The Applications of Elliptic Functions
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of 70°20', by means of which the figures can be drawn.
Fig. 19 shows poristie heptagons, to the same modular angle of 75°, laid out by means of the relations ^i = am+Z=c.m. of 22°8', 91)3 = am !■.«■= cm. of 56°49', 05 = am -fir = cm. of 77°6'.
G.B.r. I 130 THE ADDITION THEOEEM D 128. The poristic relation between the quantities R, r, c has been obtained by placing the polygon in a symmetrical position; but another method is employed by Wolstenholme {Proceedings London Math. Society, vol. VIII.,... p. 136 ; also by Halphen, F.E., II., chap. X.), where the polygon on the circle OP is considered in its limiting form, when passing through one or both of the common points B and B'.
Thus with triangles, the tangent to the circle oR at B must meet the circle OP again at a point Pi, the point of contact of a common tangent of the two circles P and B, the degenerate triangle being BPP.
For quadrilaterals, the tangents to R at B, B' must meet at A on the circle P, BAGAB being the degenerate quadrilateral.
What to read after The Applications of Elliptic Functions?
You can find similar books in the "Read Also" column, or choose other free books by Greenhill, G. (George), Sir, 1847-1927 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
of 70°20', by means of which the figures can be drawn.
Fig. 19 shows poristie heptagons, to the same modular angle of 75°, laid out by means of the relations ^i = am+Z=c.m. of 22°8', 91)3 = am !■.«■= cm. of 56°49', 05 = am -fir = cm. of 77°6'.
G.B.r. I 130 THE ADDITION THEOEEM D 128. The poristic relation between the quantities R, r, c has been obtained by placing the polygon in a symmetrical position; but another method is employed by Wolstenholme {Proceedings London Math. Society, vol. VIII.,... p. 136 ; also by Halphen, F.E., II., chap. X.), where the polygon on the circle OP is considered in its limiting form, when passing through one or both of the common points B and B'.
Thus with triangles, the tangent to the circle oR at B must meet the circle OP again at a point Pi, the point of contact of a common tangent of the two circles P and B, the degenerate triangle being BPP.
For quadrilaterals, the tangents to R at B, B' must meet at A on the circle P, BAGAB being the degenerate quadrilateral.
What to read after The Applications of Elliptic Functions?
You can find similar books in the "Read Also" column, or choose other free books by Greenhill, G. (George), Sir, 1847-1927 to read onlineMoreLess
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