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On the Inverse Trigonometrical Functions.

Functional notation, direct and inverse, 37; inverse trigono-
metrical functions, 37, 38; examples in the use of inverse symbols,
38, 39, 40.


Description of a Symbolic Calculus.

Object, 89; peculiar symbols, meanings, rules of operation, 89;

possible deficiencies of either, 90, 91; complete absence of either,

91, 92; symbolic calculus, what, 92; recovery of meaning, significant

calculus, 93; slight example, with illustration of defects, 93, 94;

possibility of more than one mode of restoration to significance, 94;

step from specific to universal arithmetic, and thence to ordinary
algebra, 95, 96; necessity for other than numerical distinction, and
mode in which distinction is suggested by algebra, 95, 96; single
algebra, phrase whence derived, 96, 97; twofold use of its signs,
directive and conjunctive, 97; remarks on the progress of algebra,
98, 99, 100.



Preliminary Remarks on Double Algebra.

Suggestion on √ −1 which gave rise to it, 109; the old algebra
to be incorporated, 109; examination of magnitude of one dimension,
time, gain and loss, 109, 110; a wider basis of significance in length
affected by direction, 110, 111; geometrical introduction extension,
not restriction, 111, 112; mode of making the application to problems
of one dimension, 112, 113, 114; separation of subject-matter and.
operative direction in arithmetical addition and multiplication,
-15, 116.

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