
Definitions 
Brief comments 
1 
Unit is that according to which each of the things which
are is one, 
This definition of 'unit' parallels Aristotle's definition of 'quality'
at Categories 8 
2. 
and the multitude composed from units is a number. 

3. 
A number is a part of a number, the smaller of the larger, whenever
it measures the larger, 

4. 
and parts whenever it does not measure, 

5. 
and the larger is a multiple of the smaller whenever it is measured
by the smaller. 

6. 
The number which is divided in two is an even number, 

7. 
and the number which is not divided in two is odd, or the number
which differs from an even number by a unit. 

8. 
The number measured by an even number taken in groups of an even number
is an eventimes even number, 

9. 
and the number measured by an even number taken in groups of an odd
number is an eventimes odd number, 

10. 
[and the number measured by an odd number taken in groups of an even
number is an oddtimes even,] 

11. 
and the number measured by an odd number taken in groups of an odd
number is an oddtimes odd number. 

12. 
The number measured only by a unit is a prime number. 

13. 
Prime numbers relative to one another are those measured only
by a unit as a common measure. 

14. 
Compound number is a number measured by a number, 

15. 
and compound numbers relative to one another are those measured
by a number as a common measure. 

16. 
A number is said to multiply a number whenever as many units
as there are in it, so many times the multiplied number is added and becomes
some number. 

17. 
Whenever two numbers multiply one another and make some number, the
number which results is called plane, and it sides are the numbers
multiplying one another, 

18. 
and whenever three numbers multiply one another and make some number,
the number which results is called solid, and its sides are the numbers
multiplying one another. 

19. 
A square number is the equaltimes equal number or the number
enclosed by two equal numbers, 

20. 
and a cube is the equaltimes equal equaltimes or enclosed
by three equal numbers. 

21. 
Numbers are proportional whenever the first is an equal multiple
or the same part or the same parts of the second as the third of the fourth. 

22. 
Similar plane and solid numbers are those having proportional
sides. 

23. 
A perfect number is one which is equal to all its parts. 
