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Despite your attempt to obfuscate the issue with your wall of text, the simple fact of the matter is that you didn't give a single example of analytic geometry

Despite your attempt to obfuscate the issue with your wall of text, the simple fact of the matter is that you didn't give a single example of analytic geometry (i.e. coordinate geometry), which is based on the explicit use of a coordinate system. > Use of formulae is outside the scope of pure geometry ala Euclidian style. Like Heron's formula? > Trigonometry using algebra is part of analytic geometry. Yes, a part of analytic geometry. Distances and angles are also a part of analytic geometry. > Explicit use of coordinate system is not essential. Yes it is. That's literally what analytic geometry (i.e. coordinate geometry) means.

jimsimmons 5y ago
You use coordinate and analytic interchangeably but coordinate system is not a requirement nor equivalent to analytic geometry. It doesn’t even relate to mathematical analysis. Analysis, to the extent that it’s series and limits, also existed in India before Descartes. Herons formula doesn’t count because it’s the end result. Not a means to an end. You don’t need to go to Heron for that. Area of a square also has a formula and that would have made your point. Using trigonometric identities to derive area of cyclic quadrilateral is different as algebraic equations are means and not the end. Again, analytic literally doesn’t mean “coordinate”. It only usually does. Also it wasn’t a wall of text to obfuscate. I sincerely laid out the full argument the best I could. Half the wall is Wikipedia quotes. The other half was itemized to make it easy to parse. But sure whatever floats your boat mate.
- alentist 5y ago
  > coordinate system is not a requirement... to analytic geometry Yes it is. That's what analytic geometry means [0][1][2][3]. If you mean something different, use a different word. > Herons formula doesn’t count because it’s the end result. It came with a derivation that can be found in Heron's 60 AD book Metrica, and may have been known centuries earlier. [0] https://www.merriam-webster.com/dictionary/analytic%20geometry https://www.merriam-webster.com/dictionary/analytic%20geomet... [1] https://www.dictionary.com/browse/analytic-geometry https://www.dictionary.com/browse/analytic-geometry [2] https://www.collinsdictionary.com/dictionary/english/analytic-geometry https://www.collinsdictionary.com/dictionary/english/analyti... [3] https://www.thefreedictionary.com/analytic+geometry https://www.thefreedictionary.com/analytic+geometry

jimsimmons 5y ago

You use coordinate and analytic interchangeably but coordinate system is not a requirement nor equivalent to analytic geometry. It doesn’t even relate to mathematical analysis. Analysis, to the extent that it’s series and limits, also existed in India before Descartes. Herons formula doesn’t count because it’s the end result. Not a means to an end. You don’t need to go to Heron for that. Area of a square also has a formula and that would have made your point. Using trigonometric identities to derive area of cyclic quadrilateral is different as algebraic equations are means and not the end. Again, analytic literally doesn’t mean “coordinate”. It only usually does. Also it wasn’t a wall of text to obfuscate. I sincerely laid out the full argument the best I could. Half the wall is Wikipedia quotes. The other half was itemized to make it easy to parse. But sure whatever floats your boat mate.

alentist 5y ago
> coordinate system is not a requirement... to analytic geometry Yes it is. That's what analytic geometry means [0][1][2][3]. If you mean something different, use a different word. > Herons formula doesn’t count because it’s the end result. It came with a derivation that can be found in Heron's 60 AD book Metrica, and may have been known centuries earlier. [0] https://www.merriam-webster.com/dictionary/analytic%20geometry https://www.merriam-webster.com/dictionary/analytic%20geomet... [1] https://www.dictionary.com/browse/analytic-geometry https://www.dictionary.com/browse/analytic-geometry [2] https://www.collinsdictionary.com/dictionary/english/analytic-geometry https://www.collinsdictionary.com/dictionary/english/analyti... [3] https://www.thefreedictionary.com/analytic+geometry https://www.thefreedictionary.com/analytic+geometry