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Hannibal lecter

Member

From: Iraq

Registered: 2016-02-11

Posts: 402

English translation of Apollonius’s Conics

I read from that book first pages: The most accurate English translation of Apollonius’s Conics (which is his main work) is by R. Catesby Taliaferro and Michael N. Fried, published by Green Lion Press.

I read: Apollonius’s his predecessor characterized the
curves by using the unique diameter that makes right angles with the chords,,

The question is where is that chord they mean here can u show me simple diagram as example

I didn't understand the full sentence where is the unique diameter and the right angle and the cord?

Last edited by Hannibal lecter (2026-01-17 07:37:12)

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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: 10,823

Re: English translation of Apollonius’s Conics

Yes, I understand your confusion. The language is English but it's not how a modern English person would put it.

I used Google AI to get to the modern meaning.  As it's a topic I am familiar with, I'll re-phrase myself.

The diagram shows a set of conic sections: a circle, an ellipse, a parabola, and (part of) a hyperbola.  All these geometric shapes have a line of symmetry, usually called the axis. (The circle has many and the ellipse has two.)

Chords drawn across the axis at right angles to the axis are always bisected (cut in half) by the axis.

Hope that helps. 

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

From: Iraq

Registered: 2016-02-11

Posts: 402

Re: English translation of Apollonius’s Conics

Yes, I understand your confusion. The language is English but it's not how a modern English person would put it.

I used Google AI to get to the modern meaning.  As it's a topic I am familiar with, I'll re-phrase myself.

The diagram shows a set of conic sections: a circle, an ellipse, a parabola, and (part of) a hyperbola.  All these geometric shapes have a line of symmetry, usually called the axis. (The circle has many and the ellipse has two.)

Chords drawn across the axis at right angles to the axis are always bisected (cut in half) by the axis.

Hope that helps. 

Bob

Can you please show me a diagram or imge
Pointing at the chord and the right angle and the unique diameter

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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: 10,823

Re: English translation of Apollonius’s Conics

Success with posting image:

This shows a parabola f(x) = x² with the y axis as the line of symmetry.  This is the axis your book is referring to.

The red and green lines are at 90 degrees to this axis and, as the axis is a line of symmetry, each is bisected by the axis.

You can try the same with the other curves.  Circle is easy. You'll need a good equation plotter for the ellipse and hyperbola. There is  one here:

https://www.mathsisfun.com/data/grapher-equation.html

Hope that helps.

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

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,920

Re: English translation of Apollonius’s Conics

Hi Bob;

Success with posting image:

Your image displays fine for me, but its code is in live url tags and clicking the image opens a Postimages webpage containing the image (amongst other things!)

This is the correct code for just the image:

[img]https://i.postimg.cc/4KJ9rhFk/symmetry-on-parabola.gif[/img]

Postimages has an img-tag issue that I mentioned here, but I probably wasn't clear enough. Fixed now.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Bob

Administrator

Registered: 2010-06-20

Posts: 10,823

Re: English translation of Apollonius’s Conics

Many thanks Phro,

I knew you had said that before but I was in a hurry to get the picture up. I've corrected it now.

I can access Imgur if I I use a VPN.  I've chosen Australia for this purpose. 

The UK's Ofgov site has a checking device, according to which the forum is not subject to the new law. So I've kept a copy of their statement about this and I'll just carry on for now and hope the police don't come knocking. 

Bob

---

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

From: Iraq

Registered: 2016-02-11

Posts: 402

Re: English translation of Apollonius’s Conics

Success with posting image:

https://i.postimg.cc/4KJ9rhFk/symmetry-on-parabola.gif

This shows a parabola f(x) = x² with the y axis as the line of symmetry.  This is the axis your book is referring to.

The red and green lines are at 90 degrees to this axis and, as the axis is a line of symmetry, each is bisected by the axis.

You can try the same with the other curves.  Circle is easy. You'll need a good equation plotter for the ellipse and hyperbola. There is  one here:

https://www.mathsisfun.com/data/grapher-equation.html

Hope that helps.

Bob

The image is not showing bob

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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: 10,823

Re: English translation of Apollonius’s Conics

Sorry. There's an internet 'war' going on between The UK government and Imgur so it has become more difficult to add images. Phrontister has found out how and my image should now be showing in post 4.  But I'll add the image again here. Let me know is it now shows.

Bob

---

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

From: Iraq

Registered: 2016-02-11

Posts: 402

Re: English translation of Apollonius’s Conics

Can u send me a link I'll open

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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: 10,823

Re: English translation of Apollonius’s Conics

I'm so sorry this is proving so hard for you. My new image site offers the following possibilities. I'll number them so you can say which works for you.

(1) https://postimg.cc/4KJ9rhFk

(2) https://i.postimg.cc/bvn9SxxJ/symmetry_on_parabola.gif

(3) [symmetry_on_parabola.gif](https://postimg.cc/4KJ9rhFk)

(4)

(5) <a href="https://postimg.cc/4KJ9rhFk" target="_blank"><img src="https://i.postimg.cc/4KJ9rhFk/symmetry_on_parabola.gif" alt="symmetry_on_parabola"></a>

(6)

(7) <a href="https://postimages.org/" target="_blank"><img src="https://i.postimg.cc/bvn9SxxJ/symmetry_on_parabola.gif" alt="symmetry_on_parabola"></a>

(4) is the one they says should work for forums.  That's what used when I changed post 4.

If none then what?

What device are you using?  Does your own image show ok?

Maybe Phrontister will have some ideas for you. He has been a great help in sorting out the image problem for me.

Bob

---

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

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,920

Re: English translation of Apollonius’s Conics

Hi Bob;

I did exactly as you did, testing all the Postimages link options, but had to go out before I could post about it...and you beat me to it.

We really need to have Hannibal's answers to your questions before going much further, but here's some info anyway in case it helps:

     - My Android smartphone gives me several options if I do a long press on your image: eg, 'Download image', 'Copy image', and 'View image'.
     - On my PC, right-clicking your image also gives some options: eg, 'Save image as' and 'Copy image'.

Btw, I've noticed you've changed your image to a better quality one.

EDIT: Something I should've said about my test results that might be helpful: any Postimages link that displayed just your image here on MIF did so only when BBCode 'img' tags were used. When used outside of MIF, any links that displayed the image at all always showed it within a full Postimages web page (along with other content).

Last edited by phrontister (2026-01-21 08:39:31)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

Hannibal lecter

Member

From: Iraq

Registered: 2016-02-11

Posts: 402

Re: English translation of Apollonius’s Conics

I'm so sorry this is proving so hard for you. My new image site offers the following possibilities. I'll number them so you can say which works for you.

(1) https://postimg.cc/4KJ9rhFk

(2) https://i.postimg.cc/bvn9SxxJ/symmetry_on_parabola.gif

(3) [symmetry_on_parabola.gif](https://postimg.cc/4KJ9rhFk)

(4) https://i.postimg.cc/4KJ9rhFk/symmetry_on_parabola.gif

(5) <a href="https://postimg.cc/4KJ9rhFk" target="_blank"><img src="https://i.postimg.cc/4KJ9rhFk/symmetry_on_parabola.gif" alt="symmetry_on_parabola"></a>

(6) https://i.postimg.cc/bvn9SxxJ/symmetry_on_parabola.gif

(7) <a href="https://postimages.org/" target="_blank"><img src="https://i.postimg.cc/bvn9SxxJ/symmetry_on_parabola.gif" alt="symmetry_on_parabola"></a>

(4) is the one they says should work for forums.  That's what used when I changed post 4.

If none then what?

What device are you using?  Does your own image show ok?

Maybe Phrontister will have some ideas for you. He has been a great help in sorting out the image problem for me.

Bob

mr bob can u upload it using another sites there is too much sites in web for free and past the link here pls

---

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,823

Re: English translation of Apollonius’s Conics

But you haven't answered any of my questions.

I'm at the limit of the help I can offer.

Try here:

https://www.mathsisfun.com/geometry/conic-sections.html

Bob

---

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

From: Iraq

Registered: 2016-02-11

Posts: 402

Re: English translation of Apollonius’s Conics

(4) is the one they says should work for forums.  That's what used when I changed post 4.

If none then what?

What device are you using?  Does your own image show ok?

Maybe Phrontister will have some ideas for you. He has been a great help in sorting out the image problem for me.

Bob

I used imgur as you can see how I show me photo in my post I used it like that :

[img]https://i.imgur.com/ulr1DUQ.png(here type if image png or jpeg)[/img]
and I'm using a laptop windows 11 on chrome browser and my own image is showing no problems
I used a lot of methods at first it not worked untell i USED THAT CODE

[img]THE LINK[/img]

I only put the link image in the middle https://i.imgur.com/ulr1DUQ.png

but with .png or .jpeg at the end so it show perfectly

---

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,823

Re: English translation of Apollonius’s Conics

Thanks for the reply.

Can you see this image?

And what about this?

The first looks small and a bit blurred for me.

The second is larger and much sharper.

Both have the img /img format.

I'll repeat what I said in post 4.  The y axis is the line of symmetry. The red and green lines are at 90 degrees to the axis and are bisected by it.

Bob

---

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