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Al-Allo

Member

Registered: 2012-08-23

Posts: 324

Euclid's elements proposition 15 book 3

Hi,

http://aleph0.clarku.edu/~djoyce/java/elements/bookIII/propIII15.html

I have understood the proof in general. It is only a small detail which i'm not sure. Maybe it's because english isn't my first language. Anyway, the part of the proof which says : "Then, since BC is nearer to the center and FG more remote, EK is greater than EH." I have no problem understanding what is said here. This is supported by this definition : "And that straight line is said to be at a greater distance on which the greater perpendicular falls." (Definition 5 of book 3) Now, this is where i'm unsure. From what I understand of it, it says that if I have a perpendicular that is bigger than the other, than my straight line is said to be at a greater distance. (This is how I understand it) Now, in the proof, we do the inverse. We know that one line is at a greater distance than the other and we conclude with the definition that one perpendicular is bigger than the other. How is this correct ? Unless the definition implies that the reverse is also ok, then this works. But if the definition implies only one direction, (The one which is defined) then how is the proof valid ?

By the way, you don't need to read all of the proof. Only the things at beginning are needed.

Thank yoU!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Euclid's elements proposition 15 book 3

If {statement A} => {statement B}                 then               {not B} => {not A}

B

Last edited by Bob (2015-06-19 05:19:02)

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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

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,436

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Re: Euclid's elements proposition 15 book 3

You mean {not B} => {not A}?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Euclid's elements proposition 15 book 3

Yes I do.  Thanks for spotting that.  I've edited it now.

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