. On the Theory of Consistence of Logical Class-Frequencies, and Its Geometrical Representation. its edges being truncated more or less by the planes (A).Only six of the planes (A) cU most can of course come into account at one time,the remaining six lying outside the surface. The lines (ct/3), (^-y), (^^S), &c., in which, the planes a, yS, y, 8 meet, are all parallelto one or other of the co-ordinate planes : thus we have for (a/3) {ay)(aS) (/Sy) m (yS) z y XX y z ¥ (Ih + Vi ? \ {P\ + Pi ? ¥ (ill + Po ? a (2^1 + Vi)h (Ih + Ih) ^)1I) 1) / (C). OF LOGICAL CLASS-FREQUENCIES, ETC. 109 The plan an
. On the Theory of Consistence of Logical Class-Frequencies, and Its Geometrical Representation. its edges being truncated more or less by the planes (A).Only six of the planes (A) cU most can of course come into account at one time,the remaining six lying outside the surface. The lines (ct/3), (^-y), (^^S), &c., in which, the planes a, yS, y, 8 meet, are all parallelto one or other of the co-ordinate planes : thus we have for (a/3) {ay)(aS) (/Sy) m (yS) z y XX y z ¥ (Ih + Vi ? \ {P\ + Pi ? ¥ (ill + Po ? a (2^1 + Vi)h (Ih + Ih) ^)1I) 1) / (C). OF LOGICAL CLASS-FREQUENCIES, ETC. 109 The plan and elevation of the complete tetrahedron are thus both squares of side0*5. But, comparing equations (C) with (A), the edge (a/3) is truncated unless p^ + Ps (^r) .^ .. i^i ^ p^ (^8) .. .. Pi ^ Ps- § 16. Case (1). Pi -^^ P2 = Ih ^ 0*5. In this case the congruence-surface reduces to the fundamental tetrahedron,fig. la,^ the planes (A) only passing through its edges and not truncating them. Theform is more clearly shown by fig. lb, which is drawn from a photograph of an actual. Fig.
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