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    A motion is quam proxime governed purely by centripetal f... — Carmelics
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    A motion is quam proxime governed purely by centripetal forces if and only if equal areas are quam proxime swept out in equal times

    Causation
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    CausationTruth & Knowledge

    Connections

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    Modality & Possibility1 linked

    Related

    George Smith and William Harper argue that Newton's quam proxime reasoning is me...Newton's own Corollary 1 to Proposition 3 requires the residual force to vanish ...Non-centripetal force combinations (e.g., tangential perturbations) can produce ...Propositions 1 and 2 establish the exact biconditional between centripetal force...
    +4 moreShow less
    The biconditional's quam proxime generalization presupposes that approximation e...The quam proxime extension introduces an asymmetry: approximate area-sweeping is...The second and third corollaries of Proposition 3 yield the quam proxime general...Without that proportionality assumption, the quam proxime biconditional collapse...

    Similar

    A motion is governed purely by centripetal forces if and only if equal...90%The 3/2 power rule holds quam proxime for uniform circular orbits if a...84%The quam proxime forms of the centripetal force and inverse-square pro...81%Proposition 1 establishes that equal areas swept in equal times implie...80%

    Source

    AI-extracted1/3 agreementValid
    SEP: newton-principia
    View source passageHide passage
    This is not the only place in Book 1 where Newton takes the trouble to derive an “If…quam proxime, then…quam proxime” version of an exact “If…, then…” proposition. Propositions 1 and 2 establish that a motion is governed purely by centripetal forces if and only if equal areas are swept out in equal times. The second and third corollaries of Proposition 3 then yield the conclusion that a motion is quam proxime governed purely by centripetal forces if and only if equal areas are quam proxime swept
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit