To cut off from the greater of two given unequal straight lines a straight line equal to the less.

# | Statement | Reason |
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1. | Straight line exists. | given |

2. | Straight line , greater than , exists. | given |

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QEF. Given the two straight lines AB and C, AE has been cut off from AB the greater equal to C the less. Success! Name: |
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Add to proof | Summary | |
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Definition of a point. | ||

Definition of a straight line => A line exists | ||

Definition of a straight line => Choose an arbitrary point | ||

Definition of a circle | ||

Definition of an equilateral triangle. | ||

Draw a straight line from any point to any point. | ||

Extend a finite straight line continuously in a straight line. | ||

Draw a circle with center and radius. | ||

All right angles equal one another. | ||

The Parallel Postulate | ||

Things equal to the same thing are equal to each other. | ||

If equals are added to equals, then the wholes are equal. | ||

If equals are subtracted from equals, then the remainders are equal. | ||

Things which coincide with one another equal one another. | ||

The whole is greater than the part. | ||

Construct an equilateral triangle on a given finite straight line. | ||

Place a straight line equal to a given straight line with one end at a given point. |