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Hannibal lecter

Member

From: Iraq

Registered: 2016-02-11

Posts: 396

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: 10,818

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: 396

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: 10,818

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: 4,919

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: 10,818

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

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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