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Subject: "Question on Descartes"     Previous Topic | Next Topic
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Cliff P
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Aug-06-07, 08:50 PM (EST)
 
"Question on Descartes"
 
   Gulberg in "Mathematics From the Birth of Numbers" (p. 367) writ's of Descartes famous geometry book:

"La géométrie does not actually use 'Cartesian' coordinate axes or any other coordinate system."

The Wikipedia entry on "La géométrie" seems to contradict Gulberg:

"The work was responsible for introducing the Cartesian coordinate system, which is a mathematical graph in which x is the horizontal line and y is the vertical line, and in which the positive numbers on the x line are on the right and the negative numbers on the left, and the positive numbers on the y line are on the top and the negative numbers are on the bottom, and specifically discussed the representation of points of a plane, via real numbers; and the representation of curves, via equations."

Do you feel that one of these is closer to the truth than the other? Thanks, Cliff


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alexbadmin
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2064 posts
Aug-06-07, 11:13 PM (EST)
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1. "RE: Question on Descartes"
In response to message #0
 
   >Do you feel that one of these is closer to the truth than
>the other? Thanks, Cliff

Well, I may of course follow in the steps of a former president and inquire innocently for the meaning of "is". The question absolutely affords several such metaphysical quandaries. What indeed is the truth or being responsible?

As a matter of fact, La géométrie does not mention any coordinate system. This is as true as the facts go.

On the other hand, there is no doubt that analytic geometry has evolved from the work of Descartes (and Fermat), although no one seems to know for sure who and when first used the notion of Cartesian coordinate system.

So, as far as the hard boiled truth is concerned, the first of the two opinions is unquestionable. The second is commonly accepted as truthful provided "being responsible" is understood broadly. However, if "being responsible for introducing" is understood as a diluted version of "having introduced," then we can say that the second opinion is rather farther from the truth even though the latter did not reveal itself in its entirety.

As an aside: truth be told, I have no feeling in the above matter. The whole of the response is the result of mental activity.


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