Proof
Apply I.31 to draw a parallel through the apex; apply I.29 twice and
Common Notion 2.
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Depends on (3)
- I.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
- I.31Proposition I.31Through a given point to draw a straight line parallel to a given straight line.
- 2Common notion 2If equals be added to equals, the wholes are equal.
Required by (dependents) (17)
- 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…
- III.16Proposition III.16The straight line drawn at right angles to the diameter of a circle from its extremity will fall outside the circle,…
- III.20Proposition III.20In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same…
- III.22Proposition III.22The opposite angles of quadrilaterals in circles are equal to two right angles.
- III.31Proposition III.31In a circle the angle in the semicircle is right, that in a greater segment less than a right angle, and that in a less…
- III.32Proposition III.32If a straight line touch a circle, and from the point of contact there be drawn across, in the circle, a straight line…
- IV.2Proposition IV.2In a given circle to inscribe a triangle equiangular with a given triangle.
- IV.3Proposition IV.3About a given circle to circumscribe a triangle equiangular with a given triangle.
- IV.10Proposition IV.10To construct an isosceles triangle having each of the angles at the base double of the remaining one.
- IV.15Proposition IV.15In a given circle to inscribe an equilateral and equiangular hexagon.
- VI.4Proposition VI.4In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which…
- VI.7Proposition VI.7If two triangles have one angle equal to one angle, the sides about other angles proportional, and the remaining angles…
- VI.8Proposition VI.8If in a right-angled triangle a perpendicular be drawn from the right angle to the base, the triangles adjoining the…
- XI.21Proposition XI.21Any solid angle is contained by plane angles less than four right angles.
- XIII.7Proposition XIII.7If three angles of an equilateral pentagon, taken either in order or not in order, be equal, the pentagon will be…
- XIII.18Proposition XIII.18To set out the sides of the five figures and to compare them with one another; and that no other figure, besides the…
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