Proposition Replicated
Proposition I.32
In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:I.32
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
Neighborhood at a glance
Full neighborhood
Depends on (2)
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…
Discussion
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