The following tasks are required to complete this lesson:
- Study the Lesson carefully.
- Complete the lesson Assessment.
Lesson
The first and incomposite number indeed, is that which has no other part except that which is denominated from the whole quantity of the number; so that the part itself is no other than unity. And such are the numbers 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.
In each of these numbers therefore, no other part can be found except that which is denominated from them, and this, as we have before observed, is unity alone. For in 3 there is only one part, i.e. a third, which is denominated from 3, and this third part is unity. After the same manner in 5 there is only one part which is a fifth, and this is unity. And the same consequence will be found to take place in the rest.
This number however, is called “first and incomposite”, because no other number measures it than unity, which is the mother of all number. And this is owing to its not being composed from any other numbers, and to its being generated from unities alone multiplied into themselves. For thrice one is three, five times one is 5, seven times one is seven, and so of the rest. But these being multiplied into themselves produce other numbers like themselves. Being allotted also a primary essence, they will be found to be as it were certain elements of all the numbers generated from them; because they are incomposite, and formed by a simple generation; and all the numbers proceeding from them are resolved into them, but they are neither produced from others, nor resolved into other numbers.
Assessment
