Denoting the areas of the three strips by A, B, and C, and introducing the middle ordinate ug, we can express A + B; B -{- C; A + B -FC; and B in terms of uo, u 1, u 2; u 1, u2, u3; uo, u, u 3; and u 1, ug, u 2 respectively.

21(i) If m is even, ug m will be onejof the given ordinates, and we can express h 2 u, m, 4 u" m, ...

10denote 2 (ug 'm _ z + ug m+ g), ?

10Thus we get two expressions for A + B -}- C, from which we can eliminate ug.

00The breadth of the trapezette being mh, it may be shown that its area is 2 2 N 4 4 iv I mh ug m + 24 m h u gm + 1920 m h u g m + 322560 no/tourgm -}- m3l1gu i„?

00., where l aug m, µ6 2 ug m,.

00The general formulae of § 54 (p being replaced (i) by 2m) may in the same way be applied to obtain formulae giving the area of the trapezette in terms of the mid-ordinates of the strips, the series being taken up to b 2f ul m or /th 2J ug m at least, where u is of degree 2f or 2f + I in x.

0024) we owe the triple distinction into inference from particular to particular (irapf16ecy i ug, example, or what we call " analogy "), inference from particular to universal (i raywy17, induction), and inference from universal to particular (ouXXoyco-Os, syllogism, or deduction).

00in terms of ug m and its even central differences (see Differences, Calculus Of).

00In short, the Ainu suggest much closer affinity with Europeans than does any other of the types that go to make ug the population of Japan.

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