Proposition Replicated
Proposition III.37
If a point be taken outside a circle and from the point there fall on the circle two straight lines, if one of them cut the circle, and the other fall on it, and if further the rectangle contained by the whole of the straight line which cuts the circle and the straight line intercepted on it outside between the point and the convex circumference be equal to the square on the straight line which falls on the circle, the straight line which falls on it will touch the circle.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:III.37
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
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Full neighborhood
Depends on (5)
- III.17Proposition III.17From a given point to draw a straight line touching a given circle.
- 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.19Proposition III.19If a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the…
- III.36Proposition III.36If a point be taken outside a circle and from it there fall on the circle two straight lines, and if one of them cut…
- I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
Discussion
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