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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that A motion is quam proxime governed purely by centripetal forces if and only if equal areas are quam proxime swept out in equal times

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The quam proxime extension introduces an asymmetry: approximate area-sweeping is necessary but not sufficient for approximate centripetal governance.
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    • 2.Non-centripetal force combinations (e.g., tangential perturbations) can produce near-equal areas while systematically violating centripetal conditions.
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    • 3.Newton's own Corollary 1 to Proposition 3 requires the residual force to vanish quam proxime, a condition independent of the areal law itself.
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    Reason for 2 of 2
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    • 1.George Smith and William Harper argue that Newton's quam proxime reasoning is methodologically asymmetric: deviations from equal areas measure force perturbations only under idealizing assumptions.
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    • 2.The biconditional's quam proxime generalization presupposes that approximation errors in the areal law and in centripetal force magnitude scale proportionally, which is an independent empirical commitment not derivable from Props. 1–2.
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    • 3.Without that proportionality assumption, the quam proxime biconditional collapses into a one-directional inference, undermining the 'if and only if' structure of the original claim.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Propositions 1 and 2 establish the exact biconditional between centripetal force governance and equal areas in equal times
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    • 2.The second and third corollaries of Proposition 3 yield the quam proxime generalization of this biconditional
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