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Greeks, Circles, Small Straight lines and Calculus

  1. Jan 11, 2016 #1

    I VAGUELY recall reading, some many years ago, a statement to the following...

    "The Greeks were obsessed with circles. Had they relaxed this obsession, they may have seen the significance of modeling curves with small straight lines, and thereby anticipated the Calculus."

    Is there any credence to this assertion (OR SOMETHING LIKE IT) and, if so (and more importantly) can you provide a reference?

    (I am marking this "advanced" because, while the question is ostensibly simple in its math, it beckons a more philosophical and historical response with references.)
  2. jcsd
  3. Jan 11, 2016 #2


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    Staff: Mentor

    What about him? IMO that counts.
    "Archimedes was able to use infinitesimals in a way that is similar to modern integral calculus."
  4. Jan 11, 2016 #3


    Staff: Mentor

    I have removed the 'A' thread prefix, which would be more appropriate for advanced mathematics questions.
  5. Jan 12, 2016 #4
    OK; I found the quote. Could someone read this quote....

    It is from the book “Foundations of Physics,” Robert Bruce Lindsay and Henry Margenau, Dover, 1936

    Page 88.

    "There is now the rather now common view that the first law is really a definition of force. In other words, the first law does not make a statement about what happens to a particle when a force acts on it; rather it purports to say that a force is anything which acts to change the state of the particle from rest or uniform motion in a straight line.

    However, the utility of this is in doubt because it conveys no notion on how to measure force. Furthermore, another drawback to the utility of Newton’s first law as a definition of zero force comes from the experimental fact that uniform motion in a straight lie is the exception and not the rule. Indeed we may go so far as to say that it is never encountered in large scale motions save approximately (as in the case of rain drops, parachutes, etc.). This is possibly the reason why the Greek philosophers paid so little attention to it, preferring instead to look upon uniform motion in circles as the perfect motion. They would have been astonished to see so much emphasis laid on a kind of motion that is practically never observed."

    So can one make the claim that had the Greeks not been so obsessed with circles, they might have seen the utility of small straight lines, sooner?
  6. Jan 12, 2016 #5


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    I seriously doubt that for IMO it it simply not true.

    The ancient Greeks have been put much effort on geometry. This does include 'small lines' as well as circles. In fact, lines are the fundamental part of Euclidean geometry.
    Furthermore they were able to build pretty accurate tunnels which you certainly can't do with circles alone.
    Their main field of examination has been to consider the relations between objects, geometrical as well as numerical objects. In fact in Geometry their circles were often only been used to build angels - angels between lines! And the relation established by Pythagoras' theorem is one between the length of lines.

    However, it is rather difficult to guess what a) they could have done and b) what do you think they should have done.
    If your question is why they did not find Newton's first law we can only do guesswork. Plus we don't know whether they did! Perhaps it just wasn't worth to them to write it down. (Btw. I have no clue whether this is correct. Maybe there is a source which I simply do not know.)
    Or it was so clearly true to them that they did not care. The quoted author above says it's not even clear to him whether it should be called a law. A point of view I would not follow.

    To extrapolate from doing geometry that this keeps you from doing mechanics is at least edgy. Moreover, Archimedes did a lot of what we call nowadays classical physics. You won't ask a particle physicist why he isn't doing solid-state physics, won't you? Neither would you postulate that his engagement in particle physics keeps him from knowing crystal structures.
    IMO your hypothesis isn't sound.
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