Proof
Use I.2 to construct, at one extremity of the longer line, a segment
equal to the shorter. Then by Definition I.15 the desired cut-off is
obtained.
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Full neighborhood
Depends on (2)
Required by (dependents) (12)
- I.5Proposition I.5In isosceles triangles the angles at the base are equal to one another; and if the equal straight lines be produced…
- I.6Proposition I.6If in a triangle two angles are equal to one another, the sides which subtend the equal angles will also be equal to…
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- I.18Proposition I.18In any triangle the greater side subtends the greater angle.
- I.20Proposition I.20In any triangle two sides taken together in any manner are greater than the remaining one.
- I.22Proposition I.22Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is…
- I.23Proposition I.23On a given straight line and at a point on it to construct a rectilineal angle equal to a given rectilineal angle.
- I.46Proposition I.46On a given straight line to describe a square.
- II.11Proposition II.11To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the…
- II.14Proposition II.14To construct a square equal to a given rectilineal figure.
- IV.1Proposition IV.1Into a given circle to fit a straight line equal to a given straight line which is not greater than the diameter of the…
- VI.9Proposition VI.9From a given straight line to cut off a prescribed part.
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