Proof
Superpose and apply I.7 to rule out a non-coincident image of the
contained angle; conclude by Common Notion 4.
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Full neighborhood
Depends on (2)
Required by (dependents) (14)
- I.9Proposition I.9To bisect a given rectilineal angle.
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- I.12Proposition I.12To draw a perpendicular straight line to a given infinite straight line from a given point not on it.
- 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.48Proposition I.48If in a triangle the square on one of the sides be equal to the squares on the remaining two sides of the triangle, the…
- III.1Proposition III.1To find the centre of a given circle.
- III.3Proposition III.3If in a circle a straight line through the centre bisect a straight line not through the centre, it also cuts it at…
- III.9Proposition III.9If a point be taken within a circle, and more than two equal straight lines fall from the point on the circle, the…
- III.27Proposition III.27In equal circles angles standing on equal circumferences are equal to one another, whether they stand at the centres or…
- III.28Proposition III.28In equal circles equal straight lines cut off equal circumferences, the greater equal to the greater and the less to…
- IV.9Proposition IV.9About a given square to circumscribe a circle.
- VI.5Proposition VI.5If two triangles have their sides proportional, the triangles will be equiangular and will have those angles equal…
- XI.4Proposition XI.4If a straight line be set up at right angles to two straight lines which cut one another, at their common point of…
- XI.10Proposition XI.10If two straight lines meeting one another be parallel to two straight lines meeting one another, not in the same plane,…
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