Proof
Drop a perpendicular by I.11; Common Notions 1–2 sum the resulting
two right angles to the unequal-case angle sum.
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Depends on (4)
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- 1Common notion 1Things which are equal to the same thing are also equal to one another.
- 2Common notion 2If equals be added to equals, the wholes are equal.
- I.10Definition I.10When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles…
Required by (dependents) (9)
- I.14Proposition I.14If with any straight line, and at a point on it, two straight lines not lying on the same side make the adjacent angles…
- I.15Proposition I.15If two straight lines cut one another, they make the vertical angles equal to one another.
- I.17Proposition I.17In any triangle two angles taken together in any manner are less than two right angles.
- I.28Proposition I.28If a straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on…
- I.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
- 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…
- IV.3Proposition IV.3About a given circle to circumscribe a triangle equiangular with a given triangle.
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