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In the video at 4:30 there's a illustration about spreads in four sides, that are equal. I get that oppsite side spread is same. What I don't get is that spread between quadrance R and P is equal to the spreads that are adjacent(the wider one).

Please explain why they are same.

I was confused about the cross law a little bit. So After reviewing this and previous videos several times, and I realized that due to the cyclic property of the cross law and the cross law being quadratic equation gives the formula able to manipulate its internal signs, practically there exists ...

This may be a silly question, but as I heard from the previous video triple quad formula is (internal large interval + internal small interval - whole interval) squared equal 4 times (internal large interval times internal small interval), and the triple quad formula from this video seems differe...

Another question.

In previous examples of cross ratios, It seems that it's all about straight lines. But suddenly in Chasles theorem the cross ratio is applied in conic including a circle.

I'm curious. Is cross ratio work on curved interval, like the arc interval between alpha and beta. Or Is it ...

I've tried several times to solve exercise2.1 using CaR program. But I can't plot the tangent line for gamma. As you know it is easy to find a null point starting 'from a pole outside circle'. It's just a result of first definition of pole, that includes a tangent line.

But in exercise2.1 null po...