Elements of analysis as applied to the mechanics of engineering and machinery . I parallelogram AGBD. Fig. For a surface B G G^B^ = F^ between the abscissas AG^ = C-^^ andA G =^ c^ Fig. 3t, there is, according to Art. It, For y = —, there is, for example: F = ^ a^dx X = a^ (nat. log. c^ — not. log. c), : ?F = a^ nat. log. I —- i. The curve P Q, Fig. 38, with which we have become familiar in a^Art. 3, corresponds to the equation —-, and hence, if we have ^if^c and AN = c. (f) F = a^ nat. log. I —- ^ c . will give the area of MX Q P. If, for the sake of simplicity, weassume a = c = 1, a
Elements of analysis as applied to the mechanics of engineering and machinery . I parallelogram AGBD. Fig. For a surface B G G^B^ = F^ between the abscissas AG^ = C-^^ andA G =^ c^ Fig. 3t, there is, according to Art. It, For y = —, there is, for example: F = ^ a^dx X = a^ (nat. log. c^ — not. log. c), : ?F = a^ nat. log. I —- i. The curve P Q, Fig. 38, with which we have become familiar in a^Art. 3, corresponds to the equation —-, and hence, if we have ^if^c and AN = c. (f) F = a^ nat. log. I —- ^ c . will give the area of MX Q P. If, for the sake of simplicity, weassume a = c = 1, and c^ == ^, we obtain F —- nat. log. x^and the areas (IJ/Pl), {INQl)^ &c., are the natural logarithmsof the abscissas AM^ AN^ &c. The curve itself is an equilateralhyperbola., in which the two semi-axes a and b are equal, conse-quently the angle of asymptotes a r= 45^, and the straight lines A X 44 ELEMENTS OF ANALYSIS. [Art. 30 and A F, to which the curve approaches nearer and nearer without reaching them, are the asymptotes of the same. On account of this Fig. 33. connection between
Size: 1644px × 1519px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1860, bookpublisherphiladelphiakingba
