Proposition Replicated
Proposition III.16
The straight line drawn at right angles to the diameter of a circle from its extremity will fall outside the circle, and into the space between the straight line and the circumference another straight line cannot be interposed.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:III.16
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 (4)
- I.11Proposition I.11To draw a straight line at right angles to a given straight line from a given point on it.
- I.17Proposition I.17In any triangle two angles taken together in any manner are less than two right angles.
- 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,…
- 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…
Required by (dependents) (8)
- III.17Proposition III.17From a given point to draw a straight line touching a given circle.
- 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.4Proposition IV.4In a given triangle to inscribe a circle.
- IV.7Proposition IV.7About a given circle to circumscribe a square.
- IV.8Proposition IV.8In a given square to inscribe a circle.
- IV.12Proposition IV.12About a given circle to circumscribe an equilateral and equiangular pentagon.
- IV.13Proposition IV.13In a given pentagon, which is equilateral and equiangular, to inscribe a circle.
Discussion
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