Chambers's encyclopædia; a dictionary of universal knowledge . nerves of special sense is manifested by phan-tasms, illusions, &c. The following points arecommon to the whole class of these affections: , or the alternations of paroxysms andintermissions; 2. Uniformity and jiersistence ofthe sjmiptoms, however long the duration of thedisease; 3. No danger to life; 4. Freedom fromthis class of diseases in early life. Of the diseasespredisposing to hyi:)era2sthesia, hysteria is far themost frequent; but it is sometimes induced byliieumatism, gout, skin-diseases, &c. HYPERBOLA. If two
Chambers's encyclopædia; a dictionary of universal knowledge . nerves of special sense is manifested by phan-tasms, illusions, &c. The following points arecommon to the whole class of these affections: , or the alternations of paroxysms andintermissions; 2. Uniformity and jiersistence ofthe sjmiptoms, however long the duration of thedisease; 3. No danger to life; 4. Freedom fromthis class of diseases in early life. Of the diseasespredisposing to hyi:)era2sthesia, hysteria is far themost frequent; but it is sometimes induced byliieumatism, gout, skin-diseases, &c. HYPERBOLA. If two similar cones be placedapex to apex, and with the lines joining the apexand centre of base in each, in a straight line ;then if a plane which does not pass through theapex be made to cut both cones, each of thetwo sections will be a hyperbola, as PBN, is, viewed analytically, the locus of the point towhich the straight lines EP, FP diifering by aconstant quantity are drawn from two given points,E and F. These given points are called the foci,. one being situated in each hy|>erbola. The pointGr, midway between the two foci, is called thecentre, and the line EF the transverse axis of thehy^ierbola. A line through G- perpendicular totlio transverse axis is called the conjugate axis; anda circle described from centre B, with a radiusequal to FG, will cut the conjugate axis in C and G be taken for the origin of co-ordinates, and EMand EF for the axes, the hyperbola is expressed by the equation -^ - |^ = 1. (GB = a, GO = b). The a^ b-hyperbola is the only conic section which hasAsymptotes (q. v.); in the figure these are GT, GT;GS, GS. It also appears that if the axes of co-ordinates be turned at right angles to their formerposition, two additional curves, HCK, HDK, will f be formed, whose equation is p = 1. These two are called conjugate hypej-bolas, and have thesame asymptotes as the original hy[ierbolas. Theseasymptotes have the following remarkable property :If (
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Keywords: ., bookcentury1800, bookdecade1860, bookpublisherlondo, bookyear1868
