Proof
Cut equal segments by I.3, construct the matching triangle by I.22,
apply I.8.
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Full neighborhood
Depends on (3)
- I.3Proposition I.3Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
- I.8Proposition I.8If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they…
- I.22Proposition I.22Out of three straight lines, which are equal to three given straight lines, to construct a triangle: thus it is…
Required by (dependents) (12)
- I.24Proposition I.24If two triangles have the two sides equal to two sides respectively, but have the one of the angles contained by the…
- I.31Proposition I.31Through a given point to draw a straight line parallel to a given straight line.
- I.42Proposition I.42To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
- III.33Proposition III.33On a given straight line to describe a segment of a circle admitting an angle equal to a given rectilineal angle.
- III.34Proposition III.34From a given circle to cut off a segment admitting an angle equal to a given rectilineal angle.
- IV.2Proposition IV.2In a given circle to inscribe a triangle equiangular with a given triangle.
- IV.3Proposition IV.3About a given circle to circumscribe a triangle equiangular with a given triangle.
- VI.5Proposition VI.5If two triangles have their sides proportional, the triangles will be equiangular and will have those angles equal…
- VI.6Proposition VI.6If two triangles have one angle equal to one angle and the sides about the equal angles proportional, the triangles…
- VI.7Proposition VI.7If two triangles have one angle equal to one angle, the sides about other angles proportional, and the remaining angles…
- VI.18Proposition VI.18On a given straight line to describe a rectilineal figure similar and similarly situated to a given rectilineal figure.
- XI.26Proposition XI.26At a given point on a given straight line to construct a solid angle equal to a given solid angle contained by three…
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