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In the image for A+A=C (multiply by 2) I see the intersection point C, but what if you wanted to multiply by 3? That would be A+C=D and I don't see any point on the curve that the line through A and C intersects. In fact it looks like for any A you choose, adding A+A gives a C which has that property (in other words A*3=0 for any A). This is just by visual inspection. What am I missing?

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Seems to have labelled "C" and "-C" in a very misleading manner. Take point A. Draw a tangent, that cuts the curve at point C. That's not the point 2A. That's the point C.

Reflect C across the X axis, and that's point 2A.

So you're not missing anything, the article is misleading at best.

In short, to take the sum of two points A and B, draw a line through them both to find a third point on the curve, reflect that point across the X-axis, and the result (which will also be on the curve) is A+B.

If A and B coincide then use the tangent at A.

The point at (vertical) infinity plays the role of the zero.

Ohh OK! Thank you. Makes more sense now.

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