Proof
Apply I.29 and I.26 to the two triangles cut by the diameter, then
Common Notion 2.
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Depends on (3)
- I.26Proposition I.26If two triangles have the two angles equal to two angles respectively, and one side equal to one side, namely either…
- I.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
- 2Common notion 2If equals be added to equals, the wholes are equal.
Required by (dependents) (19)
- I.35Proposition I.35Parallelograms which are on the same base and in the same parallels are equal to one another.
- I.37Proposition I.37Triangles which are on the same base and in the same parallels are equal to one another.
- I.38Proposition I.38Triangles which are on equal bases and in the same parallels are equal to one another.
- I.41Proposition I.41If a parallelogram have the same base with a triangle and be in the same parallels, the parallelogram is double of the…
- I.43Proposition I.43In any parallelogram the complements of the parallelograms about the diameter are equal to one another.
- I.46Proposition I.46On a given straight line to describe a square.
- II.1Proposition II.1If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by…
- II.2Proposition II.2If a straight line be cut at random, the rectangle contained by the whole and both of the segments is equal to the…
- II.4Proposition II.4If a straight line be cut at random, the square on the whole is equal to the squares on the segments and twice the…
- II.5Proposition II.5If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole…
- II.6Proposition II.6If a straight line be bisected and a straight line be added to it in a straight line, the rectangle contained by the…
- II.9Proposition II.9If a straight line be cut into equal and unequal segments, the squares on the unequal segments of the whole are double…
- IV.7Proposition IV.7About a given circle to circumscribe a square.
- IV.8Proposition IV.8In a given square to inscribe a circle.
- VI.1Proposition VI.1Triangles and parallelograms which are under the same height are to one another as their bases.
- XI.24Proposition XI.24If a solid be contained by parallel planes, the opposite planes in it are equal and similar parallelograms.
- XI.28Proposition XI.28If a parallelepipedal solid be cut by a plane through the diagonals of the opposite planes, the solid will be bisected…
- XI.39Proposition XI.39If there be two prisms of equal height, and one have a parallelogram as base and the other a triangle, and if the…
- XII.3Proposition XII.3Any pyramid which has a triangular base is divided into two pyramids equal and similar to one another, similar to the…
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