Proof
Apply I.1 to erect an equilateral triangle on the segment; bisect the
opposite angle by I.9; the bisector meets the segment at its midpoint
by I.4.
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Full neighborhood
Depends on (3)
Required by (dependents) (18)
- I.12Proposition I.12To draw a perpendicular straight line to a given infinite straight line from a given point not on it.
- I.16Proposition I.16In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and…
- I.42Proposition I.42To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
- 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…
- II.10Proposition II.10If a straight line be bisected and a straight line be added to it in a straight line, the square on the whole with the…
- II.11Proposition II.11To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the…
- II.14Proposition II.14To construct a square equal to a given rectilineal figure.
- III.1Proposition III.1To find the centre of a given circle.
- 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.25Proposition III.25Given a segment of a circle, to describe the complete circle of which it is a segment.
- III.30Proposition III.30To bisect a given arc.
- III.33Proposition III.33On a given straight line to describe a segment of a circle admitting an angle equal to a given rectilineal angle.
- IV.5Proposition IV.5About a given triangle to circumscribe a circle.
- IV.8Proposition IV.8In a given square to inscribe a circle.
- XI.38Proposition XI.38If the sides of the opposite planes of a cube be bisected, and planes be carried through the points of section, 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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