Page:Euclid's Elements 1714 Barrow translation.djvu/156

144 3. That Addition, Subraction, Multiplication, Divion; and the Extractions of roots or des of quare and cube numbers, be alo granted as poble.

Hatoever agrees with one or many equal numbers, agrees likewie with the re.

2. Thoe parts that are the ame to the ame part, or parts, are the ame amongt themelves.

3. Numbers that are the ame parts of equal numbers, or of the ame number, are equal among themelves.

4. Thoe numbers, of whom the ame number, or equal numbers, are the ame parts, are equal among themelves.

5. Unity meaures every number by the units that are in it; that is, by the ame number.

6. Every number meaures it elf by a unity.

7. If one number, multiplying another, produce a third, the multiplier all meaure the product by the multiplicand; and the multiplicand all meaure the ame by the multiplier.

Hence, No prime number is either a plane, olid, quare, or cube number.

8. If one number meaures another, that number by which it meaures all meaure the ame by the units that are in the number meauring, that is by the number itelf that meaures.

9. If a number meauring another, multiply that by which it meaures, or be multiplied by it, it produces that number which it meaures.

10. How many numbers oever any number meaures, it likewie meaures the number compoed of them.

11. If a number meaure any number, it alo meaures every number which the aid number meaures.

12. A number that meaures the whole and a part taken away doth alo meaure the redue.

PROP.