Give all seven Euclid's definition.
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Definition 1A unit is that by virtue of which each of the things that exist is called one.
Definition 2A number is a multitude composed of units.
Definition 3A number is a part of a number, the less of the greater, when it measures the greater;
Definition 4But parts when it does not measure it.
Definition 5The greater number is a multiple of the less when it is measured by the less.
Definition 6An even number is that which is divisible into two equal parts.
Definition 7An odd number is that which is not divisible into two equal parts, or that which differs by a unit from an even number.
Definition 2A number is a multitude composed of units.
Definition 3A number is a part of a number, the less of the greater, when it measures the greater;
Definition 4But parts when it does not measure it.
Definition 5The greater number is a multiple of the less when it is measured by the less.
Definition 6An even number is that which is divisible into two equal parts.
Definition 7An odd number is that which is not divisible into two equal parts, or that which differs by a unit from an even number.
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1. A straight line segment can be drawn joining any two points.
2. Any straight line segment can be extended indefinitely in a straight line .
3. Given any straight line segment , a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent .
5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles , then the two lines inevitably must
intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the
parallel postulate .
2. Any straight line segment can be extended indefinitely in a straight line .
3. Given any straight line segment , a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent .
5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles , then the two lines inevitably must
intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the
parallel postulate .
Similar questions
Definition 2
A number is a multitude composed of units.
Definition 3
A number is a part of a number, the less of the greater, when it measures the greater;
Definition 4
But parts when it does not measure it.
Definition 5
The greater number is a multiple of the less when it is measured by the less.