3. That Addition, Subſtraction, Multiplication, Diviſion; and the Extractions of roots or ſides of ſquare and cube numbers, be alſo granted as poſſible.
Axiomes.
1. WHatſoever agrees with one or many equal numbers, agrees likewiſe with the reſt.
2. Thoſe parts that are the ſame to the ſame part, or parts, are the ſame amongſt themſelves.
3. Numbers that are the ſame parts of equal numbers, or of the ſame number, are equal amongſt themſelves.
4. Thoſe numbers, of whom the ſame number, or equal numbers, are the ſame parts, are equal amongſt themſelves.
5. Unity meaſures every number by the units that are in it; that is, by the ſame number.
6. Every number meaſures it ſelf by a unity.
7. If one number, multiplying another, produce a third, the multiplier ſhall meaſure the product by the multiplicand; and the multiplicand ſhall meaſure the ſame by the multiplier.
Hence, No prime number is either a plane, ſolid, ſquare, or cube number.
8. If one number meaſures another, that number by which it meaſures ſhall meaſure the ſame by the units that are in the number meaſuring, that is by the number itſelf that meaſures.
9. If a number meaſuring another, multiply that by which it meaſures, or be multiplied by it, it produces that number which it meaſures.
10. How many numbers ſoever any number meaſures, it likewiſe meaſures the number compoſed of them.
11. If a number meaſure any number, it alſo meaſures every number which the ſaid number meaſures.
12. A number that meaſures the whole and a part taken away doth alſo meaſure the reſidue.
PROP.
