers 9, 15, 21, 25, 27, 33, 39. Each of these therefore has parts denominated from itself, viz. its proper unities. Thus 9 has a ninth part which is 1; 15 has a fifteenth part, which is also 1; and the like takes place in the rest. But they have also a part denominated from a foreign word. Thus 9 has a third part which is 3; and 15 has a third part which is 5, and also a fifth part, 3. Thus too, 21 has a third part, i.e. 7, and a seventh part which is 3; and there is the same consequence in all the rest.
This number however, is called “second”, because it is not only measured by unity, but also by another number, by the conjunction of which it is formed. Nor does it contain any thing in itself of a principal nature; for it is generated from other numbers; 9 indeed from 3; 15 from 3 and 5; 21 from 3 and 7; and the rest after the same manner.
But it is called “composite”, because it may be resolved into those numbers from which it is said to be composed, viz. into those which measure a composite number. Nothing however which can be dissolved is incomposite, but is by every necessity a composite.
Assessment
