What are Euclid axioms
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euclid based his approach upon ten axioms. they are statements that could be accepted as truths. he called these axioms his 'postulates' and divided them into two groups of five.
FIRST GROUP
1. things which are equal to the same thing are also equal to each other.
2. if equals are added to equals, the results are equal
3. if equals are subtracted from equals, the remainders are equals.
4. things that coincide with each other are equal to each other
5. the whole is greater than the part.
SECOND GROUP
1. a straight line can be drawn between any two points.
2. any finite straight lines can be extended indefinitely in a straight line.
3. for any line segment, it is possible to draw a circle using the segment as the radius and one end point as the center.
4. all right angles are the same
5. if a straight line falling across two other straight lines results in the sum of the angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on the same side as the side where the angle sums are less than two right angles.
FIRST GROUP
1. things which are equal to the same thing are also equal to each other.
2. if equals are added to equals, the results are equal
3. if equals are subtracted from equals, the remainders are equals.
4. things that coincide with each other are equal to each other
5. the whole is greater than the part.
SECOND GROUP
1. a straight line can be drawn between any two points.
2. any finite straight lines can be extended indefinitely in a straight line.
3. for any line segment, it is possible to draw a circle using the segment as the radius and one end point as the center.
4. all right angles are the same
5. if a straight line falling across two other straight lines results in the sum of the angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on the same side as the side where the angle sums are less than two right angles.
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