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    Denying the straightness assumption undermines the deriva... — Carmelics
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    Supports→Leibniz's argument that Δx² = 0 depends crucially on the assumption that the portion of the curve between abscissae 0 and Δx is straight.

    Denying the straightness assumption undermines the derivation of Δx² = 0.

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    If the portion of the curve between abscissae 0 and Δx is not assumed to be stra...Leibniz's argument that Δx² = 0 depends crucially on the assumption that the por...

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    Leibniz's argument that Δx² = 0 depends crucially on the assumption th...87%If the portion of the curve between abscissae 0 and Δx is not assumed ...83%The argument shows that e² = 0 given the assumption of an infinitesima...78%ABb = 0 (ABb is a contradiction)77%

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    Now Leibniz could retort that that this argument depends crucially on the assumption that the portion of the curve between abscissae 0 and \(\Dx\) is indeed straight. If this be denied, then of course it does not follow that \(\Dx ^2 = 0\). But if one grants, as Leibniz does, that that there is an infinitesimal straight stretch of the curve (a side, that is, of an infinilateral polygon coinciding with the curve) between abscissae 0 and \(e\), say, which does not reduce to a single point then \(e

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