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@@Chillagma_Work-ok9kz Thank you sir for the compliment. Much much appreciated.

You are amazing!!!

@@ArchieUplifts GeoGebra.org

@@ArchieUplifts you can do it all on the website itself.

Have you had a look at the pdf book. Any feedback would be appreciated.

@@VishyKN I will

@@rameshks8449 Thank you sir. Actually in 2D when we say a figure is to a figure as something is to something we are talking of their area. In case of solids it is volume.

@@VishyKN yes sir

Can't change the caption font and color. Geogebra default settings get applied. Sorry about that.

@@VishyKN OK sir

Sir, took care of it. Have a look in this video ruclips.net/video/QNnF8nnbEWg/видео.html Proposition 11.22. Thanks for the feedback.

@@rameshks8449 so true

@@rameshks8449 Yes sir.

@@rameshks8449 Thank you sir.

It would be better if you start from the 1st proposition of book 10. Most of these terms have been covered in previous propositions.

Dear Martand Puri, Have a look at ruclips.net/video/bYdctpLuoWY/видео.html. Formulas for the various terms used is given.

Done Sir. Sorry about that.

@@VishyKN Perfect! Thanks again. 😇

Hi James, We could have joined B and D rather than A and C. The steps in the proof would have been the same. In that case, the triangle BDC would have been equal to the triangle BEC since these triangles are also on the same base and between same parallel lines. The proof would not have been any more or less efficient. I believe that it not the number of propositions or steps that define efficiency but the ease of understanding. In any case, since we are looking at Euclid's Elements, I am being as faithful to his choices in developing the proof. Thank you for pointing out the missing Proposition 42. Can't figure out how I missed it. By the way, have you had a look at the Book. Any comments on that would be much appreciated. Thanks for the appreciation and feedback.

Hi again, Just browsed through the playlist of Book 1. Euclid's Book 1 - Proposition 42 is there.

True, but the definition of a circle says that on a circle all the points are equidistant from the center. So we are choosing two points - point of contact and an arbitrary point somewhere else for comparison. In any case, remember the center is the assumed center. If we take the actual center, FE and FB will not be equal at any point since the centers of the two circles are not the same.

Yes Sir, you are absolutely right. Follow the steps by incorporating the change and you should be able to arrive at the limit as n goes to infinity. Thank you for identifying the error. You should end up with p < sqrt(2x / (n(n-1)) which will tend to 0 as n goes to infinity.

Long time!

GeoGebra.org

You are most Welcome. 🙏

Kindly goto About page in which the working link is there.

No.

Thank you sir.

Well, i am really having fun making them. If it benefits others, thats a bonus.

@@VishyKN Definitely a huge benefit for all math students! 👍

Thank you sir.