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Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Euclid book 1 of elements proposition 28

What is wrong in proposition 28 Book 1 of Euclid elements the sum of the interior angles on the same side equal to two right angles, then the straight lines are parallel to one another
I can draw easily with handwrite on a papers two lines adds up two right angels but they are not parallel? So what's wrong?

and I draw an example in the following photo and here is the link and Quote of the proposition 28

proposition 28 book 1
If a straight line falling on two straight lines makes the exterior angle equal to the interior and opposite angle on the same side, or the sum of the interior angles on the same side equal to two right angles, then the straight lines are parallel to one another

the photo I draw and tried as u will see the straight line fall on the two lines and and draw the first left angel 100 degree and the other 80 so they add up to 180 but not parallel! the proposition consist of two sections the first section is clear and I understand it but after "or the sum of the interior angles on the same side equal to two right angles, then the straight lines are parallel to one another.... is not clear"

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Euclid book 1 of elements proposition 28

In your diagram the line made by 100 degrees should slope away from the other line as 100 is obtuse.  These lines are parallel.

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

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Euclid book 1 of elements proposition 28

your line on th eleft is leaning right so its less than 90 deg
100 deg would lean left

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: Euclid book 1 of elements proposition 28

In your diagram the line made by 100 degrees should slope away from the other line as 100 is obtuse.  These lines are parallel.

Bob

But if O extend them from the top won't they meet?

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Euclid book 1 of elements proposition 28

I have made an accurate diagram and put a protractor image over point D.

When you measure an angle using a protractor you will see there is a choice of angles.

If angle BDE is measured the zero on the protractor is on the inner scale. Going round anticlockwise when we reach the line DE the scale says 100.

If angle ADE is measured the zero is on the outer scale. Going round clockwise when we reach the line DE the scale says 80.

As you can see 80 + 100 makes a straight line and is equal in total to 180. Lines DE and BC are parallel.

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

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: Euclid book 1 of elements proposition 28

oh thanks for that golden information now I can use the protractor professional

but why when trying to extend them in my draw sheet they meet from up side?
they shouldn't meet right
I always draw the same lines angles and they meet!
is that because the direction of the second line maybe it called negative? or it's from another plane or what I know the parallel lines won't meet in the two directions

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Euclid book 1 of elements proposition 28

Go back to your sketch in post 1.  The line marked with an angle of 100 is not correctly drawn. As 100 > 90 this angle should be obtuse so the line should slope the other way.  I chose to make an accurate diagram hoping you'd realise this. I added a protractor so you'd be able to see how 100 and 80 are related on the diagram.

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