Changes

Observe that the secular inference rules, used by themselves, involve a loss of information, since nothing in them can tell us whether the momenta <math>\{ (\operatorname{d}A), \operatorname{d}A \}</math> are changed or unchanged in the next instance.  In order to know this, one would have to determine <math>\operatorname{d}^2 A,</math> and so on, pursuing an infinite regress.  Ultimately, in order to rest with a finitely determinate system, it is necessary to make an infinite assumption, for example, that <math>\operatorname{d}^k A = 0</math> for all <math>k\!</math> greater than some fixed value <math>M.\!</math>  Another way to escape the regress is through the provision of a dynamic law, in typical form making higher order differentials dependent on lower degrees and estates.

Observe that the secular inference rules, used by themselves, involve a loss of information, since nothing in them can tell us whether the momenta <math>\{ (\operatorname{d}A), \operatorname{d}A \}</math> are changed or unchanged in the next instance.  In order to know this, one would have to determine <math>\operatorname{d}^2 A,</math> and so on, pursuing an infinite regress.  Ultimately, in order to rest with a finitely determinate system, it is necessary to make an infinite assumption, for example, that <math>\operatorname{d}^k A = 0</math> for all <math>k\!</math> greater than some fixed value <math>M.\!</math>  Another way to escape the regress is through the provision of a dynamic law, in typical form making higher order differentials dependent on lower degrees and estates.

===Example 1. A Square Rigging===

===Example 1. A Square Rigging===

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