Proposition Replicated
Proposition III.32
If a straight line touch a circle, and from the point of contact there be drawn across, in the circle, a straight line cutting the circle, the angles which it makes with the tangent will be equal to the angles in the alternate segments of the circle.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:III.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 (5)
- III.18Proposition III.18If a straight line touch a circle, and a straight line be joined from the centre to the point of contact, the straight…
- 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.21Proposition III.21In a circle the angles in the same segment are equal to one another.
- 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…
- I.32Proposition I.32In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles,…
Required by (dependents) (4)
- III.33Proposition III.33On a given straight line to describe a segment of a circle admitting an angle equal to a given rectilineal angle.
- III.34Proposition III.34From a given circle to cut off a segment admitting an angle equal to a given rectilineal angle.
- IV.2Proposition IV.2In a given circle to inscribe 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.
Discussion
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