Math Is Fun Forum

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Euclid's elements proposition 7 book 4

http://aleph0.clarku.edu/~djoyce/java/elements/bookIV/propIV7.html

I was just wondering something . We know that if a line touches a circle at one point, then this means that this line is forming a right angle with the diameter of the circle. (“From this it is clear that the straight line drawn at right angles to the diameter of a circle from its end touches the circle.” According to corollary of proposition 16 from book 3)
http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII16.html

In our construction, we would just draw the line at right angle to the diameter and with the corollary justify that is in fact touching the circle.

So, we already know that the angle made with the line touching the circle and the diameter is right, yet Euclid goes to prove it a second time by saying : “Then, since FG touches the circle ABCD, and EA has been joined from the center E to the point of contact at A, therefore the angles at A are right. For the same reason the angles at the points B, C, and D are also right.”

There’s no problem with what he’s saying, but it seems a little repetitive to prove something which is already known. Maybe it’s me doing an error. Could someone to me what’s wrong here ? Thank you

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Euclid's elements proposition 7 book 4

pls someone.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Euclid's elements proposition 7 book 4

Sorry.  I could not follow what you are asking.  Life for me is too short to read and follow all of Euclid's elements.  Problems with geometry I may be able to do, but getting inside his head is beyond me.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Re: Euclid's elements proposition 7 book 4

Sorry.  I could not follow what you are asking.  Life for me is too short to read and follow all of Euclid's elements.  Problems with geometry I may be able to do, but getting inside his head is beyond me.

Bob

It's ok. The ideas still holds and it doesn't make it false it's just the way it is done which I found weird.