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    If the portion of the curve between abscissae 0 and Δx is... — 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.

    If the portion of the curve between abscissae 0 and Δx is not assumed to be straight, it does not follow that Δx² = 0.

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    Denying the straightness assumption undermines the derivation of Δx² = 0.Leibniz's argument that Δx² = 0 depends crucially on the assumption that the por...

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    Denying the straightness assumption undermines the derivation of Δx² =...83%Leibniz grants that there is an infinitesimal straight stretch of the ...82%A point lying on the axis of abscissae has a y-coordinate of zero, so ...78%If the curve y = x² is an infinilateral polygon, then the infinitesima...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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