Proof
Apply I.34 and I.37; double via Common Notion 2.
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Full neighborhood
Depends on (3)
- I.34Proposition I.34In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas.
- I.37Proposition I.37Triangles which are on the same base and in the same parallels are equal to one another.
- 2Common notion 2If equals be added to equals, the wholes are equal.
Required by (dependents) (4)
- I.42Proposition I.42To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
- I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
- VI.1Proposition VI.1Triangles and parallelograms which are under the same height are to one another as their bases.
- VI.15Proposition VI.15In equal triangles which have one angle equal to one angle the sides about the equal angles are reciprocally…
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